# Black Hole Questions

### Question:

What is a wormhole? What does it mean to say that the wormhole solution is unstable?

If one takes the Schwarzschild metric and performs a somewhat complicated coordinate transform, one will discover that the Schwarzschild solution to Einstein's equations is more extensive than first thought. The new solution consists of two asymptotically flat spaces connected together at the event horizon. At first blush, it appears as if one can travel from one of these spaces into the other, thus this wormhole seems to provide a bridge between two universes. However: no timelike worldline can bridge the gap. The other universe is strictly elsewhere from our universe. The best you could hope for is to meet someone from the other universe as you were falling into the singularity. Once inside the horizon, both universes lie in your past light cone.

Now for the wormhole's stability: If we examine the wormhole solution in our modified coordinates, we find that the solution evolves as measured in the modified time coordinate. Basically, the Schwarzschild "throats" form in both universes, connect, and then pinch off into singularities. Viewed from outside, using "ordinary" time coordinates, the whole thing just sits there, but in the modified time coordinates, those which would be more appropriate for someone falling in, time is very finite and ends at the singularity.

Are wormholes real? They are a real solution, but that doesn't mean that they exist in the universe. They do not result from the collapse of a star. They just have to be built in ab initio. There are several known weird solutions to Einstein's equations that probably don't have much to do with the real world. They are worth studying though because they provide fascinating insights into properties of the theory general relativity.

If you want to know more about wormholes, may I recommend Kip Thorne's well-written book Einstein's Outrageous Legacy.

### Question:

Can the entire universe be a black hole?

Technically, no, because the black hole solution is a vacuum solution that has an external region that goes to flat space outside of the hole. The universe is not a vacuum and there is no known (or required) external spacetime. However, the closed model (see Chapter 11) shares some features with the internal solution of a black hole, in that gravity is going to bring everything to a collapse and a singularity, and no worldline can escape that fate.

### Question:

If time stands still at the event horizon and a ship drifts down to the horizon, how can we know what happens to that ship? Wouldn't we see it stuck forever on the horizon?

We never see the ship cross the horizon, that is true. Time does seem to come to a halt. But we don't watch the ship hovering there forever. Very quickly the last photon that we will be able to see from the ship would reach us and we would see the ship no more. The redshift effectively goes to infinity in a finite time.

### Question:

We see black holes, e.g., the one in M87. Does this preclude the idea that the universe is a black hole, or could one black hole exist inside another black hole?

Actually a black hole could exist inside a black hole. Imagine turning a whole galaxy into a black hole by bringing all its stars extremely close together. All these stars might themselves be black holes. The individual black holes won't even be touching when they are all surrounded by a larger event horizon with a radius corresponding to the mass of the galaxy. However, once they are all within the event horizon they will end up merging together in a final collapse to a singularity.

### Question:

Can black holes be used to explain the "missing mass" in the universe?

Black holes would be hard to detect, and a great deal of unseen mass could be stored inside black holes. However, based on how we think black holes must form (from collapsing cores of relatively rare supermassive stars) there can't be that many black holes in comparison to more normal stars. Hence we expect that the total mass in black holes is only a small fraction of the mass we can see, so that they don't constitute a major component of the unseen, or "missing" mass in the universe. (See Chapter 14)

### Question:

It is stated that radio jets can appear to be moving faster than the speed of light. How can this be, when nothing can move faster than light?

They aren't actually moving faster than light. The simply appear to be moving faster than light. The jet is beamed toward us, nearly along our line of sight. It moves only slightly slower than light, so the light carrying the history of its motion tends to be bunched up when it gets to us. Imagine somebody flying from Alpha Centari at close to c while you watch through a telescope. By the time the light gets here telling you that they have left, they are about to arrive, so to you the journey speed appears to be superluminal. But by subtracting out the known light travel time, you can compute the true speed, and verify that it is less than c.

### Question:

In intro astronomy we briefly discussed how tiny black holes might have formed in the big bang. Do cosmologists believe that that occurred and if so would the holes be destroyed by Hawking radiation since then?

It is possible that tiny black holes could have formed and that they would be radiating away via the Hawking process by now. But none has ever been detected. Most cosmologist don't regard this as very likely.

