Crossing the event horizon of a black hole

[MasterD]

I am struggling with an understanding on what the longest proper time an observer can spend before he will be destroyed into the singularity. How should I approach this problem?

 

[Dale]

Try http://arxiv.org/PS_cache/arxiv/pdf/0705/0705.1029v1.pdf" .

 

[Ich]

Hey, I just looked for exactly this paper with keywords "proper time singularity" in the abstract. Nothing.

 

[aranoff]

The word singularity means division by zero. This is not allowed. Therefore, the solution of the GR equations for the observer crossing the event horizon is not valid. Instead, we observe someone falling down the black hole, and note that it takes forever to reach the horizon. The horizon is like the end of the universe. GR tells us that mass changes geometry.

 

[JesseM]

The word singularity means division by zero. This is not allowed. Therefore, the solution of the GR equations for the observer crossing the event horizon is not valid. Instead, we observe someone falling down the black hole, and note that it takes forever to reach the horizon. The horizon is like the end of the universe. GR tells us that mass changes geometry.

There is no physical singularity at the event horizon of a black hole. Schwarzschild coordinates do go to infinity there, but you can pick different coordinate systems (like some of the ones mentioned on this page) where there is no coordinate singularity at the event horizon, and you can show it only takes the infalling observer a finite proper time to pass the event horizon. The singularity at the center of the black hole is a real physical one though, since infinities appear there no matter what coordinate system you choose.

 

[aranoff]

Yes, the singularity is at the center of the black hole. However, the center does not exist. There is no such thing as the inside of the black hole, as it takes forever to reach the surface, i.e., the event horizon. When we talk about the "inside", we are referring to the solution of the General Relativity (GR) equations from the point of view of the observer falling down. However, this solution is not valid, due to the existence of the singularity. This is like boundary conditions restricting which solutions can be allowed; this is the basis of the physics of music. In other words, since it is impossible to observe an object crossing the horizon, then nothing can cross the horizon. Can you travel past the end of the universe? Remember, geometry is not Euclidean near the horizon. The horizon is an end of the universe, as it takes forever to get there.

Ah, but great physicists have discussed this singularity! So what! They are wrong! Very simple! Division by zero is not allowed!

 

[JesseM]

Yes, the singularity is at the center of the black hole. However, the center does not exist. There is no such thing as the inside of the black hole, as it takes forever to reach the surface, i.e., the event horizon.

No, not for the infalling observer it doesn't--it takes only a finite proper time (time as measured by a clock they're carrying) for them to cross the event horizon. See What happens to you if you fall into a black hole? for example.

In other words, since it is impossible to observe an object crossing the horizon

It's quite possible, if you're willing to dive in after it.

Can you travel past the end of the universe?

No, although it would be a bit silly to claim that nothing exists beyond the edge of the visible universe (a sphere centered on Earth with a radius of about 50 billion light years--see here) just because light from those regions wouldn't have had time to reach us since the Big Bang.

Ah, but great physicists have discussed this singularity! So what! They are wrong! Very simple! Division by zero is not allowed!

If you are not familiar with this board's policy on claims which contradict mainstream physics, please read the IMPORTANT! Read before posting message which appears at the top of the board.

 

[aranoff]

tan(x) has a singularity at x = 90°. The tan function is not defined here. It is not infinity, but not defined. A singularity is simply a point where the function or equation is not defined.

 

[stevebd1]

I am struggling with an understanding on what the longest proper time an observer can spend before he will be destroyed into the singularity. How should I approach this problem?

This is probably in the paper posted by DaleSpam but one equation that I've seen a number of times for the fall-in time for Schwarzschild black holes is-

\tau_{max}\text{[seconds]}=\frac{\pi M}{c}=\frac{\pi Gm}{c^3}\ \equiv\ 1.548\times10^{-5}\ \times\ \text{sol mass}

where τ is the wristwatch time (proper time) in seconds, M is the gravitational radius (M=Gm/c^2), G is the gravitational radius, m is mass and c is the speed of light.

For a 10 sol mass black hole, the maximum free-float horizon to crunch time is 1.548x10^-4 seconds or 0.155 milliseconds, for a 3 million sol mass black hole, the time is ~46 seconds.

The maximum free-float horizon to crunch distance is-

\tau_{max}\text{[metres]}=\pi M

 

[JesseM]

tan(x) has a singularity at x = 90°. The tan function is not defined here. It is not infinity, but not defined. A singularity is simply a point where the function or equation is not defined.

The limit of tan(x) as you approach 90 is certainly infinity, but you're right, a singularity can be any undefined point. Anyway, the fact remains that you can find perfectly good coordinate systems where all physical quantities have well-defined finite values on the event horizon, so there is no physical singularity there.

