Regular (2 + 1)-dimensional spatially homogeneous α′-corrected BTZ-like black hole in string theory

We consider a [Formula: see text]-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 [Formula: see text]-field in the presence of central charge deficit term [Formula: see text], 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 [Formula: see text], with emphasis on including the higher order [Formula: see text] corrections. Considering the two-loop (first order [Formula: see text]) [Formula: see text]-function equations of [Formula: see text]-model, we also present the [Formula: see text]-corrected black hole solutions.