Non-extremal, $\alpha'$-corrected black holes in 5-dimensional Heterotic Superstring Theory

TL;DR

This paper calculates first-order string corrections to non-extremal black holes in 5D heterotic superstring theory, analyzing their thermodynamics and duality properties, and confirming consistency with known extremal solutions.

Contribution

It provides the first detailed computation of $oldsymbol{ ext{α'}}$ corrections for non-extremal heterotic black holes, extending previous extremal results and exploring their thermodynamic behavior.

Findings

Hawking temperature and Wald entropy are consistent with the first law and Smarr formula.

T duality maps solutions to solutions with T dual charges.

$oldsymbol{ ext{α'}}$ acts as a thermodynamic variable in the corrected solutions.

Abstract

We compute the first-order $\alpha'$ corrections of the non-extremal Strominger-Vafa black hole and its non-supersymmetric counterparts in the framework of the Bergshoeff-de Roo formulation of the heterotic superstring effective action. The solution passes several tests: its extremal limit is the one found in an earlier publication and the effect of a T duality transformation on it is another solution of the same form with T dual charges. We compute the Hawking temperature and Wald entropy showing that they are related by the first law and Smarr formula. On the other hand, these two contain additional terms in which the dimensionful parameter $\alpha'$ plays the role of thermodynamical variable.