 

[aranoff]

The limit of tan(x) as you approach 90 is certainly infinity, but you're right, a singularity can be any undefined point. Anyway, the fact remains that you can find perfectly good coordinate systems where all physical quantities have well-defined finite values on the event horizon, so there is no physical singularity there.

Again, I repeat, the singularity is at the center of the black hole. The equation of motion which is the solution of GR, is not valid at this point. Is it valid near the singularity? I say no. I view the singularity as a boundary condition saying that this solution is not valid.

 

[JesseM]

Again, I repeat, the singularity is at the center of the black hole. The equation of motion which is the solution of GR, is not valid at this point. Is it valid near the singularity? I say no. I view the singularity as a boundary condition saying that this solution is not valid.

I agree with this, but it's not what you seemed to be saying before. Before you seemed to be saying the event horizon was a singularity, and that an observer could never really pass it. Your words:

The word singularity means division by zero. This is not allowed. Therefore, the solution of the GR equations for the observer crossing the event horizon is not valid. Instead, we observe someone falling down the black hole, and note that it takes forever to reach the horizon. The horizon is like the end of the universe.

 

[aranoff]

The singularity is at the center. This means that the equation of motion, the solution of GR, is not valid at the center. This means the equation is not valid anywhere inside the black hole. The singularity acts like a boundary condition, restricting the validity of equations. A valid solution of the wave equation must satisfy the boundary conditions.

But wait! How can a black hole, which in the simplest case, can be imagined as a sphere, not have a center? Answer: the geometry near the event horizon is not Euclidean.

 

[JesseM]

The singularity is at the center. This means that the equation of motion, the solution of GR, is not valid at the center. This means the equation is not valid anywhere inside the black hole.

Uh, how do you figure? It's not valid right at the singularity, but what about, say, halfway between the singularity and the event horizon? You have no justification for saying that the equations cease to give valid predictions at the event horizon just because GR breaks down at the singularity, that's a total non sequitur.

 

[coelho]

Well... where is located the mass of the black hole? If it is inside the event horizon, how its gravitational atraction acts upon anything outside the horizon? Wouldnt it involve travel faster than light?

 

[stevebd1]

There seems to be plenty of maths that supports the fact that there is an 'inside' to the event horizon, basically put s^2<0 exists inside the event horizon where s^2=c^2\Delta t^2-\Delta r^2 (or c^2\Delta t^2<\Delta r^2) while s^2>0 exists in space outside the EH (or outside the ergosphere as in the case of a rotating black hole). There seems to be plenty of metric out there that support this with SR taking care of infinities that crop up at the EH. I cannot remember who said the following but 'the event horizon is not where GR ends but where GR begins to end as it starts to unravel towards the singularity'. Of course, the idea of GR unravelling might change as a theory of quantum gravity is established and the 'singularity' is better understood.

Steve

 

[aranoff]

Uh, how do you figure? It's not valid right at the singularity, but what about, say, halfway between the singularity and the event horizon? You have no justification for saying that the equations cease to give valid predictions at the event horizon just because GR breaks down at the singularity, that's a total non sequitur.

This is a sequitur! Boundary conditions (BC) are very basic in mathematics and physics. The singularity at the center means that the solution of GR inside the hole is not valid at the center. Therefore, it is not valid period. The motion of a vibrating string is an example where possible solutions are rejected due to BC.

I suggest you do some research on BC. The concept of BC is very sophisticated in mathematics.

 

[JesseM]

This is a sequitur! Boundary conditions (BC) are very basic in mathematics and physics. The singularity at the center means that the solution of GR inside the hole is not valid at the center. Therefore, it is not valid period. The motion of a vibrating string is an example where possible solutions are rejected due to BC.

I suggest you do some research on BC. The concept of BC is very sophisticated in mathematics.

Sorry, no, you're talking nonsense here. Of course I'm familiar with the idea of boundary conditions, a basic idea in physics which is not particularly "sophisticated" at all, but it does not somehow allow you to say that nothing inside the event horizon is valid, physicists only believe that GR becomes significantly wrong in the immediate neighborhood of the singularity, not the entire region inside the event horizon. Perhaps you are confusing the physical boundary of the black hole (the event horizon) with the notion of "boundary conditions", but they are unrelated, boundary conditions are just the conditions at the boundary of whatever region of spacetime you wish to consider when you're setting up the problem, they have nothing to do with the event horizon. Nor is there any notion in physics that a singularity at one point in a solution invalidates the solution as a whole.

 

[aranoff]

The solutions of GR are continuous functions. If we allow the solution of GR inside the BH, then there is a discontinuity, which invalidates this solution.

 

[JesseM]

The solutions of GR are continuous functions. If we allow the solution of GR inside the BH, then there is a discontinuity, which invalidates this solution.

