# Do Black Holes Really Exist?

The first order of business is to define what we mean by the term “black hole”. The common pop science definition, “a region from which nothing, not even light, can escape”, is actually a pretty good starting point (which is not always the case with pop science definitions). The key thing we need to tighten it up into something rigorous is to define exactly what “escape” means. In the usual idealized model of a black hole, it is viewed as being surrounded by empty space, and the hole’s gravity gets weaker and weaker as we move farther and farther away from it in this empty space, so the geometry of spacetime gets closer and closer to being flat. The technical term for a spacetime like this is “asymptotically flat”.

We might think that this is enough: “escape” just means that spacetime is asymptotically flat, and whatever it is that is escaping can get arbitrarily far away from the hole, into the region where the geometry of spacetime is arbitrarily close to being flat. The usual shorthand expression for this is “escape to infinity”. Only something outside the hole’s horizon can do this.

But it turns out that there is an additional wrinkle here: there is more than one possible “infinity” in an asymptotically flat spacetime. In fact there are five; they are called future and past timelike infinity, future and past null infinity, and spacelike infinity. Why is this? Because spacetime includes time as well as space, so there are three kinds of curves, timelike, null, and spacelike, and the first two kinds have two different directions, future and past. (Technically speaking, the light cone at every event in spacetime has two interior regions–future and past–which are disconnected, but only one exterior region–the spacelike region.) Each of these, if extended indefinitely, ends up at a different “infinity”.

So the question now is, which of the five infinities do we pick to define “escape”? The answer turns out to be future null infinity. If you think about it, this makes sense: “escape” should be to the future, not the past, and light moves faster than anything else, so if light rays can’t reach future null infinity from some region of spacetime, it seems evident that timelike objects certainly won’t be able to reach future timelike infinity either. And that turns out to be the case when we do the math, so we arrive at our rigorous definition of a black hole: it is a region of spacetime that cannot send light signals to future null infinity. Or, in somewhat more technical language, a black hole is a region of spacetime that is not in the causal past of future null infinity.

Now we can look at the first common misconception about black holes, which is that they can’t be formed at all because it takes an infinite amount of time for an object to fall to the event horizon. The usual counterargument to this is to point out that “infinite time” as it is used here is coordinate-dependent: the “time” in question is not an invariant, and so it doesn’t in itself have any physical meaning. And we can compute invariants, such as the proper time needed to reach the horizon by the infalling object’s clock, and show that they are finite.

But armed with the above definition, we have a much simpler response: is there a region of spacetime that is not in the causal past of future null infinity? If there is, a black hole is present, regardless of whether there is some coordinate chart in which it takes an infinite amount of time for something to fall into it. And can such a region form in a spacetime that starts out not containing one? Yes, it can; this has been demonstrated by explicitly constructing models that have this property (the first was the classic Oppenheimer-Snyder model published in their 1939 paper). So the first common misconception is indeed a misconception: there definitely are self-consistent solutions of the Einstein Field Equations that contain black hole regions, and objects that can form such regions by collapse, even though coordinate charts exist for these solutions in which coordinate time on the horizon becomes infinite (where “becomes infinite” is a sloppy way of saying “is not well-defined”).

So far we have been discussing “classical” black holes, without considering any quantum effects. A well-known theorem due to Hawking says that such a black hole can never decrease in size (where “size” here means the area of its horizon); and a well-known argument due to Bekenstein says that this is in fact just an application of the second law of thermodynamics to black holes, with the horizon area being the hole’s entropy. But Hawking also discovered something else: if we include quantum effects, the area theorem can be violated, and a black hole can lose mass, in a process known as Hawking radiation. (Note that the second law still holds in this case; the hole’s entropy decreases, but the entropy of the radiation must be included as well, and when it is, the total entropy still increases.)

