Extending Sibgatullin's ansatz for the Ernst potential to generate a richer family of axially symmetric solutions of Einstein's equations

The scope of this talk is to present some preliminary results on an effort, currently in progress, to generate an exact solution of Einstein's equation, suitable for describing spacetime around a rotating compact object. Specifically, the form of the Ernst potential on the symmetry axis and its connection with the multipole moments is discussed thoroughly. The way to calculate the multipole moments of spacetime directly from the value of the Ernst potential on the symmetry axis is presented. Finally, a mixed ansatz is formed for the Ernst potential including parameters additional to the ones dictated by Sibgatullin. Thus, we believe that this talk can also serve as a comment on choosing the appropriate ansatz for the Ernst potential.Comment: Talk given in the 11th Conference on Recent Developments in Gravity, 2-5 June 2004, Lesbos, Greec

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

f(R) gravity, torsion and non-metricity

For both f(R) theories of gravity with an independent symmetric connection (no torsion), usually referred to as Palatini f(R) gravity theories, and for f(R) theories of gravity with torsion but no non-metricity, called U4 theories, it has been shown that the independent connection can actually be eliminated algebraically, as long as this connection does not couple to matter. Remarkably, the outcome in both case is the same theory, which is dynamically equivalent with an \omega_0=-3/2 Brans--Dicke theory. It is shown here that even for the most general case of an independent connection with both non-metricity and torsion one arrives at exactly the same theory as in the more restricted cases. This generalizes the previous results and explains why assuming that either the torsion or the the non-metricity vanishes ultimately leads to the same theory. It also demonstrates that f(R) actions cannot support an independent connection which carries dynamical degrees of freedom, irrespectively of how general this connection is, at least as long as there is no connection-matter coupling.Comment: v2: slightly shortened version published in CQG as a Fast Track Communicatio

Reply to "Can gravitational dynamics be obtained by diffeomorphism invariance of action?"

In a previous work we showed that, in a suitable setting, one can use diffeomorphism invariance in order to derive gravitational field equations from boundary terms of the gravitational action. Standing by our results we reply here to a recent comment questioning their validity.Comment: Accepted for publication in PR

Horava Gravity and Gravitons at a Conformal Point

Recently Horava proposed a renormalizable gravity theory with higher derivatives by abandoning the Lorenz invariance in UV. Here, I study the Horava model at $\lambda=1/3$, where an anisotropic Weyl symmetry exists in the UV limit, in addition to the foliation-preserving diffeomorphism. By considering linear perturbations around Minkowski vacuum, I show that the scalar graviton mode is completely disappeared and only the usual tensor graviton modes remain in the physical spectrum. The existence of the UV conformal symmetry is unique to the theory with the detailed balance and it is quite probable that $\lambda=1/3$ be the UV fixed point. This situation is analogous to $\lambda=1$, which is Lorentz invariant in the IR limit and is believed to be the IR fixed point.Comment: Added comments and references, Accepted in GER

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

f(R) Gravity with Torsion: The Metric-Affine Approach

The role of torsion in f(R) gravity is considered in the framework of metric-affine formalism. We discuss the field equations in empty space and in presence of perfect fluid matter taking into account the analogy with the Palatini formalism. As a result, the extra curvature and torsion degrees of freedom can be dealt as an effective scalar field of fully geometric origin. From a cosmological point of view, such a geometric description could account for the whole Dark Side of the Universe.Comment: 12 page

T-Duality For String in Horava-Lifshitz Gravity

We continue our study of the Lorentz breaking string theories. These theories are defined as string theory with modified Hamiltonian constraint which breaks the Lorentz symmetry of target space-time. We analyze properties of this theory in the target space-time that possesses isometry along one direction. We also derive the T-duality rules for Lorentz breaking string theories and show that they are the same as that of Buscher's T-duality for the relativistic strings.Comment: 17 pages, references adde

Constraining f(R) gravity in the Palatini formalism

Although several models of $f(R)$ theories of gravity within the Palatini approach have been studied already, the interest was concentrated on those that have an effect on the late-time evolution of the universe, by the inclusion for example of terms inversely proportional to the scalar curvature in the gravitational action. However, additional positive powers of the curvature also provide interesting early-time phenomenology, like inflation, and the presence of such terms in the action is equally, if not more, probable. In the present paper models with both additional positive and negative powers of the scalar curvature are studied. Their effect on the evolution of the universe is investigated for all cosmological eras, and various constraints are put on the extra terms in the actions. Additionally, we examine the extent to which the new terms in positive powers affect the late-time evolution of the universe and the related observables, which also determines our ability to probe their presence in the gravitational action.Comment: reference update and minor changes to match published versio

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