# What is Expanding Horizon of a black hole?

## Main Question or Discussion Point

What is Expanding Horizon of a black hole?

Recently, I want to read something general on Expanding Horizon...

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PAllen
2019 Award
See sections 5.1.7, 5.1.8, and 5.4.1 from Poisson's notes,

http://www.physics.uoguelph.ca/poisson/research/agr.pdf,

which evolved into the excellent book, A Relativist's Toolkit: The Mathematics of black hole Mechanics.
Thanks George! Really cool link! I never thought about this before, but after reading the details, the most surprising conclusion seems 'obvious' in hindsight. That is, the causal boundary now must be affected by the indefinite future of the black hole. I propose the following simple conceptual argument:

Imagine at some future time, a small chunk of matter will fall into the black hole. However small, and however far in the future, there is some point sufficiently close the apparent horizon that whether its outgoing light ever makes it to the 'distance' depends on that matter falling in, in the future.

Imagine at some future time, a small chunk of matter will fall into the black hole. However small, and however far in the future, there is some point sufficiently close the apparent horizon that whether its outgoing light ever makes it to the 'distance' depends on that matter falling in, in the future.
Hi PAllen,

I was hoping to catch you while you were still online so I have not had time to read the linked material posted by George. Could you elaborate a bit more on the above quoted text and what exactly you mean by the "distance"?

PAllen
2019 Award
Hi PAllen,

I was hoping to catch you while you were still online so I have not had time to read the linked material posted by George. Could you elaborate a bit more on the above quoted text and what exactly you mean by the "distance"?
Normally, light gets to null infinity (in asymptotically flat spacetime). For events within a BH event horizon, they don't. I was just describing this in a non-technical way as 'getting to distant observers'.

And my argument is simply that for some event whose light is 'almost trapped' by the current curvature, whether it ultimately gets to null infinity or not depends on the future infall of matter. No matter how small or far in the future such an infall is, there is, in principle, some event now whose light's failure to escape depends on that infall.

Think, simplistically, of a light ray 'almost orbiting' the black hole, that would take a thousand years (distant observer time) to escape. If, instead, matter falls in after 999 years, the light fails to escape because of the increased mass of the BH. Thus the true causal boundary now is affected by the the arbitrarily distant future of the BH.

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thanks...