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

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.

arXiv comment15 pages, 9 figures, 4 appendices, two-column format

References in corpus (23)

• f(R) Theories Of Gravity
• f(R) theories
• GW170817: Measurements of Neutron Star Radii and Equation of State
• Equation of state and neutron star properties constrained by nuclear physics and observation
• Stellar structure models in modified theories of gravity: lessons and challenges
• Black Holes in f(R) theories
• Dark Matter from R^2-gravity
• Observation of Gravitational Waves from the Coalescence of a $2.5\text{-}4.5M_{\odot }$ Compact Object and a Neutron Star
• The realistic models of relativistic stars in f(R) = R + alpha R^2 gravity
• Junction Conditions in f(R) Theories of Gravity
• Junction conditions for F(R)-gravity and their consequences
• Collapsing spherical stars in f(R) gravity
• Gravitational collapse in f(R) theories
• On neutron stars in f(R) theories: small radii, large masses and large energy emitted in a merger
• Spherically Symmetric Solutions to Fourth-Order Theories of Gravity
• A new framework for studying spherically symmetric static solutions in f(R) gravity
• Buchdahl-Bondi limit in modified gravity: Packing extra effective mass in relativistic compact stars
• A special class of solutions in $F(R)$-gravity
• Gravitational Collapse in General Relativity and in $R^2$-gravity: A Comparative Study
• Exploring the distribution and impact of bosonic dark matter in neutron stars
• Revisiting the Darmois and Lichnerowicz junction conditions
• Is gravitational collapse possible in $f(R)$ gravity?
• Numerical solutions for the $f(R)$-Klein-Gordon system

Cited by in corpus (1)

• Solar system tests and neutron stars in $f(R)$ gravity revisited