An exact rotating black hole solution in Palatini Kalb-Ramond gravity

Abstract

We construct an exact stationary axisymmetric vacuum configuration in metric affine Kalb-Ramond gravity with zero cosmological constant. Independent variation of the metric, connection, and antisymmetric field yields the complete field equations and the algebraic relation between the physical and auxiliary geometries. A Kerr auxiliary metric and a closed corotating vacuum two form of fixed positive norm determine the physical metric. The tensor kernel contains the horizon generator, and the metrics, independent connection, and vacuum field share a smooth extension across the nonextremal physical Killing horizon and the rotation axes at finite radius for unequal deformation factors. We obtain an explicit sufficient domain for a causal exterior and an asymptotically locally flat end at fixed nonpolar angles. The physical Hamiltonian yields the timelike and null equations, equatorial effective potentials, circular orbit properties, radial stability, and perihelion advance. Numerical photon evolution determines the critical curve on an orthonormal observer screen. Its size, shape, and centroid depend on $ε=ξ_2b^2/[2(1+ξ_1b^2)]$ at fixed normalized mass scale and spin, with Kerr recovered at $ε=0$. Geometric observations probe this combination and retain an exact degeneracy between the curvature couplings. A static equatorial comparison with Mercury gives a conditional sensitivity of $2.30\times10^{-11}$ for $|2ε|$ under the stated angular convention and mass setting.