Black Holes

[petrushkagoogol]

Can a black hole absorb another black hole ?

[A-wal]

According to standard theory their masses combine.

 

In reality, I don't think it's at all possible for their event horizons to ever reach each other due to time dilation an length contraction approaching infinity as the horizons are approached. The black holes will die before they can touch because it would take an infinite amount of proper time for an event horizon to be reached by anything, including another event horizon.

 

This is exactly what the Schwarzschild coordinate system (and indirectly, the Rindler coordinate system) shows and switching to a coordinate system that shows that they can reach each other in a finite amount of proper time is a direct contradiction.

[A-wal]

According to standard theory their masses combine.

Although presumably some of the overall mass will be lost due to release of gravitational waves, although maybe not. A gravitational wave is a change in the strength of gravity that propagates at the speed of light so I don't know if it can be thought of as an energy wave in its own right. I don't think it makes sense for the loss of mass to be thought of escaping as the energy of the gravitational wave if the wave itself is caused by a loss of mass/energy from the system. Hmm, maybe. Seems like circular reasoning though.

[CraigD]

Can a black hole absorb another black hole ?

Unless practically every astronomer and astrophysicist in the field is very wrong about everything on the scale of galaxies, not only can a black hole swallow another one, but this is a common event. Every galaxy is believed to contain a supermassive black hole of at least 100,000 solar masses, but the biggest black hole that can form from a collapsed star is about 100 SM, while the biggest that can form from weird, ancient quasi-star gas clouds is 30 to 1000 SM. Since there’s no known way a 100,000+ SM black hole could form from a single collapse event, they must be formed by intermediate-mass BHs swallowing other stellar-mass objects, some of which must be black holes.

 

In reality, I don't think it's at all possible for their event horizons to ever reach each other due to time dilation an length contraction approaching infinity as the horizons are approached. The black holes will die before they can touch because it would take an infinite amount of proper time for an event horizon to be reached by anything, including another event horizon.

For years, I felt there was some profound paradox around the evidence that black holes must combine, and GR’s prediction that the ratio [math]\frac{t_0}{t_f}[/math], of the proper time [math]t_0[/math] of a “slow observer” approaching an event horizons and [math]t_f[/math] of something at a distant point, approaches zero. So, my paradox reasoning went, from the point of view of [math]t_0[/math], and infinite amount of time would be needed to reach the event horizon, before which, as A-wal put it, the black hole will die.

 

The resolution of this false paradox is that GR predicts not only time dilation, something akin to “gravitational length contraction” happens. So as [math]\frac{t_0}{t_f}[/math] approaches 0, the radial distance measured by the slow observer approaches zero, the two effects canceling one another so that, while their t₀ and t_f don’t agree with one another, they agree on when the slow observer reaches the event horizon. Alas, I must rely on experts for the details of this, since my physics education didn’t teach me enough to actually do the formal math on the subject :(

 

I blame some of my confusion on Fred Pohl’s 1977/78 Hugo and Nebula awards winning novel Gateway. Gateway and its sequils tell an engaging story and are full of ahead-of-their-time ideas, but they take major liberties with physics. In 1978, in my late teens, I often had a hard time keeping science fiction and science separate. One of the major plot devices in Gateway involves the rescue of main character Robinette Broadhead’s crewmates from an impending crash into a black hole. While the novel rightly has Broadhead aging years while his crewmates age only days, it wrongly has Broadhead realizing that he has practically an infinite amount of time to mount his crewmates’ rescue.

 

Although presumably some of the overall mass will be lost due to release of gravitational waves, although maybe not.

The scientific consensus, which went back and forth for a few decades on the question, settled on “yes, gravitational waves are actual, radiation that can do physical work” vs. “gravitational waves are just moving changes in length of space that can’t”.

 

The most direct evidence of this is from observations of the orbit of unusually dense bodies, like the neutron stars of a pulsar. The period of their orbits increase, showing that the system is losing energy and the orbits spiraling inward. In principle, if you could collect the energy from the gravity waves the system is emitting, it would be exactly enough to restore the system to its original orbit. This discovery in 1974 won Hulse and Taylor the Nobel prize in 1993.

[A-wal]

For years, I felt there was some profound paradox around the evidence that black holes must combine, and GR’s prediction that the ratio [math]\frac{t_0}{t_f}[/math], of the proper time [math]t_0[/math] of a “slow observer” approaching an event horizons and [math]t_f[/math] of something at a distant point, approaches zero. So, my paradox reasoning went, from the point of view of [math]t_0[/math], and infinite amount of time would be needed to reach the event horizon, before which, as A-wal put it, the black hole will die.

 

The resolution of this false paradox is that GR predicts not only time dilation, something akin to “gravitational length contraction” happens. So as [math]\frac{t_0}{t_f}[/math] approaches 0, the radial distance measured by the slow observer approaches zero, the two effects canceling one another so that, while their t₀ and t_f don’t agree with one another, they agree on when the slow observer reaches the event horizon. Alas, I must rely on experts for the details of this, since my physics education didn’t teach me enough to actually do the formal math on the subject :(

 

I blame some of my confusion on Fred Pohl’s 1977/78 Hugo and Nebula awards winning novel Gateway. Gateway and its sequils tell an engaging story and are full of ahead-of-their-time ideas, but they take major liberties with physics. In 1978, in my late teens, I often had a hard time keeping science fiction and science separate. One of the major plot devices in Gateway involves the rescue of main character Robinette Broadhead’s crewmates from an impending crash into a black hole. While the novel rightly has Broadhead aging years while his crewmates age only days, it wrongly has Broadhead realizing that he has practically an infinite amount of time to mount his crewmates’ rescue.

It's not a false paradox and that in no way resolves it.

 

Look at it like this:

 

An object falling towards a black hole will never reach the event horizon from the perspective of any external observer. This is not merely some kind of illusion, the falling object is always be able to escape the black hole from the perspective of the external observer, a finite amount of energy will always be enough because it hasn't (and never will) cross the event horizon.

 

Now, the black hole shrinks over time. If it were possible for a falling object to cross the event horizon from their own perspective then the black hole would be a certain size when it crosses and from that point on it would be impossible for them to escape. That would mean it would be impossible for them to escape from the perspective of the distant observer after the black hole has shrunk to a certain size, although a different size because of length contraction, but an equivalent size once that's been taken into account. That's not what happens. It's always possible for the falling object to escape from the perspective of the distant object, if they had a strong enough rope, they could pull them out.

 

At no time in the black hole's life is it ever possible for an object to reach it's event horizon. Of course there's gravitational length contraction as well as time dilation but they don't cancel each other out, just the opposite. Length contraction decreases the distance between the event horizon and the singularity as an object falls towards it, in the same way that time dilation increases the rate the black hole loses mass from the perspective of the falling object, again making the event horizon recede away from them. If they were able to reach the singularity/event horizon then length contraction and time dilation would reach infinity and the black hole would have no volume in space or time. The black hole is a singularity, that's all it is. It only looks like it has length in time and space from a distance.