Geometric Flows and Black Holes

Details Geometric Flows and Black Holes Geometric Flows and Black Holes

2006-10-08

arxiv.org/abs/gr-qc/0610030v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

3 pages

Scientific paper

Motivated by the newest progress in geometric flows both in mathematics and physics, we apply the geometric evolution equation to study some black-hole problems. Our results show that, under certain conditions, the geometric evolution equations satisfy the Birkhoff theorem, and surprisingly, in the case of spherically symmetric metric field, the Einstein equation, the Ricci flow, and the hyperbolic geometric flow in vacuum spacetime have the same black-hole solutions, especially in the case of $\Lambda=0$, they all have the Schwarzschild solution. In addition, these results can be generalized to a kind of more general geometric flow.

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