Relativistic black hole
Robert Lukassen
This is bothering me for a while now. I hope someone can shed some light on
this.
Suppose one observer is at rest w.r.t. a certain (heavy) body. This observer
will observe
a normal (heavy) body, with no abnormalities. Now consider an observer which
is travelling
with a great velocity w.r.t. this body (and the other observer). This moving
observer will
see this body moving at great velocity, and according to what I understand,
will also observe
the mass of the body being greater than the mass of the body at rest.
I wonder what happens when the relative velocity between body and moving
observer is very close to the speed of light (in vacuum). Then the observed
mass of the body will appear to increase without limit. The size of the body
will appear to decrease as well (but only in the direction of motion). At
some point, the mass of the moving body will cross a limit, and
an event-horizon will form (as observed from the moving observer). The body
will appear
to be a black hole.
Is this possible? Or am I missing something fundamental here (something like
relativistic mass having no gravitational effect).
Regards, and appreciating any help,
Robert Lukassen
Steve Carlip
> Suppose one observer is at rest w.r.t. a certain (heavy) body.
> This observer will observe a normal (heavy) body, with no
> abnormalities. Now consider an observer which is travelling
> with a great velocity w.r.t. this body (and the other observer).
> [...] At some point, the mass of the moving body will cross
> a limit, and an event-horizon will form (as observed from
> the moving observer). The body will appear to be a black
> hole.
> Is this possible?
This is a FAQ. See
http://www.math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_fast.html
(``If you go too fast do you become a black hole?'')
The short answer is that the gravitational field in general
relativity is not determined by mass alone (neither rest mass
nor ``relativistic'' mass), but by the stress-energy tensor,
which depends on mass, energy, velocity, and a variety of
other things. The GR field equations are covariant, and in
particular Lorentz invariant; a black hole in one frame is
a black hole in any frame. In your example, the gravitational
field seen by the moving observer is not the same as that
seen by a stationary observer---just as the electric and
magnetic fields of a charge are not the same as seen by a
moving observer as they are as seen by a stationary observer
---but the change cannot be described as anything as simple
as an increased gravitational mass, and no observer sees an
event horizon.
Steve Carlip