### Question:

I have heard that miniature black holes traveling through space might come in contact with the Earth. If this happened what would result?

Somebody once seriously suggested that a mini black hole could account for the Tunguska event in Siberia. Depending on the size of the black hole (let's assume it truly is a mini-hole with a Schwarzschild radius that is submicroscopic) it would pass straight through the Earth, possibly wreaking a little havoc at the entry and exit points due to its strong tidal forces. It would actually accrete very little mass in its passage.

### Question:

What are the chances that Earth will one day encounter a big black hole?

Over the lifetime of the solar system (10 billion years or so) there is virtually no chance that we will encounter a black hole. (Or any other star, for that matter.) If the universe expands forever, the matter that presently makes up the Earth may one day end up in a black hole. Most things may very well end up in black holes in the incredibly huge distant future. Then in an even longer period of time those black holes will evaporate.

### Question:

What exactly is a singularity? What does infinite density mean?

We might say that the singularity is where all matter was crushed to infinite density (finite matter in zero volume). A better definition might be a point at which world lines come to an abrupt end, marking the end of time and space as it were.

### Question:

If the black hole singularity has infinite density, doesn't that imply either infinite mass or zero volume, neither of which seems to be a sensible concept?

It is generally regarded as a finite mass packed into zero volume. Most physicists regard zero volume as a not well-posed idea, hence the expectation that there must be a way within a larger theory (quantum gravity) to avoid zero volume and instead end in some finite, albeit extreme, state. However, we don't know for sure.

### Question:

What are the chances of a black hole forming near enough to the Earth for us to be affected by it?

Pretty close to zilch. The only way we know how to form a black hole is through the collapse of a supermassive star, and there aren't any such stars close enough that their black holes would affect us. (The supernova itself could affect us, however, by raining down high energy radiation on the Earth.)

However, if you want to worry about black holes, consider the chance encounter with a wandering black hole, one moving through the galaxy relative to the rotating plane of the disk in which we live. While the likelihood of this is small, it is at least conceivable. In fairness, it wouldn't have to be a close encounter with a black hole. Any star would do to cause possibly catastrophic problems with the Earth's orbit or the orbit of other planets (catastrophic as far as our personal existence goes at least). Pleasant dreams.

### Question:

Is it possible that there is a black hole in our Galaxy?

It is almost certain that there are black holes in binary systems in our galaxy. Another question is whether or not there is a really big black hole in the center of our galaxy. In recent years the answer has emerged: yes! Direct observations of the center of the Galaxy have been able to follow the orbits of massive stars over a number of years. Using Kepler's laws we can calculate the mass of the thing that they are orbiting and it comes out to about 3 million solar masses. Thus, although we don't directly observe the black hole, we see the effects of its gravitational field.

### Question:

Do stars always collapse to a point. Could a spinning star collapse to a ring? Under such circumstance, would the black hole have infinite curvature if approached horizontally, but finite curvature if approached vertically?

The singularity in a Kerr hole forms as a ring, strangely enough. Toroidal, prolate, oblate, etc. event horizons can form, but black hole horizons always radiate away gravitational waves until they settle down into spherical symmetry.

### Question:

Are there any new developments that you know of regarding the LIGO gravity wave detector. Has it become operational yet? If not - is there some kind of expected date for when it will begin to yield some results?

Construction is complete at both the Hanford Site and the Livingston site. Test data runs have been carried out. You can follow the developments through the LIGO home page, Interesting pictures from each site are available in the on-line LIGO newsletters.

### Question:

Once a black hole has formed will it ever go away or will it just keep getting larger?

A black hole can shrink by Hawking radiation (see chapter 9) but this effect is extremely small for normal sized black holes; at the present time in the universe black holes only grow in size.

### Question:

What would happen if a massive star underwent a supernova while aside a smaller Kerr hole? Would a good portion of the exploded star enter the hole? Would the spin of the hole be affected?

