Astronomy and Astrophysics – Astrophysics
Scientific paper
Mar 1977
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977a%26a....55..439d&link_type=abstract
Astronomy and Astrophysics, vol. 55, no. 3, Mar. 1977, p. 439-443.
Astronomy and Astrophysics
Astrophysics
Relativity, Stellar Models, Supermassive Stars, Main Sequence Stars, Partial Differential Equations, Perturbation Theory, Roots Of Equations
Scientific paper
A general relativistic version of the classical cubic equation is derived for the complex radial pulsation frequencies of hydrogen-burning relativistic stars. The influence of general-relativistic corrections on the nonadiabatic terms is treated to the first order in the relativistic parameter. This implies that the 'thermal imbalance' nature of the unperturbed 'equilibrium' state, due to the conversion of rest mass into energy by thermonuclear reactions, must be taken into account. Eckart's (1940) formalism has been used to deal with the radiative or convective flux, but the influence of radiative viscosity terms has been neglected in the derivation of the structure and pulsation equations. Finally, relativistic expressions for the vibrational stability coefficient and the secular root are given, the latter being used to recover and clarify the general-relativistic secular instability found in supermassive stars above a certain critical mass.
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