The Entropy of Dynamical Black Holes

Understand

We propose a new formula for the entropy of a dynamical black hole$-$valid to leading order for perturbations off of a stationary black hole background$-$in an arbitrary classical diffeomorphism covariant Lagrangian theory of gravity in $n$ dimensions.

• In stationary eras, this formula agrees with the usual Noether charge formula, but in nonstationary eras, we obtain a nontrivial correction term.
• In general relativity, our formula for the entropy of a dynamical black hole is $1/4$ of the horizon area plus a term involving the integral of the expansion of the null generators of the horizon, which we show is $1/4$ of the area of the apparent horizon to leading order.
• Our formula for entropy in a general theory of gravity obeys a "local physical process version" of the first law of black hole thermodynamics.