Schwarzschild radius question.

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Discussion Overview

The discussion centers on the concept of the Schwarzschild radius in relation to relativistic mass and the implications of acceleration near the speed of light. It explores theoretical aspects of black holes, causal connections between observers, and specific solutions to Einstein's equations.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions whether the relativistic mass of an object accelerated close to the speed of light contributes to the Schwarzschild radius as perceived by an observer, suggesting a paradoxical state of being both a black hole and not a black hole.
  • Another participant discusses the implications of constant relative velocity and causal connections between observers, noting that if one observer accelerates away, they may lose causal contact, referencing the concept of the Rindler Horizon.
  • A later reply introduces the C-metric as an exact solution to Einstein's equations, which describes the gravitational field of a uniformly accelerating black hole, highlighting the presence of both a Schwarzschild horizon and a Rindler horizon.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between relativistic effects and black hole formation, with no consensus reached on the implications of acceleration and the nature of horizons.

Contextual Notes

The discussion involves complex theoretical constructs and assumptions about relativistic physics and gravitational fields, which may not be fully resolved within the thread.

Katamari
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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?
 
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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.
 
Thanks.
 
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.
 

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