2006/10/08 by Fu-Wen Shu, Shu, Fu-Wen, You-Gen Shen +1 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #gr-qc
paper · pdf · doi:10.48550/arxiv.gr-qc/0610030
3 pages
openalex publication_date 2006/10/08 · arxiv created 2007/04/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Λ=0, they all have the Schwarzschild solution. In addition, these results can be generalized to a kind of more general geometric flow.