Curvature singularity of the distributional BTZ black hole geometry

Abstract

For the non-rotating BTZ black hole, the distributional curvature tensor field is found. It is shown to have singular parts proportional to a $\delta$-distribution with support at the origin. This singularity is related, through Einstein field equations, to a point source. Coordinate invariance and independence on the choice of differentiable structure of the results are addressed.

Latex, 7 pages

References in corpus (3)

• Remarks on the distributional Schwarzschild geometry
• Metrics with distributional curvature
• Distributional Sources in General Relativity: two point-like examples revisited

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