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?

DaleSpam

Try this paper.

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

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

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

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-

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

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-

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

JesseM

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

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

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:

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

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 [itex]s^2<0[/itex] exists inside the event horizon where [itex]s^2=c^2\Delta t^2-\Delta r^2[/itex] (or [itex]c^2\Delta t^2<\Delta r^2[/itex]) while [itex]s^2>0[/itex] 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

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.