T-duality and high-derivative gravity theories: the BTZ black hole/string paradigm

TL;DR

This paper demonstrates that T-duality preserves the temperature and entropy of BTZ black holes in high-derivative gravity theories, extending previous results and suggesting T-duality as a tool for constraining effective actions.

Contribution

It shows invariance of black hole thermodynamics under T-duality in a broad class of theories including but not limited to String Theory, and introduces new black string solutions.

Findings

Temperature and entropy invariance under T-duality

Extension of Horowitz and Welch's results to higher-order theories

Generation of new regular black string solutions

Abstract

We show that the temperature and entropy of a BTZ black hole are invariant under T-duality to next to leading order in $M_\star^{-2}$, $M_\star$ being the scale suppressing higher-curvature/derivative terms in the Lagrangian. We work in the framework of a two-parameter family of theories exhibiting T-duality, which includes (but goes beyond) String Theory. Interestingly enough, the AdS/CFT correspondence enforces quantization conditions on these parameters. In the particular case of bosonic/heterotic string theory, our results extend those of a classical paper by Horowitz and Welch. For generic (albeit quantized) values of the parameters, it suggests that T-duality might be an interesting tool to constrain consistent low-energy effective actions while entailing physical equivalences outside String Theory. Moreover, it generates a new family of regular asymptotically flat black string solutions in three-dimensions.