$\alpha'$ corrections to 4-dimensional non-extremal stringy black holes

TL;DR

This paper calculates first-order string theory corrections to 4D non-extremal black holes, analyzing their thermodynamics and confirming consistency with known physical laws and dualities.

Contribution

It provides fully analytic $ ext{alpha'}$ corrections to a family of 4-charge, non-extremal black holes in heterotic supergravity, including thermodynamic and duality properties.

Findings

Corrected black hole solutions reproduce extremal limits

Thermodynamics relations are consistent with extended laws

Scalar charges receive $ ext{alpha'}$ corrections, not poles at infinity

Abstract

We compute the first-order $\alpha'$ corrections to a family of 4-dimensional, 4-charge, non-extremal black hole solutions of Heterotic Supergravity in the case with 3 independent charges. The solutions are fully analytic, reproduce the extremal limit previously found in the literature and, applying T-duality, they transform as expected. If we reduce to the case with a single independent charge we obtain the corrections to four embeddings of the Reissner-Nordstr\"om black hole in string theory. We completely characterize the black hole thermodynamics computing the Hawking temperature, Wald entropy, mass, gauge charges and their dual thermodynamic potentials. We verify that all these quantities are related by the first law of extended black hole mechanics and the Smarr formula once we include a potential associated to the dimensionful parameter $\alpha'$ and the scalar charges. We found that the latter are not identified with the poles at infinity of the scalar fields because they receive $\alpha'$ corrections.