Frozen Neutron Stars in Four-Dimensional Non-polynomial Gravities

TL;DR

This study explores neutron stars within four-dimensional non-polynomial gravities, revealing that increasing the modification parameter leads to larger stars and the formation of frozen states resembling black holes, consistent across different equations of state.

Contribution

It introduces the concept of frozen neutron stars as a universal endpoint in this gravity theory and derives observational bounds on the modification parameter.

Findings

Neutron stars grow in size and mass with increasing alpha.

Frozen states form at high alpha, resembling black holes.

Frozen neutron stars are consistent with observational constraints.

Abstract

This paper investigates the structure and properties of neutron stars in four-dimensional non-polynomial gravities. Solving the modified Tolman-Oppenheimer-Volkoff equations for three different equations of state (BSk19, SLy4, AP4), we confirm that neutron star solutions remain in existence. As the modification parameter $\alpha$ increases, neutron stars grow in both radius and mass. We find that, when the parameter $\alpha$ is sufficiently large, a frozen state emerges at the end of the neutron-star sequence. In this state, the metric functions approach zero extremely close to the stellar surface, forming a critical horizon, making it nearly indistinguishable from a black hole to an external observer. Such a frozen neutron star constitutes a universal endpoint of the neutron-star sequence in this theory, independent of the choice of the equation of state. Based on our results and current observational constraints, we derive bounds on the modification parameter $\alpha$ and show that frozen neutron stars remain allowed in the bounds.