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arXiv · 2306.00225

Geometry of static perfect fluid space-time

Johnatan Costa·Rafael Diógenes·Neilha Pinheiro·Ernani Ribeiro Jr
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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 $n\geq 4.$

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Johnatan Costa, Rafael Diógenes, Neilha Pinheiro, Ernani Ribeiro Jr. 2023-05-31. Geometry of static perfect fluid space-time. https://arxiv.org/abs/2306.00225

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