transparent gif

 

Ej inloggad.

Göteborgs universitets publikationer

Sharp bounds on 2m/r of general spherically symmetric static objects

Författare och institution:
Håkan Andréasson (Institutionen för matematiska vetenskaper, matematik, Chalmers/GU)
Publicerad i:
Journal of Differential Equations, 245 ( 8 ) s. 2243-2266
ISSN:
0022-0396
E-ISSN:
1090-2732
Publikationstyp:
Artikel, refereegranskad vetenskaplig
Publiceringsår:
2008
Språk:
engelska
Fulltextlänk:
Sammanfattning (abstract):
In 1959 Buchdahl [H.A. Buchdahl, General relativistic fluid spheres, Phys. Rev. 116 (1959) 1027-1034] obtained the inequality 2 M / R ≤ 8 / 9 under the assumptions that the energy density is non-increasing outwards and that the pressure is isotropic. Here M is the ADM mass and R the area radius of the boundary of the static body. The assumptions used to derive the Buchdahl inequality are very restrictive and for instance neither of them hold in a simple soap bubble. In this work we remove both of these assumptions and consider any static solution of the spherically symmetric Einstein equations for which the energy density ρ ≥ 0, and the radial and tangential pressures p ≥ 0 and pT satisfy p + 2 pT ≤ Ω ρ, Ω > 0, and we show thatunder(sup, r > 0) frac(2 m (r), r) ≤ frac((1 + 2 Ω)2 - 1, (1 + 2 Ω)2), where m is the quasi-local mass, so that in particular M = m (R). We also show that the inequality is sharp under these assumptions. Note that when Ω = 1 the original bound by Buchdahl is recovered. The assumptions on the matter model are very general and in particular any model with p ≥ 0 which satisfies the dominant energy condition satisfies the hypotheses with Ω = 3.
Ämne (baseras på Högskoleverkets indelning av forskningsämnen):
NATURVETENSKAP ->
Matematik ->
Matematisk analys
Nyckelord:
Buchdahl inequality; Static Einstein equations; Tolman-Oppenheimer-Volkov equation
Postens nummer:
63119
Posten skapad:
2007-12-14 15:40
Posten ändrad:
2016-07-14 13:45

Visa i Endnote-format

Göteborgs universitet • Tel. 031-786 0000
© Göteborgs universitet 2007