# nLab event horizon

### Context

#### Gravity

gravity, supergravity

# Contents

## 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?.

## References

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