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Sharp Bounds on the Critical Stability Radius for Relativistic Charged Spheres

Författare och institution:
Håkan Andréasson (Institutionen för matematiska vetenskaper, matematik, Chalmers/GU)
Publicerad i:
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 288 ( 2 ) s. 715-730
ISSN:
0010-3616
Publikationstyp:
Artikel, refereegranskad vetenskaplig
Publiceringsår:
2009
Språk:
engelska
Fulltextlänk:
Sammanfattning (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.
Ämne (baseras på Högskoleverkets indelning av forskningsämnen):
NATURVETENSKAP ->
Fysik ->
Annan fysik ->
Matematisk fysik
Nyckelord:
einstein-vlasov system, buchdahl inequality, general-relativity, fluid spheres, static shells, objects, regularity
Postens nummer:
124937
Posten skapad:
2010-08-20 11:00
Posten ändrad:
2016-07-14 13:42

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