On Black Hole Stability in Multidimensional Gravity

Abstract

Exact static, spherically symmetric solutions to the Einstein-Maxwell-scalar equations, with a dilatonic-type scalar-vector coupling, in $D$-dimensional gravity with a chain of $n$ Ricci-flat internal spaces are considered. Their properties and special cases are discussed. A family of multidimensional dilatonic black-hole solutions is singled out, depending on two integration constants (related to black hole mass and charge) and three free parameters of the theory (the coordinate sphere, internal space dimensions, and the coupling constant). The behaviour of the solutions under small perturbations preserving spherical symmetry, is studied. It is shown that the black-hole solutions without a dilaton field are stable, while other solutions, possessing naked singularities, are catastrophically unstable.

18 pages, LaTeX, Potsdam University, preprint AIP 94-01

References in corpus (2)

• On black holes in multidimensional theory with Ricci-flat internal spaces
• Quantum Effects near Charged Dilatonic Black Holes

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• Multitemporal generalization of Schwarzschild solution
• Dynamics of Dimensions in Factor Space Cosmology
• Photon Sphere for a Dilatonic Dyonic Black Hole in a Model with an Abelian Gauge Field and a Scalar Field