Curvature singularities, tidal forces and the viability of Palatini f(R) gravity

In a previous paper we showed that static spherically symmetric objects which, in the vicinity of their surface, are well-described by a polytropic equation of state with 3/2<Gamma<2 exhibit a curvature singularity in Palatini f(R) gravity. We argued that this casts serious doubt on the validity of Palatini f(R) gravity as a viable alternative to General Relativity. In the present paper we further investigate this characteristic of Palatini f(R) gravity in order to clarify its physical interpretation and consequences.Comment: 15 pages. CQG in press. Part of the material moved to an appendix, discussion on the meV scale predictions of Palatini f(R) gravity adde

Corrections and Comments on the Multipole Moments of Axisymmetric Electrovacuum Spacetimes

Following the method of Hoenselaers and Perj\'{e}s we present a new corrected and dimensionally consistent set of multipole gravitational and electromagnetic moments for stationary axisymmetric spacetimes. Furthermore, we use our results to compute the multipole moments, both gravitational and electromagnetic, of a Kerr-Newman black hole.Comment: This is a revised and corrected versio

Spontaneous scalarization of black holes and compact stars from a Gauss-Bonnet coupling

We identify a class of scalar-tensor theories with coupling between the scalar and the Gauss–Bonnet invariant that exhibit spontaneous scalarization for both black holes and compact stars. In particular, these theories formally admit all of the stationary solutions of general relativity, but these are not dynamically preferred if certain conditions are satisfied. Remarkably, black holes exhibit scalarization if their mass lies within one of many narrow bands. We find evidence that scalarization can occur in neutron stars as well

f(R)f(R) theory and geometric origin of the dark sector in Horava-Lifshitz gravity

Inclusion of $f(R)$ term in the action of Horava-Lifshitz quantum gravity with projectability but without detailed balance condition is investigated, where $R$ denotes the 3-spatial dimensional Ricci scalar. Conditions for the spin-0 graviton to be free of ghosts and instability are studied. The requirement that the theory reduce to general relativity in the IR makes the scalar mode unstable in the Minkowski background but stable in the de Sitter. It is remarkable that the dark sector, dark matter and dark energy, of the universe has a naturally geometric origin in such a setup. Bouncing universes can also be constructed. Scalar perturbations in the FRW backgrounds with non-zero curvature are presented.Comment: Mod. Phys. Lett. A26, 387-398 (2011

Cosmological perturbations in Palatini modified gravity

Two approaches to the study of cosmological density perturbations in modified theories of Palatini gravity have recently been discussed. These utilise, respectively, a generalisation of Birkhoff's theorem and a direct linearization of the gravitational field equations. In this paper these approaches are compared and contrasted. The general form of the gravitational lagrangian for which the two frameworks yield identical results in the long-wavelength limit is derived. This class of models includes the case where the lagrangian is a power-law of the Ricci curvature scalar. The evolution of density perturbations in theories of the type $f(R)=R-c /R^ b$ is investigated numerically. It is found that the results obtained by the two methods are in good agreement on sufficiently large scales when the values of the parameters (b,c) are consistent with current observational constraints. However, this agreement becomes progressively poorer for models that differ significantly from the standard concordance model and as smaller scales are considered

Torsion and accelerating expansion of the universe in quadratic gravitation

Several exact cosmological solutions of a metric-affine theory of gravity with two torsion functions are presented. These solutions give a essentially different explanation from the one in most of previous works to the cause of the accelerating cosmological expansion and the origin of the torsion of the spacetime. These solutions can be divided into two classes. The solutions in the first class define the critical points of a dynamical system representing an asymptotically stable de Sitter spacetime. The solutions in the second class have exact analytic expressions which have never been found in the literature. The acceleration equation of the universe in general relativity is only a special case of them. These solutions indicate that even in vacuum the spacetime can be endowed with torsion, which means that the torsion of the spacetime has an intrinsic nature and a geometric origin. In these solutions the acceleration of the cosmological expansion is due to either the scalar torsion or the pseudoscalar torsion function. Neither a cosmological constant nor dark energy is needed. It is the torsion of the spacetime that causes the accelerating expansion of the universe in vacuum. All the effects of the inflation, the acceleration and the phase transformation from deceleration to acceleration can be explained by these solutions. Furthermore, the energy and pressure of the matter without spin can produce the torsion of the spacetime and make the expansion of the universe decelerate as well as accelerate.Comment: 20 pages. arXiv admin note: text overlap with gr-qc/0604006, arXiv:1110.344

Conformal transformation in f(T)f(T) theories

It is well-known that $f(R)$ theories are dynamically equivalent to a particular class of scalar-tensor theories. In analogy to the $f(R)$ extension of the Einstein-Hilbert action of general relativity, $f(T)$ theories are generalizations of the action of teleparallel gravity. The field equations are always second order, remarkably simpler than $f(R)$ theories. It is interesting to investigate whether $f(T)$ theories have the similar conformal features possessed in $f(R)$ theories. It is shown, however, that $f(T)$ theories are not dynamically equivalent to teleparallel action plus a scalar field via conformal transformation, there appears an additional scalar-torsion coupling term. We discuss briefly what constraint of this coupling term may be put on $f(T)$ theories from observations of the solar system.Comment: 4 pages, Revision to be publishe

The influence of the Lande gg-factor in the classical general relativistic description of atomic and subatomic systems

We study the electromagnetic and gravitational fields of the proton and electron in terms of the Einstenian gravity via the introduction of an arbitrary Lande $g$-factor in the Kerr-Newman solution. We show that at length scales of the order of the reduced Compton wavelength, corrections from different values of the $g$-factor are not negligible and discuss the presence of general relativistic effects in highly ionized heavy atoms. On the other hand, since at the Compton-wavelength scale the gravitational field becomes spin dominated rather than mass dominated, we also point out the necessity of including angular momentum as a source of corrections to Newtonian gravity in the quantum description of gravity at this scale.Comment: 11 pages, 2 figure

The phase portrait of a matter bounce in Horava-Lifshitz cosmology

The occurrence of a bounce in FRW cosmology requires modifications of general relativity. An example of such a modification is the recently proposed Horava-Lifshitz theory of gravity, which includes a ``dark radiation'' term with a negative coefficient in the analog of the Friedmann equation. This paper describes a phase space analysis of models of this sort with the aim of determining to what extent bouncing solutions can occur. A simplification, valid in the relevant region, allows a reduction of the dimension of phase space so that visualization in three dimensions is possible. It is found that a bounce is possible, but not generic in models under consideration. Apart from previously known bouncing solutions some new ones are also described. Other interesting solutions found include ones which describe a novel sort of oscillating universes.Comment: 14 pages, 8 figure