Geometry of static perfect fluid space-time
Differential Geometry
2023-09-08 v3 General Relativity and Quantum Cosmology
Mathematical Physics
math.MP
Abstract
In this article, we investigate the geometry of static perfect fluid space-time on compact manifolds with boundary. We use the generalized Reilly's formula to establish a geometric inequality for a static perfect fluid space-time involving the area of the boundary and its volume. Moreover, we obtain new boundary estimates for static perfect fluid space-time. One of the boundary estimates is obtained in terms of the Brown-York mass and another one related to the first eigenvalue of the Jacobi operator. In addition, we provide a new (simply connected) counterexample to the Cosmic no-hair conjecture for arbitrary dimension
Cite
@article{arxiv.2306.00225,
title = {Geometry of static perfect fluid space-time},
author = {Johnatan Costa and Rafael Diógenes and Neilha Pinheiro and Ernani Ribeiro},
journal= {arXiv preprint arXiv:2306.00225},
year = {2023}
}
Comments
To appear in Classical and Quantum Gravity