These are questions astrophysicists would like to know the answers to in some detail. The exploding star must interact with the black hole, at least by losing some of its ejected matter down the hole. The hole would grow in mass. The transfer of gas with a relative rotation (angular momentum) to the hole could also affect its rotation, since angular momentum is one of the fundamental properties of the hole. Possibly the binary system would be disrupted in the explosion, though it might also hold together. Systems such as the binary pulsar system had to form somehow. How many such systems might there be in our galaxy?

### Question:

What happens to stuff that is drawn into black holes?

It is crushed into the singularity at the center and its mass-energy goes into the gravitational field of the black hole.

### Question:

Since no one knows the properties of a singularity, could there be a white hole on the other side emptying into another universe and it just so happens that our universe is on the side with all the black holes?

It has been speculated that there could be other universes on the "other side" of singularities. However, there really isn't any support for this based on what we do know about singularities. But since GR must break down into some quantum gravity that we don't yet understand, there remains room for speculation.

### Question:

What changes to physical properties occur near a black hole?

As we have seen with the study of General Relativity, time dilation and length contraction (and related effects) occur due to gravitational fields. Time and space are altered by gravity. The gravitational field near a black hole is particularly strong, so these relativistic effects become quite large.

### Question:

Since light can't escape from a black hole doesn't this imply a force that moves faster than the speed of light?

Presumably you mean that gravity itself seems to be escaping from the hole. But a better way to think about it is that the gravity is left behind when the hole forms, and no message could get out to tell gravity that the mass has disappeared behind an event horizon!

### Question:

If gravity propagates by means of messenger particles (gravitons) how do black holes have gravity? Shouldn't the gravitons be unable to escape?

The gravitational field of a black hole is left behind in the collapse of the star into a black hole. The field itself generates gravity, i.e. gravitons. Gravity equals energy equals mass. A black hole is a self-generating gravitational field.

### Question:

What is meant by "our gravity is mostly due to curvature in time"?

Your freefall trajectory in a gravitational field is determined by the metric (e.g. Schwarzschild, eqn. 9.2). Because your velocity is generally much less than light the (c dt)2 interval is much larger than the (dx)2 interval. Hence the metric coefficient multiplying the time factor causes this term to have much more of an effect on determining your worldline's trajectory through spacetime than does the spatial term.

### Question:

Wouldn't a black hole pull all the matter immediately around it into it, allowing other matter to move into the region vacated? Would this process eventually lead to the black hole pulling all matter in?

Black holes pull matter in the same manner as other gravitating bodies, and indeed they eventually clear out their immediate region. Other matter can move into that vacated region only if diverted (by some force) onto trajectories leading into the hole's vicinity. This "refilling" process will be very slow. However, if the universe goes on forever, then black holes will most likely eventually consume everything.

### Question:

How does quantum mechanics come into play in black holes?

Quantum mechanics must come into play directly near the singularity in the center of the black hole. Quantum mechanics is also involved in the process of Hawking radiation at the horizon of the hole. Note that Hawking radiation is quantum mechanical process taking place in the background gravitational field of the black hole which can still be regarded as determined by Einstein's equations. Near the singularity quantum gravity determines the gravitational field directly.

### Question:

Do virtual particles becoming real violate the principle that no new mass can be created?

Yes, but the principle of mass conservation is not strictly valid, and has to be replaced by the principle of mass-energy conservation. Mass and energy are equivalent by Einstein's famous formula. You can create mass if you have sufficient energy; when virtual particles become real it means that they obtained the energy to become real, so mass-energy is conserved. In Hawking radiation the necessary energy comes from the gravitational field itself.

### Question:

Will we ever know what goes on inside the horizon of a black hole?

We can't sample the conditions directly, but we can apply physical theory to the problem. If we believe that the theory is sound, and completely supported by observations that we can make, then we can use the process of deduction to learn about things that we cannot directly observe.

### Question:

If a white hole existed would its light output be infinite?

Who knows? That's one of the problems with white holes as postulated. There doesn't seem to be any constraint on what they could be producing.

### Question:

If we were to encounter a black hole could we travel back in time?

Inside the horizon you could travel backward along the coordinate direction labeled "time" by a distant observer. You couldn't travel into that distant observer's past, however. If you are outside the hole's horizon you could use gravitational time dilation to travel forward in time relative to the distant observer, but not backward.

