Causal Limit of Neutron Star Maximum Mass in $f(R)$ Gravity in View of GW190814

TL;DR

This paper explores the maximum mass limits of neutron stars within $f(R)$ gravity, considering causal equations of state, and discusses implications for the GW190814 event, suggesting the secondary could be a neutron star, black hole, or rapidly rotating neutron star, but unlikely a strange star.

Contribution

It provides the first numerical analysis of the causal mass limit for neutron stars in $f(R)$ gravity, including effects of variable sound speed and transition density, and discusses implications for GW190814.

Findings

The causal mass limit in $f(R)$ gravity is similar to general relativity, around 3 solar masses.

The secondary of GW190814 is unlikely to be a strange star based on extended gravity considerations.

The maximum neutron star mass in $f(R)$ gravity respects the general relativistic limit, with marginal deviations.

Abstract

We investigate the causal limit of maximum mass for stars in the framework of$f(R)$ gravity. We choose a causal equation of state, with variable speed of sound, and with the transition density and pressure corresponding to the SLy equation of state. The transition density is chosen to be equal to twice the saturation density $\rho_t\sim 2\rho_0$, and also the analysis is performed for the transition density, chosen to be equal to the saturation density $\rho_t\sim \rho_0$. We examine numerically the combined effect of the stiff causal equation of state and of the sound speed on the maximum mass of static neutron stars, in the context of Jordan frame of $f(R)$ gravity. This yields the most extreme upper bound for neutron star masses in the context of extended gravity. As we will evince for the case of $R^2$ model, the upper causal mass limit lies within, but not deeply in, the mass-gap region, and is marginally the same with the general relativistic causal maximum mass, indicating that the $\sim 3M_{\odot}$ general relativistic limit is respected. In view of the modified gravity perspective for the secondary component of the GW190814 event, we also discuss the strange star possibility. Using several well established facts for neutron star physics and the Occam's razor approach, although the strange star is exciting, for the moment, it remains a possibility for describing the secondary component of GW190814. We underpin the fact that the secondary component of the compact binary GW190814 is probably a neutron star, a black hole or even a rapidly rotating neutron star, but not a strange star. We also discuss, in general, the potential role of the extended gravity description for the binary merging.