Higher-dimensional regular Reissner-Nordstr\"{o}m black holes associated with linear electrodynamics

Abstract

Following the interpretation of matter source that the energy-momentum tensor of anisotropic fluid can be dealt with effectively as the energy-momentum tensor of perfect fluid plus linear (Maxwell) electromagnetic field, we obtain the regular higher-dimensional Reissner-Nordstr\"{o}m (Tangherlini-RN) solution by starting with the noncommutative geometry inspired Schwarzschild solution. Using the boundary conditions that connect the noncommutative Schwarzschild solution in the interior of the charged perfect fluid sphere to the Tangherlini-RN solution in the exterior of the sphere, we find that the interior structure can be reflected by the exterior parameter, the charge-to-mass ratio. Moreover, we investigate the stability of the boundary under mass perturbation and indicate that the new interpretation imposes a rigid restriction upon the charge-to-mass ratio. This restriction, in turn, permits a stable noncommutative black hole only in the 4-dimensional spacetime.