Turning point principle for the stability of relativistic stars

event Monday, November 30, 2020
access_time 3:30 PM (CT)
room Zoom

Abstract: I will discuss the stability of nonrotating relativistic stars (white drawfs, neutron stars etc.) modeled by the Euler-Einstein equation. 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 1960s, Zel'dovich and Wheeler et al. 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 proved the turning point principle and provided 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. I will also discuss the critical phenomena for gravitational collapse and its relation to the dynamics near unstable stars. This is joint work with Hadzic.

For more information on this event, please contact Yilun (Allen) Wu.