Slowly-rotating neutron stars in massive bigravity

Abstract

We study slowly-rotating neutron stars in ghost-free massive bigravity. This theory modifies General Relativity by introducing a second, auxiliary but dynamical tensor field that couples to matter through the physical metric tensor through non-linear interactions. We expand the field equations to linear order in slow rotation and numerically construct solutions in the interior and exterior of the star with a set of realistic equations of state. We calculate the physical mass function with respect to observer radius and find that, unlike in General Relativity, this function does not remain constant outside the star; rather, it asymptotes to a constant a distance away from the surface, whose magnitude is controlled by the ratio of gravitational constants. The Vainshtein-like radius at which the physical and auxiliary mass functions asymptote to a constant is controlled by the graviton mass scaling parameter, and outside this radius, bigravity modifications are suppressed. We also calculate the frame-dragging metric function and find that bigravity modifications are typically small in the entire range of coupling parameters explored. We finally calculate both the mass-radius and the moment of inertia-mass relations for a wide range of coupling parameters and find that both the graviton mass scaling parameter and the ratio of the gravitational constants introduce large modifications to both. These results could be used to place future constraints on bigravity with electromagnetic and gravitational-wave observations of isolated and binary neutron stars.

Stellar structure models in modified theories of gravity: Lessons and challenges

“…Finally, Sullivan and Yunes study in detail the case of ghost-free massive bigravity in [375] by considering APR, LS220 [376] and Shen EOS, finding the expected degeneracy between such EOS and the modified gravity parameter in this case, m, which is related to the graviton mass. The mass-radius and moment of inertia-to-mass relations are explored in detail, finding significant deviations with respect to GR for values of m > 10 −7 cm −1 .…”

Relativistic stars in mass-varying massive gravity

“…The detection of gravitational waves from neutron star mergers [2] has added a new dimension to our ability to unravel the nature of strong gravity and the structure of relativistic compact stars. Neutron star solutions have been previously investigated in the original dRGT model [20] and in bi-gravity [21] with a graviton mass that is much greater than typical cosmological scales. Relativistic star solutions in dRGT-like models with a singular reference metric have also been studied [22,23].…”

Properties of Neutron stars with hyperon cores in parametrized hydrostatic conditions

“…NSs are often treated as massive gravity candidates as certain theories of massive gravity, which consider the graviton mass to be non-zero, has been quite successful in describing the properties of NSs, consistent to the observational and empirical bounds on them. 45,46 It is therefore for such objects like NSs, ordinary General Relativity (GR) may not be a suitable approach. Over a decade several extended/modified gravity theories came up to explain massive gravity 47,48 and also as alternatives to the dark matter and dark energy theories to explain the total energy budget of the universe.…”

“…They may rather also constrain gravity. [49][50][51][52][53] There are several extended/modified theories of gravity like f(R) gravity, [53][54][55][56][57][58][59][60][61] scalar-tensor theories, [62][63][64][65][66][67][68][69][70][71][72][73][74][75] quadratic gravity like Einstein-dilaton-Gauss-Bonnet gravity 76,77 and Chern-Simons gravity, [78][79][80][81] extended theories of gravity, [82][83][84] massive gravity 45,46 which are used to modify the general Tolman-Oppenheimer-Volkoff (TOV) equations 85,86 to calculate the mass and radius of NSs. In certain works 51,[87][88][89] parameterization of the TOV equations has been done for the same purpose, without involving any particular theory of gravity.…”