ABSTRACT

In this talk, I will discuss the problem of formulating a sound mathematical theory of general-relativistic star evolution. After setting up the problem, I will explain its main challenges, but also how a great deal of rich physics and mathematics is involved in its study. A fundamental difficulty involves understanding the mathematics of the fluid-vacuum interface which separates the body of the star from vacuum. This interface displays a singular behavior which is not amenable to current mathematical techniques. This difficulty, however, can be circumvented if we consider stars that are spherically symmetric but not static. This corresponds to a dynamic (i.e., time-dependent) generalization of the TOV equations. I will conclude with some possible directions of future research, including the treatment of general-relativistic viscous star models. This is joint work with J. Speck.