Totally illogical. First of all, physicists have no such rule about throwing out solutions containing discontinuities; as I've said before, it is thought that the singularity is a sign that we need quantum gravity to get accurate predictions about the immediate neighborhood of the black hole's center, but that GR can be trusted far from the Planck scale. And if you think it "invalidates this solution", it's completely arbitrary for you to say it only invalidates the region inside the black hole's event horizon, but not outside it. What do you think is so special about the event horizon? A Schwarzschild spacetime is a solution containing a singularity, period, we don't use separate "solutions" for the region outside the event horizon and the region inside. Likewise, all the cosmological models in GR contain singularities at the Big Bang, would you say that we should therefore throw these cosmological solutions out, including their predictions about expanding space long after the Big Bang which have had quite a lot of experimental confirmation?

 

[aranoff]

The nature of GR is such that discontinuous solutions are not allowed. A discontinuity is not physical.

There is another point. A physical theory is a mathematical system (a collection of arbitrary self-consistent statements) which can be verified by observations and experiments. Since it is impossible to perform observations inside the event horizon, this solution does not exist.

So that's it. No solution inside. By the definition of a physical theory. By the requirement that the solution exist everywhere inside the BH.

As we watch things falling down the BH, we note that it takes forever to get there. We also note that it takes forever to go straight in a Euclidean line. Therefore, the event horizon is geometrically the same as a straight line. Remember the equation of GR: G=T.

Speaking about the inside of the BH is just as wrong as speaking about outside the universe. Geometrically impossible.

 

[JesseM]

The nature of GR is such that discontinuous solutions are not allowed. A discontinuity is not physical.

So why don't you reject the entire solution instead of just arbitrarily rejecting the region inside the event horizon? The horizon does not mark the boundary between two different "solutions", the whole spacetime is one GR solution! And do you also reject the entirety of cosmological models which contain an initial Big Bang singularity?

 

[Hurkyl]

The solutions of GR are continuous functions. If we allow the solution of GR inside the BH, then there is a discontinuity, which invalidates this solution.

Where is this alledged discontinuity? Is it at a point of space-time? Or is it merely at some point in a faux-coordinate chart that doesn't correspond to a point of space-time?

And no, continuity really isn't a hard requirement of the theory -- it (and sufficient differentiability) only a requirement for the use of the simplest mathematical framework.

As we watch things falling down the BH, we note that it takes forever to get there. We also note that it takes forever to go straight in a Euclidean line. Therefore, the event horizon is geometrically the same as a straight line.

This is patently absurd.

 

[JesseM]

I wonder if aranoff is not confusing the idea of continuity in the spacetime manifold on which the coordinate system and tensor fields are defined with the idea of continuity in the tensor fields themselves. I imagine the first probably is a requirement, but not the second. For example, take a simple example like a planet with a sharply-defined surface--doesn't the surface already mark a type of discontinuity in the matter field?

 

[MeJennifer]

So why don't you reject the entire solution instead of just arbitrarily rejecting the region inside the event horizon? The horizon does not mark the boundary between two different "solutions", the whole spacetime is one GR solution! And do you also reject the entirety of cosmological models which contain an initial Big Bang singularity?

Actually, the complete Schwarzschild solution has two event horizons. They are connected by two different universes or through a wormhole (Einstein-Rosen bridge) in spacetime.

 

[aranoff]

So why don't you reject the entire solution instead of just arbitrarily rejecting the region inside the event horizon? The horizon does not mark the boundary between two different "solutions", the whole spacetime is one GR solution! And do you also reject the entirety of cosmological models which contain an initial Big Bang singularity?

According to the external observer, there is no spacetime inside the BH.

We currently have no theory of cosmology, but hypotheses. A theory is a rigorous mathematical framework plus observations and experiments. Since all current cosmological models contain an initial singularity, they are not rigorous, and so do not qualify as a theory.

 

[aranoff]

I wonder if aranoff is not confusing the idea of continuity in the spacetime manifold on which the coordinate system and tensor fields are defined with the idea of continuity in the tensor fields themselves. I imagine the first probably is a requirement, but not the second. For example, take a simple example like a planet with a sharply-defined surface--doesn't the surface already mark a type of discontinuity in the matter field?

The gravitational field is continuous as one passes through the surface. Consider a uniform mass. As the test particle enters the mass, we draw a sphere, center the planet, radius the distance to the test particle. We calculate the mass of the sphere, and use this mass to calculate the field.

 

[aranoff]

As we watch things falling down the BH, we note that it takes forever to get there. We also note that it takes forever to go straight in a Euclidean line. Therefore, the event horizon is geometrically the same as a straight line. Remember the equation of GR: G=T.

