Neutron star masses in $R^2$-gravity

Abstract

We address the issue of the existence of inequivalent definitions of gravitational mass in $R^2$-gravity. We present several definitions of gravitational mass, and discuss the formal relations between them. We then consider the concrete case of a static and spherically symmetric neutron star, and solve numerically the equations of motion for several values of the free parameter of the model. We compare the features of the mass-radius relations obtained for each definition of gravitational mass, and we comment on their dependence on the free parameter. We then argue that $R^2$-gravity is a valuable proxy to discuss the existence of inequivalent definitions of gravitational mass in a generic modified gravity theory, and present some comments on the general case.

arXiv comment26 pages, 15 figures, pdfLatex, one subsection added and other minor changes, version accepted for publication

References in corpus (30)

• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• f(R) Theories Of Gravity
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Shapiro delay measurement of a two solar mass neutron star
• The Confrontation between General Relativity and Experiment
• A Massive Pulsar in a Compact Relativistic Binary
• f(R) theories
• Gravitational Waves and Gamma-rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• GW170817: Measurements of Neutron Star Radii and Equation of State
• Tests of general relativity with GW150914
• Curvature Quintessence
• Masses, Radii, and Equation of State of Neutron Stars
• A unified equation of state of dense matter and neutron star structure
• Conditions for the cosmological viability of f(R) dark energy models
• 1/R gravity and Scalar-Tensor Gravity
• Further stable neutron star models from f(R) gravity
• Analytical representations of unified equations of state for neutron-star matter
• The Mass-Radius relation for Neutron Stars in $f(R)$ gravity
• Maximal neutron star mass and the resolution of hyperon puzzle in modified gravity
• Nonperturbative models of quark stars in $f(R)$ gravity
• The realistic models of relativistic stars in f(R) = R + alpha R^2 gravity
• Analytical representations of unified equations of state of neutron-star matter
• Slowly rotating neutron and strange stars in $R^2$ gravity
• Non-perturbative and self-consistent models of neutron stars in R-squared gravity
• On neutron stars in f(R) theories: small radii, large masses and large energy emitted in a merger
• Compact stars in Energy-Momentum Squared Gravity
• Rapidly rotating neutron stars in $R$-squared gravity
• Dynamic and Thermodynamic Stability of Relativistic, Perfect Fluid Stars
• Pressure effects in the weak-field limit of f(R) = R + alpha R^2 gravity

Cited by in corpus (12)

• The mass-radius relation for neutron stars in $f(R)=R+\alpha R^2$ gravity: a comparison between purely metric and torsion formulations
• Anisotropic quark stars in $f(R)=R^{1+\epsilon }$ gravity
• Massive white dwarfs in $f(R,L_m)$ gravity
• Strongest constraint in $f(R)=R+\alpha R^2$ gravity: stellar stability
• Charged quark stars in metric $f(R)$ gravity
• The phase diagram of Einstein-Weyl gravity
• The gravitational field of a star in quadratic gravity
• $R^2$-gravity quark stars from perturbative QCD
• Invariant quantities of Scalar-Tensor Theories for stellar structure
• Weak field and slow motion limits in energy-momentum powered gravity
• BPS Skyrme neutron stars in generalized gravity
• Charting GLOBs in Asymptotically Safe Gravity