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–Nordström (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 an 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.
Highlights
The singularity puzzle appeared just after the general relativity was born, where the singularities of spacetime are most bewildering at the end of stars’ collapsing and at the beginning of universe
By starting with the noncommutative geometry-inspired Schwarzschild solution in n dimensions, we find that the energy-momentum tensor with the Gaussian distribution can be regarded as the linear combination of the perfect fluid’s and electromagnetic field’s energy-momentum tensors when the charge-to-mass ratio takes a special range in order to guarantee the formation of Tangherlini–RN black holes
We generalize the formulation that a regular RN black hole can be sourced from charged perfect fluid in the 4-dimensional spacetime to higher-dimensional spacetimes through decomposing the energy-momentum tensor of an anisotropic fluid effectively into the energy-momentum tensor of a perfect fluid plus linear electromagnetic field
Summary
The singularity puzzle appeared just after the general relativity was born, where the singularities of spacetime are most bewildering at the end of stars’ collapsing and at the beginning of universe. One further advance was the first construction of a nonsingular black hole (regular black hole or black hole with singularities free) by Bardeen [5] This model is asymptotically approaching a de Sitter phase at the center and asymptotically flat at infinity, and its energy-momentum tensor satisfies the weak energy condition (WEC) rather than the strong energy condition (SEC). The nonsingular RN black hole solution was constructed in the 4-dimensional spacetime [20], where the singularity at the RN center was replaced by a charged perfect fluid sphere located inside the RN inner horizon when a fixed range of charge-to-mass ratio was taken.
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