Clarification: There is no end to the universe, as one can imagine going in a straight line forever. No matter where we are, we can continue further. As we move outward, time marches on. This is what infinite means. The set of integers is infinite. Pick any number. We can find a larger number by adding one. There is no last integer. Same here. There is no last position in the universe.

The same is what happens as we approach a BH, due to the geometry. Remember that the geometry is not Euclidean. We can imagine falling forever towards the BH. No matter where we are, we can continue further. As we fall, time marches on. The distance to the BH is infinite. No matter how long we wait and how close we get to the event horizon, we can always imagine waiting longer and getting closer. There is no end point. This is what I meant by my statement "the event horizon is geometrically the same as a straight line." Sorry for the confusion. The topic is confusing enough!

 

[aranoff]

as I've said before, it is thought that the singularity is a sign that we need quantum gravity to get accurate predictions about the immediate neighborhood of the black hole's center

And I answered you. You say we need another theory, which you call quantum gravity. This means you agree that GR alone is not valid inside the BH. We agree.

I am not interested in discussing possible future developments in physics. I am focused in understanding current theories as they are. My point is GR (today's GR, not the future GR) is not valid inside the BH.

 

[aranoff]

I am struggling with an understanding on what the longest proper time an observer can spend before he will be destroyed into the singularity. How should I approach this problem?

You are a complicated entity. You have cells and organs. There is a lot of information about you. The only information about a black hole is its mass, angular momentum, and charge. Once an object falls into the BH, all the information is lost. The only information about you is your mass.

 

[JesseM]

The gravitational field is continuous as one passes through the surface. Consider a uniform mass. As the test particle enters the mass, we draw a sphere, center the planet, radius the distance to the test particle. We calculate the mass of the sphere, and use this mass to calculate the field.

I wasn't talking about the gravitational field (curvature tensor), I was talking about a discontinuity in the values of the stress-energy tensor which defines the distribution of matter and energy in the spacetime, and which is related to the curvature tensor by the Einstein field equations in GR. My point is that although the manifold on which the tensors of GR are defined may be required to be continuous, there is definitely no requirement that the values of the tensors themselves should vary continuously. I challenge you to find a single textbook or paper by a professional physicist which states that a spacetime with a discontinuity in the values of the tensor should be thrown out. Of course you won't, because that would imply physicists throw out the interior regions of black holes as well as cosmologies including a Big Bang singularity (which is not separated from the rest of the universe by an event horizon), while any GR textbook will contain detailed discussions of these solutions.

According to the external observer, there is no spacetime inside the BH.

Irrelevant to your previous argument, you said we should throw out any "solution" which includes a singularity, and at a mathematical level the entire BH spacetime (inside and out) is a single solution to the Einstein field equations, the fact that the region inside the horizon is not observable by anyone who doesn't cross it doesn't make that region a separate "solution". You are just inventing ad hoc ways of justifying your prejudices using poorly-defined terminology, not making any rigorous argument against the validity of GR anywhere inside the horizon.

The same is what happens as we approach a BH, due to the geometry. Remember that the geometry is not Euclidean. We can imagine falling forever towards the BH. No matter where we are, we can continue further. As we fall, time marches on. The distance to the BH is infinite. No matter how long we wait and how close we get to the event horizon, we can always imagine waiting longer and getting closer. There is no end point. This is what I meant by my statement "the event horizon is geometrically the same as a straight line." Sorry for the confusion. The topic is confusing enough!

Nonsense, any textbook on black holes will tell you that for an observer falling into the BH, the proper time (time as measured by a clock falling with them) to cross it is finite. The coordinate time in Schwarzschild coordinates to cross it is infinite, but there is nothing special about Schwarzschild coordinates, one can use other coordinate systems such as Eddington-Finkelstein coordinates where the time to cross it is finite, it is really only proper time that has physical significance (one could even come up with a coordinate system where it takes an infinite coordinate time for you to cross from one end of your room to the other).

You say we need another theory, which you call quantum gravity. This means you agree that GR alone is not valid inside the BH. We agree.

Wrong, I simply echo physicists in saying GR is not valid at the Planck scale. The energy densities would only approach the Planck density very close to where GR predicts a singularity (probably in the neighborhood of one Planck length from it), in regions of the interior far from the singularity there's no such reason for thinking GR would significantly disagree with quantum gravity (except perhaps in the case of the inner horizon of a rotating black hole, which calculations suggest would see infinitely blueshifted light from outside, again creating energy densities greater than the Planck density).

I am not interested in discussing possible future developments in physics. I am focused in understanding current theories as they are. My point is GR (today's GR, not the future GR) is not valid inside the BH.