This brings us to the second common misconception about black holes, which is that, when Hawking radiation is included in the picture, a black hole can’t form because it would evaporate before anything had a chance to fall into it. Again, there are counterarguments saying that, for an evaporating black hole, it no longer takes an infinite time, even by the coordinate charts referred to above, for something to fall in, and when the coordinates are adapted properly, objects fall in before the hole evaporates away. But again, armed with our definition above, there is a much simpler response: are there self-consistent models that include a region that is not in the causal past of future null infinity, even if such a region later disappears due to evaporation? Yes, there are; the simplest one is due to Hawking himself. So again, this common misconception is in fact a misconception. In fact, there are self-consistent solutions that show the whole process, from formation of a black hole by gravitational collapse where none existed before, all the way to the hole finally evaporating away due to Hawking radiation.

You might have noticed, though, that so far I have been careful to use the word “model” when describing what our physical theories say about black holes. Models are not reality. The real question is, do we have evidence that the mathematical models I described above are actually realized somewhere in our universe? That is what it would mean for black holes to “really exist”, and the fact that common misconceptions about the models are wrong does not in itself prove that the models describe nature.

The honest answer to this last question above is that we don’t know for sure. The main reason is that we don’t (yet) have a good theory of quantum gravity, so we don’t know whether Hawking radiation is really the only significant change to the classical black hole model that we have to deal with. It is possible that there are other quantum effects that, when properly taken into account, will prevent a true black hole from ever forming–i.e., will prevent any region of spacetime from ever truly leaving the causal past of future null infinity. Currently there are two schools of thought about this:

**(1)** The general heuristic that many physicists use to determine when quantum gravity effects should become important is that the spacetime curvature has to be very large–large enough to be equivalent (via the Einstein Field Equation) to a density approaching the Planck density–one Planck mass per Planck volume, or about ##10^{94}## times the density of water. But for any black hole we would expect to detect by astronomy (which would be roughly the mass of the Sun or larger), the spacetime curvature at and well inside the horizon is much, much smaller than this. So by this heuristic, we would expect classical GR to be a good approximation at and well inside the horizon, meaning that we would not expect quantum corrections to prevent true black holes–regions not in the causal past of future null infinity–from forming, even if quantum corrections did change what happened deep inside those regions.

**(2)** However, there is another rule which, at least in the view of the quantum physicists who make the argument, is much more than a general heuristic–it’s a law of nature, part of the bedrock of quantum mechanics. This law is called “unitarity”, and it basically means that quantum information can’t be created or destroyed. But at least in the simple model of a black hole, even an evaporating one, any quantum information that falls inside the horizon does get destroyed, when it hits the singularity. So on this view, at the very least, quantum effects must prevent a singularity from ever forming. But when you look at the structure of the evaporating black hole models, you see that it’s very hard, if not impossible, to remove the singularity without also removing the horizon–in other words, without changing the spacetime structure to something that does not have a region which is not in the causal past of future null infinity. So on this view, quantum effects must end up preventing true black holes from ever forming, even if we don’t understand quite how they would do this.

It’s important to note that position (2) above does not necessarily imply that there can’t be horizons at all, only that there can’t be true event horizons. But there is another kind of horizon called an “apparent horizon”, which is a surface at which, heuristically speaking, radially outgoing light does not move outward, but stays in the same place. (The technical definition is that the expansion of a congruence of radially outgoing null geodesics is zero.) This does not necessarily make the apparent horizon a true event horizon, because “stays in the same place” is only local–radially outgoing light that is staying in the same place at one event might, at some future event, start moving outward, so it would end up ultimately escaping to future null infinity. (Note that, for this to happen, the area theorem must be violated; in pure classical GR, where black holes can never decrease in mass, any apparent horizon will always have an event horizon at or outside it. The latter will be the case if matter is falling into the hole: the event horizon increases in area smoothly, while the apparent horizon “jumps” suddenly outward.)

