  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.

General Relativity and Quantum Cosmology