Indeed, this forum is not a place to debate interpretations of GR which are widely accepted among physicists, as you are doing by rejecting everything inside the horizon--you will find no textbooks which agree with you, or that say that solutions with discontinuities in tensor fields should automatically be rejected, this is just stuff you're making up with no justification. Please read the IMPORTANT! Read before posting thread at the top of the forum, attempting to disprove mainstream views on GR is explicitly forbidden, if you continue to do so I'll report your posts.

 

[aranoff]

Okay, let me understand you. We agree that T can be discontinuous. We agree that if we reject the singularity, then G is discontinuous. You therefore say that it is acceptable in GR for G to be discontinuous? What are the implications of this? Any other examples of G being discontinuous?

" challenge you to find a single textbook or paper by a professional physicist which states that a spacetime with a discontinuity in the values of the tensor should be thrown out."
Again, you agree that the solution of GR at the center of the BH is not valid. We agree! Since it is not valid there, it is not valid anywhere. If you do not like my continuity argument, okay. I actually view it as a boundary condition saying this solution is not valid. Why do you reject my boundary condition reasoning?

"a Big Bang singularity (which is not separated from the rest of the universe by an event horizon), while any GR textbook will contain detailed discussions of these solutions."
It is fine to have discussions. It is not fine to say that cosmology including the Big Bang singularity is a valid physical theory, as it contains a mathematical inconsistency. Instead, it is a working hypothesis, which hopefully will become part of a future theory. BTW, have you heard of Rosen's cosmology, in which there is no infinite big bang?

We must focus on the basic principles of physics. We cannot say just because this is what physicists say it must be so. Physicists said von Laue current is valid. I had to fight this to get my paper published in 1972. If you were the group moderator then, you would not have permitted my paper to appear on the site. I was amazed at the wrong ideas most physicists had, 75 years after SR, which is a simple theory.

What I insist is clear statements of basic principles and the conclusions drawn from them.

Why are you talking about Planck, when we are discussing GR, not QM?

What about the principle that if something cannot be observed in principle, it does not exist? The "finite time to cross the event horizon", as predicted by GR, cannot be observed in principle!

 

[MeJennifer]

According to the external observer, there is no spacetime inside the BH.

That statement is wrong as the existence of any region of spacetime is observer independent.

The event horizon simply signifies that no signals from events inside can be observed from the outside of the event horizon. The event horizon functions like a one-way membrane.

 

[aranoff]

When I said spacetime does not exist inside the BH, I am relying on the fundamental principle of physics which states that something that cannot be observed in principle does not exist. This principle is more basic than GR or QM or whatever.

 

[DaveC426913]

the fundamental principle of physics which states that something that cannot be observed in principle does not exist.

Well... it can be observed in principle (and by a non-hypothetical observer, too), it's just that those observations cannot be communicated back.

 

[Hurkyl]

When I said spacetime does not exist inside the BH, I am relying on the fundamental principle of physics which states that something that cannot be observed in principle does not exist. This principle is more basic than GR or QM or whatever.

You cannot strictly adhere to that principle without running into all sorts of problems. For example, it leads directly to strict solipsism which rejects the existence of anything but your own mind.

GR has its own pecular reason why it's a bad idea to allow regions of space-time to be excised from existence: sure, the mathematics is consistent with the inside and EH of a black hole being non-existant. But it is also consistent with there being a 1-foot-in-diameter ball of non-existant space-time that moves around so that it's 2 feet directly in front of your face.

This principle has never excluded indirect observation; we detect the effects of what GR calls a black hole, and so we infer the existence of what GR calls a black hole.

Finally, research into quantum gravity has suggested that the insides are (eventually) directly observable anyways.

We can imagine falling forever towards the BH.

We can, but it wouldn't be relevant. If I pilot my spaceship into a black hole, then GR predicts I will get there within a finite amount of time, as measured by my wristwatch. The interesting thing is that, if I can avoid being crushed, I will also run off of the edge of space-time within a finite amount of time.

 

[aranoff]

There has been confusion about the topic of the supposed inside of a black hole (BH) in general relativity (GR). I wish to clarify this properly, rather than write small pieces in response to comments.

GR is a valid theory. It has a consistent mathematical framework, and has been verified observationally. No theory is perfect, which can be proven using Gödel's arguments. Physicists try to deal with the imperfections by imagining extensions to GR, and then calculating results. This is a proper approach to advancing physics. However, we must not confuse these extensions with the theory of GR itself. My arguments refer to GR only.

I will prove the following theorem three ways. Theorem: There is no solution of GR inside the BH.

One way. A solution inside the BH must exist everywhere in the inside. The solution of GR, namely, the viewpoint of the observer falling into the BH, is not valid at the center. Physicists proved this by proving the existence of a singularity at the center. Therefore, this solution is not valid.

The counterarguments do not seem clear and logical to me. For example, some of you said that it is okay to have a solution that is not valid everywhere. This contradicts the basic philosophy of boundary conditions (BC). The BC at one point determine which solutions are valid. Same for the BH. The condition at the center determines that this solution is not valid.