The reason this is important is that all of the methods we have for actually testing, observationally, for the presence of horizons can’t tell us whether the horizon we think we have detected is a true horizon, or only an apparent horizon. The only way to know for sure would be to know the entire future of the universe, which, of course, we can’t know. So the fact that we have observed a number of compact regions in which there appear to be horizons (basically, because things fall into them and don’t come out and they’re too compact to be anything else) does not, in itself, allow us to test positions (1) vs. (2). We have to find other, indirect ways of exploring the issue, and the field is simply too young for there to have been much time to do so.

(I should also note that there are proposed mechanisms, referred to by terms like “firewalls”, by which quantum effects would destroy infalling objects before they ever reach a horizon, preventing any violation of unitarity; and there are also proposed mechanisms by which quantum effects would prevent even apparent horizons from forming, by basically pumping enough energy into collapsing matter via quantum effects to reverse the collapse and make it explode before it had a chance to become compact enough to form an apparent horizon. These proposals do not appear to be holding up very well under scrutiny, so I won’t say more about them here, but it’s important to be aware that they exist.)

So to summarize: the answer to the title question may end up being “no”, but if so, it won’t be for any of the simplistic reasons associated with common misconceptions about black holes–i.e., it won’t be because they take an infinite time to form, or because they would evaporate away before anything had a chance to fall in, or anything like that. We don’t know for sure whether the answer is “yes” or “no” at this point, but we expect to learn a lot more about the subject as we continue research into quantum gravity.

Great Insight Peter!

Yes. They really do… They are observed in galactic centers.

I find people get most confused by the characterization of event horizons, as if the proverbial event horizon of a black hole is some unique new physical entity. We pass through event horizons constantly. space-like hyper-surface is an event horizon, the future, and past light cones of any space-time event are examples of an event horizon, i.e. a boundary across which causal signals and matter can only travel one way. Event horizons don’t need some extreme circumstance to be formed. The issue is whether gravitation can curve space-time so that we can draw an event horizon into a shape we describe as a black hole. GR says yes. Astronomical observations show something in the center of most galaxies that seems to confirm this theoretical prediction so… Yea, you betcha!

What is observed in galactic centers is dense supermassive objects, which can be described as “black hole candidates”.

If General Relativity is still accurate in such extreme situations, such objects are theoretically predicted to be black holes. GR has been confirmed to give very accurate predictions for the solar system and for example for loss of energy of the Hulse-Taylor binary pulsar system through gravitational waves. However, the most sensitive test these observations have checked so far only confirms GR to one “Post-Newtonian” correction term – the ##beta## parameter in the Parameterized Post-Newtonian (PPN) model, which can be measured through the perihelion precession of Mercury and Lunar Laser Ranging. For black holes to occur, GR has to be accurate to further terms which have not yet been confirmed.

Clearly, GR is a neat and self-consistent theory and it is generally expected that black holes will eventually be confirmed, which is why there is no problem with calling these objects “black hole candidates”. However, in the mean time, there are various observations which do not fit so well with GR, such as an apparent strong magnetic field in the vicinity of the core of a quasar (where a black hole was not expected to be able to sustain such a field) and the way in which GR apparently needs to be supplemented by mysterious dark matter to explain galactic rotation curves. It is also quite tricky to tell the difference between a hypothetical extremely red-shifted object which is not a black hole (if GR has some sort of limit that prevents black holes) and an actual black hole.

For the moment, GR is the best theory of gravity that we have and it predicts black holes, but at present that is a theoretical prediction, not an experimentally confirmed one.

With so many theories Available today We cannot even prove that we Exist. If we can assume that we existThen it is every bit as possible to assume that black holes exist as well. It is even more possible to assume that black holes existGiven the immense amount of data Collected on And mathematics Referring to Black holes. There is yet to date A mathematical proof For the existence of consciousness.

I disagree. I am still unaware of any DIRECT OBSERVATION of Black Holes – not saying anyone above is wrong just that I’m not aware of such.

Indirectly, though, the evidence for Black Holes is overwhelming. The output from what used to be called ‘Quasars’ and ‘Active Galactic Nuclei’ is readily explained by current models of the energies from electromagnetic fields and the friction of the accretion material due to the incredible power of the BH frame dragging and its radial speed.

