Invariant quantities of scalar–tensor theories for stellar structure

Abstract

We present the relativistic hydrostatic equilibrium equations for a wide class of gravitational theories possessing a scalar–tensor representation. It turns out that the stellar structure equations can be written with respect to the scalar–tensor invariants, allowing to interpret their physical role.

Metric-affine gravity effects on terrestrial (exo-)planets profiles

“…Apart from the findings in regards to (exo-)planets discussed in more detail below, we have also examined carefully a possible singular behaviour of our equations, caused by the extra terms derived from Palatini quadratic model (especially the one related to the conformal transformation [24,67]). More precisely, an eventual ill behaviour of the hydrostatic equilibrium equations ( 16), leading to a non-physical behaviour of a sphericalsymmetric system such as a planet or a star, could appear for a certain value of the parameter α.…”

“…In this work we use the fact that many models of gravitation, in particular f (R) Palatini gravity (see the section II for a short review of the model), slightly alter the non-relativistic limit of (sub-)stellar structural equations by introducing new (geometric) terms proportional to functions of energy density [23][24][25] (for a review see [26,27]). Modified non-relativistic equations in the context of stars and brown dwarfs have been already widely used by the physics community, mainly to obtain limiting masses, such as e.g., the Chandrasekhar mass for white dwarf stars [28][29][30][31][32][33], the minimum Main Sequence mass 1 [34][35][36][37], or minimum mass for deuterium burning [38].…”

Stellar and substellar objects in modified gravity

“…where M = m(R). We will consider only the usual definition for the mass function (however, see the discussion in [12,15] on modified gravity issues) m (r) = 4πr 2 ρ(r).…”

“…where T c6 ≡ T c /10 6 K and f scr is the screening correction factor, while S = 7.2 × 10 10 and a = 84.72 are dimensionless parameters in the fit to the reaction rate 7 Li(p, α) 4 He [24,25,26]. The Lane-Emden formalism for Palatini gravity provides the expressions for the central temperature T c and central density ρ c (15). However, instead of the simplest polytropic model (11), we need to take into account an arbitrary electron degeneracy degree Ψ and mean molecular weight µ ef f , and thus the radius is…”

Giant planet formation in Palatini gravity

“…The fact that modified gravity introduces additional terms to the Poisson and hydrostatic equilibrium equations (see [26][27][28]); for review, [16,29], which are used to describe stellar and substellar bodies, provides that our understanding of the astrophysical objects and their evolution can slightly differ when compared to the results given by Newtonian gravity. The best known examples are altered limiting masses, such as the Chandrasekhar mass for white dwarf stars [30][31][32][33][34][35][36][37], the minimum Main Sequence mass [38][39][40][41], minimum mass for deuterium burning [42], or Jeans [43] and opacity mass [44].…”