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

Abstract

The understanding of stellar structure represents the crossroads of our theories of the nuclear force and the gravitational interaction under the most extreme conditions observably accessible. It provides a powerful probe of General Relativity on its strong field regime, and opens fruitful avenues for the exploration of new gravitational physics. The latter can be captured via the so-called modified theories of gravity, which modify the Einstein-Hilbert action of General Relativity and/or some of its building blocks/principles. These theories typically change the Tolman-Oppenheimer-Volkoff equations of stellar's hydrostatic equilibrium, having a large impact on the astrophysical properties of the corresponding stars, and thus opening a new window to constrain these theories with present and future observations of different types of stars. For relativistic stars, such as neutron stars, the uncertainty on the equation of state of matter at supranuclear densities intertwines with the new parameters coming from the modified gravity side, providing a whole new phenomenology for the typical predictions of stellar structure models, such as mass-radius relations, maximum masses, or moment of inertia. For non-relativistic stars, such as white, brown and red dwarfs, the weakening/strengthening of the gravitational force inside astrophysical bodies via the modified Newtonian (Poisson) equation may induce changes on the star's mass, radius, central density or luminosity, having an impact, for instance, in the Chandrasekhar's limit for white dwarfs, or in the minimum mass for stable hydrogen burning for high-mass brown dwarfs. This work aims to provide a broad overview of the main such results achieved in the recent literature for many such modified theories of gravity, by combining the results and constraints obtained from the analysis of relativistic and non-relativistic stars in different scenarios. Moreover, we will build a bridge between the efforts of the community working on different theories, formulations, types of stars, theoretical modellings, and observational aspects, highlighting some of the most promising opportunities in the field.

Invariant quantities of scalar–tensor theories for stellar structure

“…The most prominent one is the fact that I 1 cannot be a strong coupling; that is, it cannot differ significantly from unity in order not to violate the solar physics. It may happen, as it was discussed in, for instance, [108][109][110], that the extra terms introduced by the invariants provide a non-zero contribution to the mass function far away from the star's surface (when p(R) = 0, where R is the star's radius); that is, the mass function does not converge when r → ∞ but can oscillate instead around a constant value. This fact has following consequences: as proposed in [108] and then discussed in more detail in [111], in the case of f (R) metric gravity and general ST theories which introduce an additional degree of freedom, this phenomena could be used to test such theories against GR by the mean of the surface gravitational redshift.…”

Structure of Neutron Stars in Massive Scalar-Tensor Gravity

“…Notwithstanding GR's success, the search for possible alternative theories of gravity has for many decades been a highly active area of research [1,[8][9][10][11][12], motivated by important theoretical considerations, such as the incompatibility of GR with quantum theory at a fundamental level, as well as open questions in observational astronomy and cosmology. Astronomical observations of galactic rotation curves, micro-lensing, primordial nucleosynthesis or the accelerated expansion of the universe cannot be explained in GR without evoking dark matter and dark energy, enigmatic entities beyond the standard model of particles; see, e.g., [13,14].…”

New metric-affine generalizations of gravitational wave geometries

“…It is worth remarking that apart from MAG and PG gravity, many theories have been formulated considering an additional connection with certain properties or restrictions. See for example Ricci-Based Gravity theories containing the well-known f (R) theories [8][9][10][11][12][13][14][15][16][17][18], or the teleparallel equivalents and their generalizations [19][20][21][22][23][24][25][26].…”

“…From now on transversal means transversal to the congruence generated by k with respect to l 10. Applied to electromagnetic waves in Maxwell theory, this quadratic condition lead us to F∧ F = 0, namely F μν F μν = 0, that corresponds to the equality δ i j E i E j = δ i j B i B j .…”