Schwarzschild radius question.

[Katamari]

An object is accelerated close to c. Does the relativistic mass contribute to the sch. radius as seen by an observer? Is it simultaneously a black hole and not a black hole?

 

[Mentz114]

Suppose something is traveling at close to c as measured by some observer. As long as the relative velocity is constant, there will be a causal connection between them. That means light signals can pass between them.

However if one observer accelerates away from another, with constant (local) acceleration, eventually they will lose causal contact. See the 'Rindler Horizon'.

But no black holes will form from any observers point of view.

 

[Katamari]

Thanks.

 

[Bill_K]

There is an exact solution of Einstein's equations known as the C-metric which represents the gravitational field of a uniformly accelerating black hole. It contains both a Scwharzschild horizon and a Rindler horizon.