Toward a realistic Buchdahl limit in f(R) theories of gravity

TL;DR

This paper extends the Buchdahl limit to f(R) gravity theories, analyzing the properties of relativistic stars and demonstrating that such stars can have higher gravitational redshifts than in General Relativity, indicating potential observable differences.

Contribution

It generalizes the Buchdahl limit for f(R) theories of gravity and analyzes the physical properties of relativistic stars within this framework, including the Starobinsky model.

Findings

Stars in f(R) theories can have gravitational redshifts greater than 2.

The analysis confirms the physical viability of these stars under various conditions.

Comparison with Schwarzschild cases highlights differences in stellar properties.

Abstract

The so-called Buchdahl limit is not yet fully understood in the context of theories of gravity beyond the Einsteinian framework. In this investigation, we generalize this limit for the case of static, spherically-symmetric, relativistic compact stars in f(R) theories of gravity within the metric formalism. We present a comprehensive analysis that ensures regularity, thermodynamic stability, fulfillment of all required junction conditions, recovery of the Newtonian potential at long distances and a correct extraction of the asymptotic mass. Our results are exemplified for the f(R)=R+ alpha R^2 Starobinsky model and several realistic equations of state describing neutron-star matter. We also compare these results with the case of compact stars immersed ad hoc in an Schwarzschild exterior vacuum, although this scenario does not fulfill all necessary f(R) junction conditions. To test the validity of viable f(R) models, we show that such stars can indeed host additional energetic content, so their gravitational redshift can be greater than 2, which is prohibited in General Relativity.