On classical thermal stability of black holes with a dynamical extrinsic curvature

We study the deformation caused by the influence of the extrinsic curvature on a vacuum spherically symmetric metric embedded in a five-dimensional bulk. We investigate the resulting black-holes obtaining general characteristics such as their masses, horizons, singularities and thermal properties by using a dynamical extrinsic curvature leading to different results as those from rigid embedded models. As a test, we also study the bending of light near such black-holes analyzing the movement of a test particle and the modification caused by extrinsic curvature on its movement. Accordingly, using the asymptotically conformal flat condition, we show that such black holes must be large and constrained by the allowed number range −1/2≤n≤1.8 for a set of n-scalar potentials. As a result, they are locally thermodynamically stable, but not globally preferred.