Turning point principle for relativistic stars

Abstract

Upon specifying an equation of state, spherically symmetric steady states of the Einstein-Euler system are embedded in 1-parameter families of solutions, characterized by the value of their central redshift. In the 1960's Zel'dovich [50] and Wheeler [22] formulated a turning point principle which states that the spectral stability can be exchanged to instability and vice versa only at the extrema of mass along the mass-radius curve. Moreover the bending orientation at the extrema determines whether a growing mode is gained or lost. We prove the turning point principle and provide a detailed description of the linearized dynamics. One of the corollaries of our result is that the number of growing modes grows to infinity as the central redshift increases to infinity.

33 pages, 1 figure

References in corpus (3)

• A numerical investigation of the stability of steady states and critical phenomena for the spherically symmetric Einstein-Vlasov system
• A non-variational approach to nonlinear stability in stellar dynamics applied to the King model
• Separable Hamiltonian PDEs and Turning point principle for stability of gaseous stars

Cited by in corpus (4)

• The relativistic Euler equations with a physical vacuum boundary: Hadamard local well-posedness, rough solutions, and continuation criterion
• A numerical stability analysis for the Einstein-Vlasov system
• Collisionless equilibria in general relativity: stable configurations beyond the first binding energy maximum
• Einstein-Vlasov system with equal-angular momenta in ${\text{AdS}}_5$