On the thermal stability of a static spherically symmetric black holes in Nash embedding framework

Abstract

We study the deformation caused by the influence of extrinsic curvature on a vacuum spherically symmetric metric embedded in a five-dimensional bulk. In this sense, we investigate the produced black-holes and derive general characteristics such as their masses, horizons, singularities and thermal properties. 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 for the extrinsic curvature, an analytical expansion of a set of \emph{n}-scalar fields can be defined and we show that the corresponding black holes must be large and constrained in the range of allowed values $-1/2\le n\le 1.8$. As a result, they are locally thermodynamically stable, but not globally preferred.

10 pages,6 figures, 1 table, extended discussion on embeddings, corrected typos and references

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Cited by in corpus (1)

• Quantum Fluctuations from Thermal Fluctuations in Jacobson Formalism