Relativistic Stellar Stability: an Empirical Approach

Abstract

The "PPN formalism"-which encompasses the post-Newtonian limit of nearly every metric theory of gravity-is used to analyze stellar stability. This analysis enables one to infer, for any given gravitation theory, the extent to which post-Newtonian effects induce instabilities in white dwarfs, in neutron stars, and in supermassive stars. It also reveals the extent to which our current empirical knowledge of post-Newtonian gravity (based on solar-system experiments) actually guarantees that relativistic instabilities exist. In particular, it shows that (i) for "conservative theories of gravity," current solar-system experiments guarantee that the critical adiabatic index, t, for the stability of stars against radial pulsations exceeds the Newtonian value of : 1' = 43 + 2KM/R, K positive and of order unity; this ensures the existence of the "relativistic instability"; (ii) for "nonconservative theories," current experiments do not permit any firm conclusion about the sign of it - 4 (iii) in the PPN approximation to every metric theory, the standard Schwarzschild criterion for convection is valid. Subject headings: gravitation - instabilities - interiors, stellar - neutron stars - relativity - white dwarf stars