nLab event horizon

Idea

Fix a timelike curve $\gamma$ in spacetime, thought of as representing an observer. If $H$ is a hypersurface in spacetime, then (at least if spacetime is orientable and possibly otherwise), $H$ separates spacetime into two regions, arbitrarily called the inside and outside. Then $H$ is an event horizon (relative to $\gamma$) if $\gamma$ never intersects the future of the inside of $H$. (It follows that $\gamma$ lies entirely outside $H$.)

Although we have given this definition relative to an observer, we can reverse the situation, beginning with a lightlike hypersurface $H$ and noting that $H$ is a horizon relative to every observer that remains in the past of $H$ (of which, unlike for a spacelike hypersurface, there are typically many). This includes the horizon around a black hole and the future light cone of any event.

Theoretically, the observer outside an event horizon will observe Bekenstein-Hawking entropy at the horizon and Hawking radiation from it. In the case of an observer accelerating to remain outside a future light cone, this is the Unruh effect?.

Related concepts

• Cauchy horizon

• naked singularity

• observable universe

• generalized second law of thermodynamics

• near-horizon geometry

References

Resolved image of the direct vicinity of the event horizon of the black hole in the center of the galaxy Messier 87:

• Event Horizon Telescope Collaboration, First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole, The Astrophysical Journal Letters, Volume 875, Number 1, 2019 (doi:10.3847/2041-8213/ab0ec7)

Discussion of event horizons of black holes in terms of AdS/CFT is in

• Kyriakos Papadodimas, Suvrat Raju, An Infalling Observer in AdS/CFT (arXiv:1211.6767)