### Question:

What could possibly happen to cause our sun or the Earth to become a black hole?

They would have to be compressed down to the size of their respective Schwarzschild radii. You would need to implode them inward, which, presumably you could do with a focused beam of energy (including gravity waves). However the total energy required would probably exceed the rest mass energy of the Earth or Sun (I haven't calculated it). Or you could just pile more mass onto them until their total mass exceeds that which can be held up by any available force. But that is sort of a cheat since the original mass of the Earth or sun would be negligible in the resulting black hole.

### Question:

What is the difference between "Schwarzschild radius" and the "event horizon"?

They are equivalent for a nonrotating black hole. Event horizon is a more general term and refers to a lightlike (null) surface in spacetime constituting a boundary between what can be observed and what can't.

### Question:

Because the black hole temperature is much cooler than the average temperature of the universe how can it be evaporating?

It wouldn't be at the present moment. Space is much warmer than the temperature of a solar mass black hole. (Smaller black holes could in principle be warmer than the 3K of space.) If the universe is open, at some remote future date space will be colder than the black holes and then they will begin to decay. This will occur at unfathomably remote times in the future. But all things come to those who wait.

### Question:

Since black holes' gravity is so great why doesn't it effect the gravity of the universe? If there are many black holes in space should they draw in most of the matter-energy of the universe? Once matter and energy enter the hole they are, in effect, gone. Does that mean matter and energy are not conserved?

If there were a lot of black holes their total mass would affect the overall gravity of the universe, but this is no different from any other object in the cosmos. If the universe lives long enough it is likely that most of the matter will end up in one black hole or another.

The matter and energy are left behind in the gravitational field of the black hole.

### Question:

If quasars are powered by massive black holes, how can we determine the degree to which their spectral lines are gravitationally redshifted versus cosmological redshift?

All redshifts are equivalent in their effect, that is, all you can measure from a given line is its wavelength and hence its shift. You can't tell just from that what is cosmological, what is doppler, and what is due to gravity. However, to get a large redshift from gravity you need to be right up next to the event horizon when the light is emitted. Also you would expect light to be emitted from a continuum of radii around the black hole resulting in not one unique redshift but a smeared spectral line.

### Question:

What limit is exceeded when two neutron stars combine and form a black hole?

The limit is the amount of mass that neutron degeneracy pressure can hold up against gravitational collapse. That value is somewhere between maybe 2 to 3 solar masses.

### Question:

If black holes could connect different parts of the universe what would that say about the shape of the universe? Should we consider more than three dimensions in conceptualizing this (and how would one do so??)?

If wormholes connected different parts of the universe it would be difficult to say much about the overall geometry of the universe. (How many wormholes are there? How do they connect things up?) Wormholes might well make time travel possible, which would create a big problem for causality and were certainly violate the cosmological principle.

Conceptualizing such a complex 3 dimensional space geometry is difficult. Conceptualizing higher dimensional spaces is very difficult except abstractly in terms of the mathematics that describes such spaces. One usually thinks about 2 dimensional surfaces curved in the third dimension, although even that is somewhat difficult and may not be adequate for the most complex set of wormholes one might imagine.

### Question:

How do black holes trap photons if photons have no mass? Or: If gravity operates between masses and light is a massless particle, how can a black hole keep light from escaping?

Light has energy, and it falls in a gravitational field (Equivalence principle). Gravity operates even on particles like the photon that have zero rest mass.

### Question:

How exactly do black holes act as power sources for binaries and galaxies? Don't these stars get their power by hydrogen burning in their cores?

The Stars do. The power that radiates from near a black hole comes from a different process. Material orbiting near a black hole is accelerated by the strong gravity to velocities near the speed of light. Mass moving near the speed of light has a lot of energy. If that gas becomes turbulent it will dissipate the energy of motion into heat, and the temperatures associated with that heat will be very high, causing the gas to radiate high energy photons.

### Question:

If the sun collapsed into a black hole would life on Earth survive? Would the sun still give off enough heat to warm the planet?

If the sun collapsed to a black hole it would not be radiating any light (and heat is a form of light). So no, life on Earth would not survive.

