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**Harvard**

Andréasson, H. (2009) *Sharp Bounds on the Critical Stability Radius for Relativistic Charged Spheres*.

** BibTeX **

@article{

Andréasson2009,

author={Andréasson, Håkan},

title={Sharp Bounds on the Critical Stability Radius for Relativistic Charged Spheres},

journal={COMMUNICATIONS IN MATHEMATICAL PHYSICS},

issn={0010-3616},

volume={288},

issue={2},

pages={715-730},

abstract={In a recent paper by Giuliani and Rothman [17], the problem of finding a lower bound on the radius R of a charged sphere with mass M and charge Q < M is addressed. Such a bound is referred to as the critical stability radius. Equivalently, it can be formulated as the problem of finding an upper bound on M for given radius and charge. This problem has resulted in a number of papers in recent years but neither a transparent nor a general inequality similar to the case without charge, i.e., M ≤ 4R/9, has been found. In this paper we derive the surprisingly transparent inequality √M≤/√R3+√/R9+/Q23R. The inequality is shown to hold for any solution which satisfies p + 2pT ≤ ρ, where p ≥ 0 and pT are the radial- and tangential pressures respectively and ρ ≥ 0 is the energy density. In addition we show that the inequality is sharp, in particular we show that sharpness is attained by infinitely thin shell solutions.},

year={2009},

keywords={einstein-vlasov system, buchdahl inequality, general-relativity, fluid spheres, static shells, objects, regularity},

}

** RefWorks **

RT Journal Article

SR Electronic

ID 124937

A1 Andréasson, Håkan

T1 Sharp Bounds on the Critical Stability Radius for Relativistic Charged Spheres

YR 2009

JF COMMUNICATIONS IN MATHEMATICAL PHYSICS

SN 0010-3616

VO 288

IS 2

SP 715

OP 730

AB In a recent paper by Giuliani and Rothman [17], the problem of finding a lower bound on the radius R of a charged sphere with mass M and charge Q < M is addressed. Such a bound is referred to as the critical stability radius. Equivalently, it can be formulated as the problem of finding an upper bound on M for given radius and charge. This problem has resulted in a number of papers in recent years but neither a transparent nor a general inequality similar to the case without charge, i.e., M ≤ 4R/9, has been found. In this paper we derive the surprisingly transparent inequality √M≤/√R3+√/R9+/Q23R. The inequality is shown to hold for any solution which satisfies p + 2pT ≤ ρ, where p ≥ 0 and pT are the radial- and tangential pressures respectively and ρ ≥ 0 is the energy density. In addition we show that the inequality is sharp, in particular we show that sharpness is attained by infinitely thin shell solutions.

LA eng

DO 10.1007/s00220-008-0690-3

LK http://dx.doi.org/10.1007/s00220-008-0690-3

OL 30