Interior spacetimes of stars in Palatinif(R)gravity

Abstract

We study the interior spacetimes of stars in the Palatini formalism of f (R) gravity and derive a generalized Tolman-Oppenheimer-Volkoff and mass equation for a static, spherically symmetric star. We show that matching the interior solution with the exterior Schwarzschild-De Sitter solution in general gives a relation between the gravitational mass and the density profile of a star, which is different from the one in General Relativity. These modifications become neglible in models for which δf (R) ≡ f (R) − R is a decreasing function of R however. As a result, both Solar System constraints and stellar dynamics are perfectly consistent with f (R) = R − µ 4 /R.PACS numbers: 98.80. -k, 95.35.+d, 04.50.+h

Solar System planetary orbital motions andf(R) theories of gravity

“…The difficulties arising in the metric formalism with the Solar System experiments, which ultimately depend on the matching between the solutions inside and outside the matter distribution (i.e. the matching between the star interior and the vacuum exterior), are not present in the Palatini formalism, as it has been recently showed [32]: in the Palatini formalism of the f (R) theories, the space-time inside a star does not affect the space-time outside it, (i.e. the vacuum solution), contrary to what happens in the metric formalism, even though in this approach the mass of the star and its density have a non standard relation.…”

Viable Palatini-f(R)cosmologies with generalized dark matter

“…Inspired by the the theoretical developments [25], the success of the Palatini-f (R) gravities within the Solar system [19] and the recent resolutions of their physical implications [11], we reconsidered the cosmological viability of these models in view of their predictions for the large-scale structure.…”

“…Though a realistic universe expansion history may be reconstructed from these models [7,8], they seem to be ruled out as alternatives to dark energy because of their consequences to the Solar system physics [9,10,11], see however [12]. If the connection Γ is promoted to an independent variable, the action (1) represents the f (R) models in the so called Palatini formalism [13,14,15,16,17,18], which instead appear to pass the Solar system tests [19]. The viability of the small-scale limit of these Palatini-f (R) models has been an issue of debate [20,21].…”

Dark stars in Starobinsky’s model

“…However, in [14] the authors showed that whether or not relativistic stars exist or not depends on the behaviour of the trace of the matter energy-momentum tensor. Relativistic stars in f (R) theories of gravity have also been studied in [15][16][17][18][19][20].…”