- #1
- 117
- 6
Main Question or Discussion Point
Suppose a black hole travels at something like v = 0.999999999c relative to some observer. Does the black hole's event horizon becomes length contracted, thus appearing to turn into a black disk?
But this reasoning doesn't apply to a black hole's horizon, because there's no way to measure the diameter; it doesn't have one.That would be the same as asking what the geometry of the event horizon would be from the POV of an observer travelling relativistically wrt it.
Note: an observer stationary wrt a large sphere would see the sphere as a disk.
Observe: Sun, Moon, Planets, near starts etc: all look like disks.
Measure the diameter, in different directions re travel direction, as you pass one at speed, and they look like ellipses.
Very fast and you get a thin ellipse.
What doesn't look black in these scenarios isn't the hole's horizon; it's stuff falling into the hole but still outside the horizon, which can radiate intensely as it falls in. The horizon itself can't be seen, since outgoing light at the horizon stays at the horizon forever, never escaping.artistic interpretations aside, BHs are unlikely to look black.
In classical GR, a black hole is quite literally space-time geometry with an event horizon generated by null curves. It isn't a time-like object i.e. the concept of length contraction doesn't apply. That being said there are a myriad of optical effects that can occur due to black holes so that might be of interest to you.Suppose a black hole travels at something like v = 0.999999999c relative to some observer. Does the black hole's event horizon becomes length contracted, thus appearing to turn into a black disk?
Relativistic mass is not the source of gravity in GR. The mass of the black hole, as far as its gravity is concerned, is an invariant. The motion of a test object relative to the black hole does affect how the hole's gravity curves its trajectory, but there's no useful way to view that as an effect of "relativistic mass increase" of the black hole.I was more interested in the ramifications for the gravity of the black hole combined with the relativistic mass increase of the black hole as it approaches c
An object falling into a black hole doesn't experience "imaginary time"; it experiences perfectly normal time flow. The "imaginary time" you are thinking of is not something physical; it's an artifact of choosing particular coordinates.What effect would this have on the imaginary time which would be experienced by an object falling into a black hole itself moving at relativistic speed?
But how does the Schwarzschild geometry outside the horizon look like in a frame where the BH is moving fast? Or, alternatively the Schwarzschild geometry of an massive star, that isn't a BH yet. Is it similar to a contracted version of the usual Schwarzschild geometry?But this reasoning doesn't apply to a black hole's horizon, because there's no way to measure the diameter; it doesn't have one.
Read the OP more carefully:The black hole is approaching a speed of c in relation to what?
I'm confused here. Its true that an EH is a null surface but that applies to non-moving BHs as well. So it seems to me its not related to the state of the motion of the BH.But the "world tube" of the event horizon is composed of null curves, not timelike curves
Something vaguely like that happens - as the black hole approaches "c", the space-time geometry approaches a plane wave solution called the Aichelberg-sexl ultraboost. See https://en.wikipedia.org/wiki/Aichelburg–Sexl_ultraboost Which is basically disc-like, in that it's basically a plane wave. It's definitely not spherically symmetrical.Suppose a black hole travels at something like v = 0.999999999c relative to some observer. Does the black hole's event horizon becomes length contracted, thus appearing to turn into a black disk?
It's the center of mass of the black hole, relative to some asymptotic Lorentz frame, that moves at subluminal speeds; the center of mass is simply the conserved charge associated with boosts so it is easily defined in terms of the ADM 4-momentum. The worldtube of the event horizon is still generated by a null congruence.So it seems to me the worldtube of the EH can't be composed of null curves.
There is no unique choice of space-like section so geometric quantities defined in this way would not be intrinsic to the black hole but instead would have some gauge freedom. Now this is all fine if all we're concerned with is geometric properties of the event horizon relative to some family of observers. However in general such space-like sections would not correspond to simultaneity surfaces of any family of observers so it isn't clear how one would measure geometric quantities calculated from them.This would imply that the cross section area will be the same (for a stationary black hole) for all observers. So it seems natural to ask about geometric properties other than area as well.
I think its a thought experiment. I cant imagine how a solar mass size object could be accelerated to such speeds.Would we find black holes moving near the speed of light in nature? Orbiting very close together or blasted out of a violent galactic nucleous? Or is it just a thought experiment?
Depends what you mean. From the perspective of a black hole, it's a cinch that there are particles passing it at very high fractions of c. From the point of view of the particles, it's the black hole that is moving at high speed, and the point of relativity is that either perspective is valid. So in that sense, yes, there are billions upon billions of particles encountering black holes moving at substantial fractions of c all the time. However, I tend to agree with Drakkith that we're unlikely to be able to see this directly ourselves.Would we find black holes moving near the speed of light in nature? Orbiting very close together or blasted out of a violent galactic nucleous? Or is it just a thought experiment?
I see. I don't see any reason black holes wouldn't have the same thing happen under similar circumstances. I guess I've just never read about relativistic stars.Thank you for clarifying about the the two perscpectives. BTW I just found dozens of serious articles about stars moving at near the speed of light. They have not yet been observed because they a far away and faint but astronomers believe that when two supermassive black holes collide, as will happen with the Milkyway and Andromeda, as they get locked in the proverbial death dance some stars will be hurled out at relativistic speeds. And if stars get accelerated that way then why not black holes?
Agreed. However, an object being ejected at relativistic speeds must be rare, since it's effectively a case of it winning big in a once-in-a-stellar-lifetime energy lottery, and black holes are rarer than stars. I'd tend to think that black holes moving at relativistic speed with respect to other stellar-mass stuff near them are extremely rare, at best.I see. I don't see any reason black holes wouldn't have the same thing happen under similar circumstances. I guess I've just never read about relativistic stars.
That was my exact thinking.Agreed. However, an object being ejected at relativistic speeds must be rare, since it's effectively a case of it winning big in a once-in-a-stellar-lifetime energy lottery, and black holes are rarer than stars. I'd tend to think that black holes moving at relativistic speed with respect to other stellar-mass stuff near them are extremely rare, at best.