Sharp Bounds on the Critical Stability Radius for Relativistic Charged Spheres
Artikel i vetenskaplig tidskrift, 2009

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.

einstein-vlasov system

static shells




fluid spheres

buchdahl inequality


Håkan Andreasson

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Communications in Mathematical Physics

0010-3616 (ISSN) 1432-0916 (eISSN)

Vol. 288 715-730


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