Two. Physical concepts must be capable of being observed in principle. If one individual can observe something, but no one else can, then the concept does not exist in physics. No observer can see something falling into the inside of the BH. Therefore, the inside does not exist.

Maybe a future theory including QM will permit the observation of the inside. This is irrelevant to my argument. I am discussing GR, not QM. In GR, the inside cannot be observed.

Some of you tried to say that although outside observers cannot see the inside of the BH, the observer falling down does see this inside. This is like saying Heaven exists. No one has observed Heaven, except for the person who died. The basic philosophy of physics is to reject ideas that people cannot observe.

Three. Okay, I gave one proof based upon mathematics, and a second based upon the philosophy of physics. I will now give a proof based upon contradiction. Normally these types of proofs are difficult for students.

Let us assume the solution exists inside the BH. Consider the simple case of a BH with zero angular momentum. Let the observer have 0 angular momentum as he falls in. Consider a time when the observer is ¼ of the way down. Let the BH be at state A at this time. At a later time, the observer is ½ of the way down. Let the BH be at state B at this time. Since the observer is at different points on the path, state A is not equal to state B.

A BH has the property that its state depends only on its mass, angular momentum, and charge. Both state A and state B have the same mass, etc. Therefore, state A is identical to state B. This contradicts the previous statement, state A is unequal to B. This proves no solution exists.

 

[JesseM]

One way. A solution inside the BH must exist everywhere in the inside. The solution of GR, namely, the viewpoint of the observer falling into the BH, is not valid at the center. Physicists proved this by proving the existence of a singularity at the center. Therefore, this solution is not valid.

Once again, you are using the word "solution" in a vague and slippery way which does not correspond to how it is used by physicists. There is no separate "solution" for inside the event horizon and outside, if your own invented rule was really "throw out all GR solutions involving singularities" then you should throw out the whole thing, including the region outside the event horizon. If you're going to divide up a single GR solution into two pieces, there is nothing special or magical about the event horizon, it's just a distance which has the interesting physical property of it becoming impossible for light to escape; logically, you could equally well divide the Schwarzschild solution into "the region from R=0 to R=0.5" and "the region from R=0.5 to R=infinity" (i.e. one part from the singularity up to half the distance to the event horizon in Schwarzschild coordinates, another part from half the distance to the event horizon out to infinity), and throw out the first part while saying the second part is valid. You have not made any logical connection between your poorly-defined notion of a "solution" and your arguments about the inside of the event being unobservable to outsiders, you're just using an arbitrary sort of free-association to justify dividing up a single GR solution into two pieces this way.

The other point is that you provide no coherent physical justification for throwing out solutions with singularities, just some weird pseudophilosophical statement that singularities violating the "philosopophy of boundary conditions" What is this "philosophy" exactly? Who says quantities can't go to infinity on boundaries? Physicists do tend to see infinities as a sign the theory is probably going wrong (although plenty of physicists have discussed the possibility that GR singularities could be real physical infinities), but they have physical arguments for just how far from the singularities they expect the theory can't be trusted, not made-up philosophical rules where if the theory gives bad predictions in a specific region the theory's predictions about other areas far from that region must automatically be disqualified.

Do you have any understanding of how past theories of physics such as Newtonian mechanics or classical electromagnetism have been show to "break down" in specific domains, and been shown to be approximations to some other more correct theory which can deal with these domains? In these cases it has always been that the predictions of the first theory and the second, more accurate, theory have been shown to continuously diverge as some parameter or parameters are varied so we get farther into the domain where the first theory "breaks down", like increasing the relative velocities of particles in Newtonian mechanics closer to the speed of light, or considering blackbody wavelengths closer to the ultraviolet catastrophe in classical electromagnetism (the more correct theories to deal with these situations are special relativity and quantum theory, respectively). Physicists assume that something similar will be true of GR vs. quantum gravity, and they have physical arguments for believing the divergence between the two theories will only become significant near the Planck scale. They don't just make up arbitrary rules to make things simpler for themselves, like "let's divide the Schwarzschild solution into two regions, one inside the horizon and one outside, and say that GR is valid outside but the inside contains a singularity so let's assume it's totally invalid anywhere inside".

Two. Physical concepts must be capable of being observed in principle. If one individual can observe something, but no one else can, then the concept does not exist in physics. No observer can see something falling into the inside of the BH. Therefore, the inside does not exist.

Any observer or community of observers who falls in after the object can see it cross the event horizon. What's more, in a universe with expanding space there will be regions of ordinary space (no black holes involved) which are in principle impossible to observe simply because the expansion of space between us and them carries them away from us faster than even a light signal sent from our position could ever catch up with them. Do you therefore conclude that nothing beyond a certain sphere centered on the Earth really "exists"? This would be a strangely solipsistic cosmology, with observers on different planets each concluding that nothing beyond the same-sized sphere centered on themselves really exists!

