Decay properties for massive Vlasov fields on Schwarzschild spacetime

Fuente: arXiv
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Main Author: Ruiz, Renato Velozo
Format: Preprint
Published: 2024
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author Ruiz, Renato Velozo
author_facet Ruiz, Renato Velozo
contents In this paper, we obtain pointwise decay estimates in time for massive Vlasov fields on the exterior of Schwarzschild spacetime. We consider massive Vlasov fields supported on the closure of the largest domain of the mass-shell where timelike geodesics either cross $\mathcal{H}^+$, or escape to infinity. For this class of Vlasov fields, we prove that the components of the energy-momentum tensor decay like $v^{-\frac{1}{3}}$ in the bounded region $\{r\leq R\}$, and like $u^{-\frac{1}{3}}r^{-2}$ in the far-away region $\{r\geq R\}$, where $R>2M$ is sufficiently large. Here, $(u,v)$ denotes the standard Eddington--Finkelstein double null coordinate pair.
format Preprint
id arxiv_https___arxiv_org_abs_2411_05124
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Decay properties for massive Vlasov fields on Schwarzschild spacetime
Ruiz, Renato Velozo
General Relativity and Quantum Cosmology
Mathematical Physics
Analysis of PDEs
In this paper, we obtain pointwise decay estimates in time for massive Vlasov fields on the exterior of Schwarzschild spacetime. We consider massive Vlasov fields supported on the closure of the largest domain of the mass-shell where timelike geodesics either cross $\mathcal{H}^+$, or escape to infinity. For this class of Vlasov fields, we prove that the components of the energy-momentum tensor decay like $v^{-\frac{1}{3}}$ in the bounded region $\{r\leq R\}$, and like $u^{-\frac{1}{3}}r^{-2}$ in the far-away region $\{r\geq R\}$, where $R>2M$ is sufficiently large. Here, $(u,v)$ denotes the standard Eddington--Finkelstein double null coordinate pair.
title Decay properties for massive Vlasov fields on Schwarzschild spacetime
topic General Relativity and Quantum Cosmology
Mathematical Physics
Analysis of PDEs
url https://arxiv.org/abs/2411.05124