Equation of states in the curved spacetime of slowly rotating degenerate stars

TL;DR

This paper calculates the equation of state for degenerate fermions in the curved spacetime of slowly rotating stars, revealing significant effects of gravitational time dilation on maximum mass and angular momentum, with minimal impact from frame-dragging.

Contribution

It introduces a method to compute the equation of state in curved spacetime, accounting for gravitational effects on neutron star properties, which was not previously considered.

Findings

Gravitational time dilation significantly increases the maximum mass of neutron stars.

Frame-dragging effects have a negligible impact on the equation of state.

Angular momentum calculations are greatly affected by using curved spacetime.

Abstract

We compute the equation of state for an ensemble of degenerate fermions by using the curved spacetime of a slowly rotating axially symmetric star. We show that the equation of state computed in such curved spacetime depends on the gravitational time dilation as well as on the dragging of inertial frames, unlike an equation of state computed in a globally flat spacetime. The effect of gravitational time dilation leads to a significant enhancement of the maximum mass limit of a degenerate neutron star. However, such an enhancement due to the frame-dragging effect is extremely small. Nevertheless, in general relativity the frame-dragging effect is crucial for computing angular momentum of the star which is also shown to be enhanced significantly due to the usage of curved spacetime in computing the equation of state.