Abstract
In this paper, pulsating white dwarfs are treated via general relativity. Numerical integration of Einstein's equations was used to find equilibrium white dwarfs models and the fundamental periods of small oscillations about these equilibrium models. In these calculations account was taken of coulomb, Thomas-Fermi, and exchange interactions as well as ion zero point energies. It is shown that general relativity makes not just a quantitative difference in the results but a qualitative differences; pure C12 models which are stable in Newtonian mechanics can be unstable against collapse (at a central density of 3×1010 g/cm3) when general relativity is taken into account. The collapsing model may become a neutron star or may continue towards the Schwarzschild radius.
More realistic white dwarf models with carbon burning products at the center, also were studied. For these models, the density at which the star becomes unstable against collapse due to electron capture (3×109 g/cm3) was found to be lower than the density at which general relativistic instability occurs.
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Cohen, J.M., Lapidus, A. & Cameron, A.G.W. Treatment of pulsating white dwarfs including general relativistic effects. Astrophys Space Sci 5, 113–125 (1969). https://doi.org/10.1007/BF00653943
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DOI: https://doi.org/10.1007/BF00653943