The first law and Wald entropy formula of heterotic stringy black holes at first order in alpha prime

TL;DR

This paper derives a gauge- and Lorentz-invariant entropy formula for heterotic stringy black holes at first order in alpha prime, enabling precise macroscopic entropy calculations for comparison with microscopic results.

Contribution

It provides the first explicit, invariant entropy formula for heterotic string black holes at first order in alpha prime, using Wald's formalism and symmetry considerations.

Findings

Derived a gauge- and Lorentz-invariant entropy formula

Established the relation between macroscopic and microscopic entropies

Introduced covariant variations and restricted generalized zeroth laws

Abstract

We derive the first law of black hole mechanics in the context of the Heterotic Superstring effective action to first order in alpha prime using Wald's formalism. We carefully take into account all the symmetries of the theory and, as a result, we obtain a manifestly gauge- and Lorentz-invariant entropy formula in which all the terms can be computed explicitly. An entropy formula with these properties allows unambiguous calculations of macroscopic black-hole entropies to first order in alpha prime that can be reliably used in a comparison with the microscopic ones. Such a formula was still lacking in the literature. In the proof we use momentum maps to define covariant variations and Lie derivatives and \textit{restricted generalized zeroth laws} which state the closedness of certain differential forms on the bifurcation sphere and imply the constancy of the associated potentials on it. We study the relation between our entropy formula and other formulae that have been used in the literature.