# Laws of black hole thermodynamics in semiclassical gravity

## TL;DR

This paper demonstrates that the fundamental laws of black hole thermodynamics naturally arise in semiclassical gravity, linking black hole entropy to quantum information and extending thermodynamic principles to dynamic spacetimes.

## Contribution

It establishes the first and second laws of black hole thermodynamics within a semiclassical gravity framework, including for non-stationary spacetimes, and relates entropy to quantum field von Neumann entropy.

## Key findings

- First law verified for stationary spacetimes
- Second law established for piecewise stationary spacetimes
- Black hole entropy linked to quantum information behind the horizon

## Abstract

The first and second laws of black hole thermodynamics are verified to emerge from a generic semiclassical theory of gravity for which a Hamiltonian can be defined. The first law is established for stationary spacetimes, and the second law is established in the here defined "piecewise stationary" spacetimes. Black hole entropy is defined in the Noether charge approach, and the entropy for the matter in its exterior is the von Neumann entropy of the quantum fields. These results strongly support the view of black hole entropy as an account of the information that is hidden behind the horizon.