Regular $(2+1)$-dimensional spatially homogeneous $\alpha'$-corrected BTZ-like black hole in string theory

TL;DR

This paper constructs a class of $ ext{(2+1)}$-dimensional $ ext{(2+1)}$-dimensional black hole solutions in string theory, incorporating higher-order $ ext{(alpha')}$ corrections, and relates them to the BTZ black hole with arbitrary negative curvature surfaces.

Contribution

It introduces $ ext{(alpha')}$-corrected $ ext{(2+1)}$-dimensional black hole solutions with arbitrary negative curvature, extending the BTZ black hole framework in string theory.

Findings

Derived $ ext{(alpha')}$-corrected black hole solutions in string theory.

Showed solutions are related to BTZ black holes via coordinate transformations.

Analyzed solutions in high curvature limit with higher-order corrections.

Abstract

We consider a $(2+1)$-dimensional spacetime whose two-dimensional space part is Weyl-related to a surface of arbitrary negative constant Gaussian curvature with symmetries of two-dimensional Lie algebra. It is shown that the geometry is a Lobachevsky-type geometry described by deformed hyperbolic function. At leading order string effective action with the source given by dilaton and antisymmetric $B$-field in the presence of central charge deficit term $\Lambda$, we obtained a solution whose line element is Weyl-related to this homogeneous spacetime with arbitrary negative Gaussian curvature. The solution can be transformed to the BTZ-like black hole by coordinate redefinition, while the BTZ black hole can be recovered by choosing a special set of parameters. The solutions appear to be in the high curvature limit $R\alpha'\gtrsim1$, with emphasis on including the higher order $\alpha'$ corrections. Considering the two-loop (first order $\alpha'$) $\beta$-function equations of $\sigma$-model, we also present the $\alpha'$-corrected black hole solutions.