Even more recent measurements of lower frequencies to penetrate the amassed dust and obscuring clouds at the heart of the Milky Way, and the measured orbital paths (size, parabolicity and speeds) of the stellar objects around the “Great Attractor” Sag A* not only fit with the model with a supermassive Black Hole at the gravitational centre, but also, there is no known, nor generally accepted reasonable alternative possibility for something so massive, yet so spatially compact to produce such results.

It’s a logical deduction that the most obvious, reasonable and plausible cause is that there MUST be a Black Hole.

I, too, would find it extremely unlikely that this is not the case, yet as a matter of direct, irrefutable proof and direct measurements confirming an actual Black Hole, there are none.

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I also would consider Cauchy surface horizons and the effective surfaces of light cones in spacetime as being Absolute Horizons, which INCLUDE Event Horizons, but the nature of a Black Hole EVENT HORIZON is more than simply a ‘one way street’, the reason for the name “Event” Horizon refers to the extreme nature of the Black Hole in warping spacetime so that no more events are applied to a causal timeline that crosses the boundary.

I am on the side that is convinced by the available information that Black Holes exist. However, everyone has a different level of proof needed to be convinced. And I am NOT a professional physicist or astronomer. Using Occam’s razor, I believe that Black Holes in the Galactic cores is the simplest explanation for what we observe. However, dark matter and other anomalies may lead to a more complex model that may not rely upon or allow something else to explain away the Black hole formation. A Black Hole seems to be the simplest and most reasonable explanation at this time, so I am convinced.

We can all see Jupiter through a modest telescope, but have ANY of us actually been there? Similar level of proof. We see activity and effects of a super massive object at the center of our Galaxy. We don’t see any object, just lots of starts racing around a darkened core. It agrees with our mathematical model of a billion solar mass object. It doesn’t radiate any perceivable light (of course we are tens of thousands of light years away, so we can’t see low levels of radiation if they were there). Hence we now assume we have a black hole (candidate for the more severe doubting Thomas’s).

“For the moment, GR is the best theory of gravity that we have and it predicts black holes”

Do we need complex ideas like GR or curved space to predict black holes? A body that falls under the force of gravitational attraction of mass

Mfrom infinity, starting with zero velocity, will strike the mass with a velocity equal to its escape velocity. Is the escape velocity or impact velocity v of a falling body on any object (even a neutron star) given exactly by the newtonian formula v^2 = 2GM/r ? Note this equation gives the Schwarzschild radius when v = c.In my opinion, this sounds like some people beginning with Albert Einstein, just wanted to make things look complex, which can in no way be true.

RealNature and Universe areindeedcomplex, regarding their mathematical description. Of course Newton’s theories were great achievements for their time, but it’s like describing an object as you see its surface, having no idea what hides inside or where it comes from. Again, this in no way relegates the great work of Newton, who after all, had nothing more than a few of previous theories and very few observations – or what did that mean back then. But Einstein went a great way further with GR and finally found very innovative ways to express his ideas. I don’t think that any mathematically rigorous prediction, can exist outside some rigorous treatment and I definitely agree that what we have so far in this regard, is GR. I think that black holes exist, but I also think that quantum world has a lot to reveal in the future.Of course Einstein didn’t want to just make things look complex. In a Newtonian sense the acceleration of a small falling object shouldn’t be affected even by a relativistic increase in its effective mass-energy. Absent other forces, can the impact velocity on any far object (even a neutron star) be given exactly by the formula v^2 = 2GM/r ?

My suspicion is that you are using a definition of “direct observation” here that it far more limited than you would use in other situations (just seeing with your eyes?). Because there are several direct observations of properties of black holes. Gravitational field strength is measured by timing orbits. Size is measured by observing radiation from infalling matter.

