XXXIX Workshop on Geometric Methods in Physics 27.06-3.07.2021
IX School on Geometry and Physics 21-25.06.2021

Ernani Ribeiro Jr

Static perfect fluid space-time on compact manifold

The purpose of this article is to investigate the geometry of static perfect fluid space-time metrics on compact manifolds with boundary. In the first part, we provide a boundary estimate for static perfect fluid space-time. In the second part, we establish a unified Böchner type formula for a large class of spaces that include the static perfect fluid space-time, critical metrics of the volume functional, static spaces and CPE metrics. Moreover, as a consequence of such a formula we obtain a gap result for a compact static perfect fluid space-time. Reference: E. Ribeiro Jr. et al.: "Static perfect fluid space-time on compact manifold". Classical and Quantum Gravity, 37 (2020) 015003.

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