The stability of supermassive stars in the Parametrized Post-Newtonian framework

Abstract

The binding energy and stability of supermassive stars (SMS's) is examined in the framework of the Parametrized Post-Newtonian (PPN) formalism of Will and Nordvedt. The PPN formalism encompasses the post-Newtonian limit of virtually every theory of gravity, differentiating between theories by means of nine PPN parameters. A general expression is derived for the energy integral in the PPN framework, and it is found that only in those theories in which the parameters ζ1=ζ2=ζ3=ζ4=α3=0 will the energy be conserved. In all such theories, a SMS of radius less than a critical radius will be unstable against adiabatic radial perturbations. Present experimental limits on the PPN parameters γ and β do not exclude the possibility of the existence of stable, non-rotating, hydrogen-burning SMS's of masses an order of magnitude larger than the upper limit for the mass of such stars predicted in general relativity.