Three. Okay, I gave one proof based upon mathematics

You obviously don't understand what a "proof" is, it's not a string of poorly-connected statements based on ill-defined terms (as I said, you use 'solution' in a way that clearly doesn't correspond to the way this term is used in GR, and you fail to provide any logical connection between your argument about event horizons and your notion that we should treat the region inside the event horizon as a different 'solution' and throw it out completely).

Let us assume the solution exists inside the BH.

Again, why the arbitrary choice of dividing up the solution into "inside the event horizon" and "outside the event horizon"? Why not "inside a sphere with a radius equal to half the radius of the event horizon" and "outside that sphere", for example?

Consider the simple case of a BH with zero angular momentum. Let the observer have 0 angular momentum as he falls in. Consider a time when the observer is ¼ of the way down. Let the BH be at state A at this time. At a later time, the observer is ½ of the way down. Let the BH be at state B at this time. Since the observer is at different points on the path, state A is not equal to state B.

A BH has the property that its state depends only on its mass, angular momentum, and charge. Both state A and state B have the same mass, etc. Therefore, state A is identical to state B. This contradicts the previous statement, state A is unequal to B. This proves no solution exists.

Uh, a systems can be in the same "state" at different coordinate times, "state" just refers to the numerical values of a certain set of physical properties, if the object has identical properties at times t1 and t2 it was in the same state at both times, you can't use the fact that t1 and t2 are different to prove that the state is different! "Same state" does not mean "same event", two events on an object's worldline are distinct even if the object was in the same state at both points. Again you are using a weird sort of pseudophilosophical reasoning in your "proof", based on your own vague and nonstandard definitions of terms which have accepted meanings in physics.

As I've said before, it is not permitted to try to dispute mainstream physics on this forum. If there are things you're confused about you can ask about them, but these sorts of confident arguments that accepted ideas are wrong won't fly--please stop it or I will report your posts to the mentors and let them deal with it.

 

[Hurkyl]

No theory is perfect, which can be proven using Gödel's arguments.

I'm not entirely sure what you mean by 'perfect', but I am virtually certain it's not something that Gödel's theorems talk about.

One way. A solution inside the BH must exist everywhere in the inside. The solution of GR, namely, the viewpoint of the observer falling into the BH, is not valid at the center. Physicists proved this by proving the existence of a singularity at the center. Therefore, this solution is not valid.

(Assuming we limit ourselves to a mathematically simple version of GR in which the metric must be finite and differentiable at all points...)

The 'solution' does exist everywhere inside the black hole. More precisely, the Schwartzchild metric really does exist at each point inside of the black hole, and satisfies the EFE there. The singularity is a hypothetical point whose existence is merely suggested -- not proven -- by the form of the Schwartzchild 'coordinates'. But the criteria imposed above imply that the point really doesn't exist.

(I put 'coordinates' in scare quotes because the Schwartzchild coordinates, taken as a whole, are not actually coordinate functions)

 

[aranoff]

I forwarded some of your comments to another physics professor. His reply:

You must have seen by now that physicsforums.com is not a good place for any
serious scientist. The noise level of pompous ignorance is too high for a
sensible discussion.

The singularity is proven, not hypothetical.

 

[Hurkyl]

I'm curious -- if you didn't want to listen to a word that anybody here is saying, then why did you post?

 

[JesseM]

I forwarded some of your comments to another physics professor. His reply:

You must have seen by now that physicsforums.com is not a good place for any
serious scientist. The noise level of pompous ignorance is too high for a
sensible discussion.

Did he have any specific criticisms of claims or arguments made on this thread?

The singularity is proven, not hypothetical.

What do you (or he) mean by that? If you're saying it's proven that black holes must form singularities according to GR, of course that's true, no one has disputed this, unless Hurkyl was disputing it above in which case I believe he is simply incorrect (my understanding is that the necessity of real physical singularities inside the event horizons of black holes according to GR was proved by the Penrose-Hawking singularity theorems). The point is that most physicists would expect that a theory of quantum gravity would predict something different about the center of the black hole, although they don't expect the predictions of a theory of quantum gravity would significantly diverge from those of GR until we reach the Planck scale.

 

[aranoff]

The point is that most physicists would expect that a theory of quantum gravity would predict something different about the center of the black hole, although they don't expect the predictions of a theory of quantum gravity would significantly diverge from those of GR until we reach the Planck scale.

I'm sorry, but I am at a loss of how to communicate with you guys. You are supposed to be physicists, either students or professors. I said very clearly that I was discussing the meaning of GR, and you mention quantum gravity!

