An Exact Single-Rotating Near-Horizon Geometry in Einstein-Gauss-Bonnet Gravity

Abstract: We construct a five-dimensional singly rotating near-horizon solution in Einstein-Gauss-Bonnet gravity. We show that the Gauss-Bonnet term removes the local curvature singularity, yielding finite curvature invariants throughout the spacetime, provided the rotation parameter remains below a certain value set by the Gauss-Bonnet coupling. To our knowledge, this is the first analytic example of a singly rotating five-dimensional solution in this framework with finite curvature invariants over a nontrivial region of parameter space. We analyze the geometry across this space, identifying regular, singular, and marginal regimes. Finally, we study the thermodynamic properties, finding that while higher-derivative corrections regularize the local curvature behavior, they also introduce unique challenges to the standard thermodynamic description of Killing horizons.