Undergrad Does Acceleration Affect Event Horizon Location?

[awardr]

TL;DR

Normal acceleration is equivalent to a uniform gravitational field throughout all of space. Thus, this extra field would shift an event horizon for an accelerating observer vs a non-accelerating observer

Normal acceleration is equivalent to a uniform gravitational field throughout all of space. Thus, if I am normally accelerating, I should observe an event horizon shifted as compared to a non-accelerating observer. Is this correct?

 

[Dale]

You are describing the Rindler horizon. This is not a true event horizon. Actual event horizons are global features of the manifold and do not depend on the observer.

 

[Ibix]

As Dale notes, an eternally accelerating observer in flat spacetime has an event horizon, the Rindler horizon, associated with them. It's different from a black hole event horizon in that it only has meaning for the accelerating observer, and if they ever stop accelerating there was never a horizon anyway.

I have not done any maths to support this, but I would expect a Rindler horizon to exist (at least in some circumstances) for an eternally accelerating observer in curved spacetime. If a black hole "passed through" the Rindler horizon then there would effectively be a single horizon that was some sort of union of the two surfaces, at least as far as the accelerating observer was concerned.

Of course, if the observer ever stops accelerating then there was never a Rindler horizon and the black hole's horizon is the only one present. So i think the answer is "no" in practice and "kind of" in an idealised eternal case.

 

[PeterDonis]

if I am normally accelerating, I should observe an event horizon shifted as compared to a non-accelerating observer. Is this correct?

No. There will be a horizon associated with you, but it is not an event horizon. See below.

As Dale notes, an eternally accelerating observer in flat spacetime has an event horizon, the Rindler horizon, associated with them.

No, as @Dale specifically noted, the Rindler horizon is not an event horizon. In more technical language, it is not the boundary of a region that cannot send light signals to infinity.

The event horizon of a black hole is the boundary of such a region. And since whether or not light signals can reach infinity from a given event is an observer-independent invariant, the event horizon of a black hole, unlike a Rindler horizon, is the same for all observers.

The Rindler horizon, by contrast, is only the boundary of a region of spacetime that cannot send light signals that will reach that particular accelerating observer, while they continue to accelerate. That obviously makes the presence of a Rindler horizon dependent on the particular observer, and whether or not they are accelerating.

I would expect a Rindler horizon to exist (at least in some circumstances) for an eternally accelerating observer in curved spacetime

As long as no other horizon intervenes, yes. See below.

If a black hole "passed through" the Rindler horizon then there would effectively be a single horizon that was some sort of union of the two surfaces

Sort of, at least for that particular observer. There would be the black hole horizon, which is a globally invariant surface, and there would be the Rindler horizon, which is specific to that particular observer while they are accelerating. If there is a portion of the Rindler horizon that goes below the black hole horizon, then the region of spacetime "in between" (below the black hole horizon but above the Rindler horizon) still can't send light signals to the observer, so it is still behind the observer's horizon; but that will remain true even if the observer stops accelerating, because even though stopping the acceleration makes the Rindler horizon go away, it doesn't make the black hole horizon go away.