Why did I post? Well, based upon your emotional reactions and immature thinking, I cannot recommend Physics Forums to my colleagues or students. I am very disappointed.

You need more openness. Names, emails, affiliations, and status. We cannot tolerate people sounding off without knowing who they are. You know who I am.

 

[JesseM]

I'm sorry, but I am at a loss of how to communicate with you guys. You are supposed to be physicists, either students or professors. I said very clearly that I was discussing the meaning of GR, and you mention quantum gravity!

As I understand it, you are not discussing purely theoretical questions about what GR predicts (it predicts singularities, and there is nothing a priori impossible about the idea that these could be real physical entities), but rather the empirical question of whether GR's predictions are correct (you reject its predictions everywhere inside the event horizon for reasons that aren't really clear, while most physicists have physical reasons for thinking its predictions are only likely to go significantly wrong at the Planck scale). Am I misunderstanding something here?

Well, based upon your emotional reactions and immature thinking,

Insulting other people's arguments in this way without actually addressing what's wrong with them seems like a knee-jerk emotional reaction to me.

You need more openness. Names, emails, affiliations, and status. We cannot tolerate people sounding off without knowing who they are. You know who I am.

your profile doesn't say what your full name or educational background is, only that you are a substitute teacher in high school. You can see my full name if you look at the website linked to in my profile (I don't have any particular desire to see this thread be one of the top results on google for my name so I won't mention it). I majored in physics in college as an undergraduate, I don't claim to have any great expertise in GR but I have read enough to know that your arguments contradict the understanding of most professional physicists.

 

[Dale]

You need more openness. Names, emails, affiliations, and status. We cannot tolerate people sounding off without knowing who they are. You know who I am.

Names, emails, affiliations, and status are appropriate for a peer-reviewed manuscript, not for an internet forum. I think you misunderstand the nature of an internet forum if you expect such things. This forum is not intended to be a substitute for traditional education nor is it intended to be a substitute for the peer-reviewed literature. Your expectations seem unrealistic.

 

[aranoff]

My discussions were what does GR predict.

I am a physics professor, and have been for many years. My website gives a paper I wrote on the topic in 1972. I am sort of retired, and so do some high school subbing.

 

[Mentz114]

My discussions were what does GR predict.

aranof,

You don't seem to understand what GR predicts. I've been following this thread and I've read it more than once. You started by not accepting that the infinite time to reach the event horizon is observer dependent, then changed to your position when this was pointed out. Your argument that the singularity at r=0 invalidates GR has also been refuted.

I take all your subsequent remarks about the forum as sour grapes.

M

 

[JesseM]

My discussions were what does GR predict.

So all discussions about whether GR's predictions are correct or incorrect are irrelevant, then? Why the long discussion about rejecting the predictions inside the event horizon? GR predicts a singularity at the center, end of story. There is nothing logically impossible about this prediction, so no reason to reject such a solution a priori.

I am a physics professor, and have been for many years.

What area of physics? Do you have much expertise in general relativity? (this would seem unlikely, given that you apparently didn't realize the proper time for a falling observer to cross the event horizon is finite, and given that you seem to use terms like 'solution' and 'boundary condition' and 'state' differently than they are used by physicists in relativity)

 

[Hurkyl]

unless Hurkyl was disputing it above in which case I believe he is simply incorrect (my understanding is that the necessity of real physical singularities inside the event horizons of black holes according to GR was proved by the Penrose-Hawking singularity theorems).

The thing is that the singularity doesn't occur at a point in space-time. GR doesn't demand that the inside of a black hole have the topology of a ball -- instead, a Schwartzchild black hole has the topology of the 3-dimensional analog to an (open) annulus. The r=0 points are inside the hole, rather than being parts of space-time.

(If we interpret Schwartzchild coordinates as if spacelike slices gave spherical coordinates on 3-space, the hole consists of a single point)


Yes, if we so desired, we can remove this interesting topological feature by filling it with a point and relaxing the condition that the metric be everywhere defined. But I don't believe that to be a good idea, since it gives up your ability to prove things by reasoning topologically. (And, of course, it is a bad idea if you're someone who absolutely insists that the metric be everywhere defined and differentiable)

 

[atyy]

Not sure whether these should go here, since the thread has deviated towards aranoff's questions. But while staying on the subject of his questions:

Would anyone care to comment on whether the cosmic censorship hypothesis is necessary for GR to make sense?

Do we have any experimental evidence for singularities as predicted by GR?

Weinberg comments in his 1972 text that the singularity theorems only prove that a singularity existed some time in the past, but need not fill all of spacetime. Is this true? Taking "big bang" theory to be the most commonly accepted cosmology, does it mean that a singularity is not an essential part of "big bang" theory?