Bianchi-Type Black Holes in Higher-Dimensional $R^2$ Gravity

Abstract

In this study, we investigate higher-dimensional static and stationary Bianchi-type solutions in an $R^2$ gravity theory using the formalism of exterior differential forms. We construct a broad class of exact higher-dimensional Bianchi-type solutions in an $R^2$-corrected gravity theory. It is shown that the theory admits hyperscaling violating black hole solutions associated with homogeneous but anisotropic horizon geometries, encompassing both static and stationary configurations. We further analyze some thermodynamic properties of these backgrounds and demonstrate that higher-curvature corrections give rise to unconventional features. In particular, we show that within the critical sector, the solutions possess a finite Hawking temperature despite an identically vanishing Wald entropy, signaling an unusual thermodynamic regime. These configurations arise at the critical point of the theory, where the effective gravitational coupling vanishes and the space of admissible constant-curvature geometries is enlarged.

19 pages, 4 figures