### Question:

If nothing can get in a white hole, and things can only come out, where does the stuff coming out of a white hole come from?

From the singularity at the center of the white hole. But this is one of the reasons why we don't think white holes exist.

### Question:

At the singularity of a black hole, time and space abruptly end. Do objects that enter the singularity simply cease to exist?

As far as we know from classical general relativity. If your world line comes to an end you cease to exist.

### Question:

Why is it impossible for wormholes to occur? And why did the idea of wormholes come about in the first place?

Wormholes represent a complete Schwarzschild type solution to Einstein's equations. They are permitted by the equations, but there do not seem to be any ways in which they could form (whereas a black hole alone can form from the collapse of a massive stellar core).

### Question:

How long is it going to take for the sun to become a black hole?

The Sun is never going to become a black hole on its own. However, the white dwarf that the Sun ends up as may one day in the incredibly vast distant future fall into a black hole.

### Question:

Could it be possible to create a mini black hole that would have the size of about an atom?

I don't know if it would be possible or not to create such a thing, but a mini black hole with the size of an atom could exist. You would just have to have the right amount of mass compressed down to the desired Schwarzschild radius.

### Question:

The centers of galaxies are hypothesized to contain supermassive black holes. Why then are those centers so bright?

The radiation is coming from matter falling into and orbiting around the supermassive black hole, not from the black hole itself.

### Question:

Is it possible that a wormhole could connect a black hole of one universe to a white hole of another universe?

It is possible in the sense that one can imagine such a thing and nobody has been able to show that the laws of GR absolutely forbid such a thing.

### Question:

What did Kip Thorne say about the possibilities of wormholes, and what were his reasons behind his theory?

Please read his book, Einsteins Outrageous Legacy. It is highly readable and makes an excellent follow on for people interested in learning more about GR, black holes and wormholes.

### Question:

When you say that Hawking radiation is blackbody radiation, what does that mean and why is that unique?

Blackbody radiation is the type of radiation emitted by matter in a state of statistical thermal equilibrium. It means that even though the black hole is naught but a great gravitational field, it acts as if it were a big chunk of matter at some very very low temperature radiating photons out into space. Isn't that strange.

### Question:

Of all the probable black holes that have been detected which is the most massive?

Black holes in the centers of galaxies are the most massive. In some galaxies, hole masses in the billions of solar masses have been inferred. Motions of the stars in the core of the Andromeda galaxy suggest it contains a black hole of 10 million solar masses.

### Question:

Are there any known black holes that are reasonably nearby? Would we be able to see them?

There are some black hole binary systems in the Milky Way. One example is Cygnus X-1 which is located about 8000 lightyears away. We can't "see" the black holes in the sense that you might be thinking, but we can see the stars that are their companions, and we can see the gas falling into the black hole.

### Question:

If you were in a black hole accretion disk would your body be flattened along with the spinning gas?

Your body could be flattened if the tidal forces were strong enough, and they could be depending on the mass of the hole and your location relative to the horizon.

### Question:

If black holes keep accreting mass why don't they become stronger and eventually suck in galaxies and the whole universe?

In principle, given enough time almost everything would end up in black holes. Because the universe is expanding, however, not all black holes would end up merged into one black hole. Unless the universe turns out to be the big crunch type.

### Question:

What are vacuum fluctuations?

In quantum mechanics it is impossible to know the energy of a system perfectly at some moment in time. This includes the vacuum. The energy in the vacuum isn't perfectly zero for all time, but fluctuates around zero in the short amounts of time required by the Heisenberg Uncertainty principle of quantum mechanics.

### Question:

Is it possible that the virtual particles in Hawking radiation are actually arriving from another universe?

Not likely. They are arriving from this universe. However, they don't carry any information anyway (except the temperature of the blackbody, hence the mass of the hole that created them), so even if they were "coming from another universe" it wouldn't mean anything.

### Question:

How can it be that white holes are theoretically possible yet don't exist in the universe?

It is an interesting question: if a theory of physics (such as GR) permits something does that thing have to occur in the universe? If it doesn't occur in the universe does the presence of something so permitted mean that the theory is incorrect in allowing that thing?