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Turning point principle for the stability of relativistic stars

Oct 21, 2020

Turning point principle for the stability of relativistic stars

Zhiwu Lin

School of Mathematics, Georgia Institute of Technology

 

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 possible relation to the dynamics near unstable stars. This is joint work with Hadzic.

 

Slides for the talk (click)

Recorded video for the talk (click)

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