Static Stellar Phase Transitions in General Relativity and a Generalized Buchdahl Limit

TL;DR

This paper constructs solutions to the Einstein-Euler equations for static stars with discontinuous density profiles, introducing a generalized Buchdahl limit that constrains stellar mass-radius relationships in General Relativity.

Contribution

It provides the first general method for constructing static stellar solutions with discontinuous densities and establishes a new generalized Buchdahl limit for these configurations.

Findings

Derived conditions for bounded pressure solutions in stellar models.

Generalized Buchdahl limit applicable to non-uniform density stars.

Examples illustrating mass-radius relationships under new constraints.

Abstract

We give the first general construction of solutions of the static spherically symmetric Einstein-Euler equations, the Tolman-Oppenheimer-Volkoff (TOV-)equation, with prescribed density functions allowed to be discontinuous and non-uniform; these solutions describe stellar phase transitions in General Relativity. Boundedness of the resulting pressure functions solving the TOV-equations, from the boundary down to the stellar center, is obtained by identifying a novel condition on the prescribed density, in generalization of the classical Buchdahl limit. Moreover, we introduce a new necessary condition for the existence of such bounded pressure functions, which in the special case of a uniform density state reduces to the classical Buchdahl limit on the stellar mass-radius relationship. We present various examples to study the stellar mass-radius relationships resulting from our new conditions.