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

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