Damien Martin and Matt Visser 2003 Class. Quantum Grav. 20 3699 doi:10.1088/0264-9381/20/16/311
Damien Martin and Matt Visser
Show affiliationsIt is a famous result of relativistic stellar structure that (under mild technical conditions) a static fluid sphere satisfies the Buchdahl–Bondi bound 2M/R < 8/9; the surprise here being that the bound is not 2M/R < 1. In this paper, we provide further generalizations of this bound by placing a number of constraints on the interior geometry (the metric components), on the local acceleration due to gravity, on various combinations of the internal density and pressure profiles and on the internal compactness 2m(r)/r of static fluid spheres. We do this by adapting the standard tool of comparing the generic fluid sphere with a Schwarzschild interior geometry of the same mass and radius—in particular, we obtain several results for the pressure profile (not merely the central pressure) that are considerably more subtle than might first be expected.
04.20.-q Classical general relativity
04.40.Dg Relativistic stars: structure, stability, and oscillations
Issue 16 (21 August 2003)
Received 10 June 2003
Published 28 July 2003
Damien Martin and Matt Visser 2003 Class. Quantum Grav. 20 3699
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