[URL]https://www.cfa.harvard.edu/seuforum/bh_reallyexist.htm[/URL]

No. By Direct Obsevration of a Black Hole, I mean, any measurement that detects the actual properties of a Black Hole directly, rather than an indirect inference from a measurement of some other property which (ALTHOUGH HIGHLY UNLIKELY) may still be yet shown to be due to some other process.

Infalling Matter tells us the gravitational power accelerating objects, there is no observation of to-what this matter is falling into.*

Now the concensus is overwhelmingly in favour of, and, again as I mentioned, seems to largely reject any reasonable alternative possibilities given the mass/energy densities involved, that it can only really be a Black Hole. HOWEVER, and I am making an extreme exaggeration for the sake of the point, consider that some alien civilisation created super powerful energy rays which, when focussed onto a single concentrated point result in an extreme gravitational event.

This event would also exist in a small space, with a high gravitational force, for all intents and purposes of the ‘indirect mweasurements’, would still accrete infalling matter and accelerate it to relativistic speeds. The nature of the energy rays may still exhibit a powerful magnetic field and emit jets of high energy charge. This phenomena would still pull nearby stars into extremely tight, fast orbits around a space in which no stable stellar object could exist and none are visible. In effect, you have an entity which ticks all the boxes for a Black Hole, but is not one.

I personally am absolutely in agreement that Black Holes exist, and do not doubt that the measurements made as described are indirectly evidencing this – however, I maintain that it’s simply not enough to warrant any claim of confirming the definite, undeniable such a phenomena as a Black Hole.

Is the concept of curved space required to predict black holes?

Light always travels in straight lines. In curved spacetime, this straight path is seen to be curved.

So although the basic idea of a highly dense, collapsed star (such as Laplace’s Dark Star) were put forth even in 18th century, they were based on inaccurate understanding of light.

Part of the definition for a Black Hole is that the gravitational strength is such that the escape velocity at a particular altitude up the gravitational potential well is faster than the speed of light. This causes light to follow a trajectory that appears as curving towards and ultimately into the Black Hole.

So in some ways, yes, curved space is necessarily part of the actual definition of what a Black Hole is, but the idea of Black Holes in essence existed in a classical form (although not entirely accurate)

Is the escape velocity from any large object (even a neutron star or black hole) described exactly by the formula v^2 = 2GM/r ? If the Schwarzschild radius (called SR) is defined as the radius where the escape velocity equals the speed of light, can we then simply say that SR = 2GM/(c^2)? The concept of an object with a mass/radius ratio large enough to contain light doesn’t require curved space along with the concept of light always traveling in straight lines. Why can’t we simply say that light bends around an object? If a neutral object from far away drops straight into a basic non-spinning and non-magnetic black hole, is its relative velocity c when it reaches the event horizon?

Because Light must travel in straight lines. If light was “bent” or curved, it would necessitate a change in velocity which necessarily entails a temporal metric which implies that light is not relativistic and violates both of Einstein’s theories in one go.

In your given equations, when dealing with relativistic speeds, one must factor in the Lorenz transformations, which you seem to be missing.

Sure, a particle falling straight down towards a black hole will have Lorenz transformations, but do the Lorenz transformations at any point affect the velocity it will have?

“[URL=’https://www.physicsforums.com/insights/black-holes-really-exist/’]Do Black Holes Really Exist?[/URL]”

Probably, but could what we think are black holes be compact stars (larger than their Schwarzschild radius) if they had the following characteristics?: (1) They were a mixture of normal matter and ultra-relativistic matter. (2) They had a crust that was mostly a light absorber.

It will have a constantly changing velocity anyway, if it’s “falling”.

Yes, but would its acceleration be affected by the Lorenz transformations?

“[URL=’https://www.physicsforums.com/insights/black-holes-really-exist/’]Do Black Holes Really Exist?[/URL]”

The suggestion of a stable compact star consisting of normal matter and ultra-relativistic matter is probably a bad idea.

Suggestion (2): Could a compact star of 5 solar masses exist if its radius was 20 or 25 km? Would it have to collapse? Could we distinguish it from a black hole?