Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

On the radial stability of ultra compact Schwarzschild stars beyond the Buchdahl limit (1811.09589v2)

Published 23 Nov 2018 in gr-qc

Abstract: In this paper we used the theory of adiabatic radial oscillations developed by Chandrasekhar to study the conditions for dynamical stability of constant energy-density stars, or Schwarzschild stars, in the unstudied ultra compact regime beyond the Buchdahl limit, that is, for configurations with radius $R$ in the range $R_{\rm S}<R<(9/8)R_{\rm S}$, where $R_{\rm S}$ is the Schwarzschild radius of the star. These recently found analytical solutions exhibit a negative pressure region in their centre and, in the limit when $R\to R_{\rm S}$, the full interior region of the star becomes filled with negative pressure. Here we present a systematic analysis of the stability of these configurations against radial perturbations. We found that, contrary to the usual expectation found in many classical works, the ultra compact Schwarzschild star is stable against radial oscillations. We computed values of the critical adiabatic index $\gamma_{c}$ for several stellar models with varying radius $R/R_{\rm S}$ and found that it also approaches a finite value as $R/R_{\rm S} \to 1$

Summary

We haven't generated a summary for this paper yet.