On the shape of bodies in General Relativistic regimes

TL;DR

This paper establishes fundamental constraints on the shape of bodies in General Relativity based on energy and rotation, independent of material properties, with implications for neutron stars.

Contribution

It introduces a stability-based method combined with minimal surface techniques to constrain the shape of relativistic bodies, independent of their material composition.

Findings

Constraints are close to optimal for neutron stars.

Results do not depend on the equation of state.

Fundamental shape limits in relativistic regimes.

Abstract

The analysis of axisymmetric spacetimes, dynamical or stationary, is usually made in the reduced space. We prove here a stability property of the quo- tient space and use it together with minimal surface techniques to constraint the shape of General Relativistic bodies in terms of their energy and rotation. These constraints are different in nature to the mechanical limitations that a particular material body can have and which can forbid, for instance, rotation faster than a certain rate, (after which the body falls apart). The relations we are describing instead are fundamental and hold for all bodies, albeit they are useful only in General Relativistic regimes. For Neutron stars they are close to be optimal, and, although precise models for these stars display tighter con- straints, our results are significative in that they do not depend on the equation of state.