Abstract
This paper present two new theorems on the theory of the stability of highly relativistic stars. Thefirst theorem states that a highly relativistic, spherical star is stable if and only if its adiabatic index (assumed to be constant in the interior regions) is greater than a certain critical value,Γ crit which depends in a specified way on the high-density equation of state. This critical value is analogous to the Newtonian value\(\Gamma _{{\text{crit}}} = \tfrac{4}{3}\), but because of relativistic effects it is typically somewhat larger than\(\tfrac{4}{3}\). Thesecond theorem shows that at high central densities, the curves of —(binding energy) vs. radius, —E B (R) for certain hot, isentropic sequences of stellar models must exhibit damped clockwise spirals. This spiraling reflects the onset of instability in one radial mode of pulsation after another as the central density increases along the sequence.
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Ipser, J.R. On the stability of ultrarelativistic stars. Astrophys Space Sci 7, 361–373 (1970). https://doi.org/10.1007/BF00653277
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DOI: https://doi.org/10.1007/BF00653277