Palatini Gravity Research Articles

Dynamical generation of wormholes with charged fluids in quadratic Palatini gravity

The dynamical generation of wormholes within an extension of General Relativity (GR) containing (Planck's scale-suppressed) Ricci-squared terms is considered. The theory is formulated assuming the metric and connection to be independent (Palatini formalism) and is probed using a charged null fluid as a matter source. This has the following effect: starting from Minkowski space, when the flux is active the metric becomes a charged Vaidya-type one, and once the flux is switched off the metric settles down into a static configuration such that far from the Planck scale the geometry is virtually indistinguishable from that of the standard Reissner-Nordstr\"om solution of GR. However, the innermost region undergoes significant changes, as the GR singularity is generically replaced by a wormhole structure. Such a structure becomes completely regular for a certain charge-to-mass ratio. Moreover, the nontrivial topology of the wormhole allows to define a charge in terms of lines of force trapped in the topology such that the density of lines flowing across the wormhole throat becomes a universal constant. To the light of our results we comment on the physical significance of curvature divergences in this theory and the topology change issue, which support the view that space-time could have a foam-like microstructure pervaded by wormholes generated by quantum gravitational effects.

Differential geometry, Palatini gravity and reduction

The present article deals with a formulation of the so called (vacuum) Palatini gravity as a general variational principle. In order to accomplish this goal, some geometrical tools related to the geometry of the bundle of connections of the frame bundle LM are used. A generalization of Lagrange-Poincaré reduction scheme to these types of variational problems allows us to relate it with the Einstein-Hilbert variational problem. Relations with some other variational problems for gravity found in the literature are discussed.

Stellar structure equations in extended Palatini gravity

We consider static spherically symmetric stellar configurations in Palatini theories of gravity in which the Lagrangian is an unspecified function of the form $f(R,R_{\mu\nu}R^{\mu\nu})$. We obtain the Tolman-Oppenheimer-Volkov equations corresponding to this class of theories and show that they recover those of $f(R)$ theories and General Relativity in the appropriate limits. We show that the exterior vacuum solutions are of Schwarzschild-de Sitter type and comment on the possible expected modifications, as compared to GR, of the interior solutions.

Black hole formation from a null fluid in extended Palatini gravity

We study the formation and perturbation of black holes by null fluxes of neutral matter in a quadratic extension of General Relativity formulated a la Palatini. Working in a spherically symmetric space-time, we obtain an exact analytical solution for the metric that extends the usual Vaidya-type solution to this type of theories. We find that the resulting space-time is formally that of a Reissner-Nordstrom black hole but with an effective charge term carrying the wrong sign in front of it. This effective charge is directly related to the luminosity function of the radiation stream. When the ingoing flux vanishes, the charge term disappears and the space-time relaxes to that of a Schwarzschild black hole. We provide two examples that illustrate the formation of a black hole from Minkowski space and the perturbation by a finite pulse of radiation of an existing Schwarzschild black hole.

Isotropic and anisotropic bouncing cosmologies in Palatini gravity

We study isotropic and anisotropic (Bianchi I) cosmologies in Palatini $f(R)$ and $f(R,R_{\mu\nu}R^{\mu\nu})$ theories of gravity and consider the existence of non-singular bouncing solutions in the early universe. We find that all $f(R)$ models with isotropic bouncing solutions develop shear singularities in the anisotropic case. On the contrary, the simple quadratic model $R+a R^2/R_P+R_{\mu\nu}R^{\mu\nu}/R_P$ exhibits regular bouncing solutions in both isotropic and anisotropic cases for a wide range of equations of state, including dust (for $a<0$) and radiation (for arbitrary $a$). It thus represents a purely gravitational solution to the big bang singularity and anisotropy problems of general relativity without the need for exotic ($w>1$) sources of matter/energy.

Gödel-type universes in Palatinif(R)gravity

We examine the question as to whether the Palatini f(R) gravity theories permit space-times in which the causality is violated. We show that every perfect-fluid G\"{o}del-type solution of Palatini f(R) gravity with density $\rho$ and pressure $p$ that satisfy the weak energy condition $\rho+p \geq 0$ is necessarily isometric to the G\"odel geometry, demonstrating therefore that these theories present causal anomalies in the form of closed time-like curves. This result extends a theorem on G\"{o}del-type models to the framework of Palatini f(R) gravity theory. We concretely examine the G\"odel-type perfect-fluid solutions in specific $f(R) = R - \alpha/R^{n}$ Palatini gravity theory, where the free parameters $\alpha$ and $n$ have been recently constrained by a diverse set of observational data. We show that for positive matter density and for $\alpha$ and $n$ within the interval permitted by the observational data, this theory does not admit the G\"odel geometry as a perfect-fluid solution of its field equations. In this sense, this theory remedies the causal pathology in the form of closed time-like curves which is allowed in general relativity. We derive an expression for a critical radius $r_c$ (beyond which the causality is violated) for an arbitrary Palatini f(R) theory, thus making apparent that the violation of causality depends on the form of f(R) and on the matter content components. We also examine the violation of causality of G\"odel-type by considering a single scalar field as the matter content. For this source we show that Palatini f(R) gravity gives rise to a unique G\"odel-type solution with no violation of causality.

Indistinguishable macroscopic behaviour of Palatini gravities and general relativity

We show that, within some modified gravity theories, such as the Palatini models, the nonlinear nature of the field equations implies that the usual naïve averaging procedure (replacing the microscopic energy–momentum by its cosmological average) could be invalid. As a consequence, the relative motion of particles in Palatini theories is actually indistinguishable from that predicted by general relativity. Moreover, there is no WEP violation. Our new and most important result is that the cosmology and astrophysics, or put more generally, the behaviours on macroscopic scales, predicted by these two theories are the same, and as a result the naturalness problems associated with the cosmological constant are not alleviated. Palatini gravity does however predict alterations to the internal structure of particles and the particle physics laws, e.g., corrections to the hydrogen energy levels. Measurements of which place strong constraints on the properties of viable Palatini gravities.

Geodesic congruences in the Palatinif(R)theory

We shall investigate the properties of a congruence of geodesics in the framework of Palatini $f(\mathcal{R})$ theories. We shall evaluate the modified geodesic deviation equation and the Raychaudhuri's equation and show that $f(\mathcal{R})$ Palatini theories do not necessarily lead to attractive forces. Also, we shall study energy condition for $f(\mathcal{R})$ Palatini gravity via a perturbative analysis of the Raychaudhuri's equation.

Microscopic and macroscopic behaviors of Palatini modified gravity theories

We show that, within modified gravity, the nonlinear nature of the field equations implies that the usual naieve averaging procedure (replacing the microscopic energy-momentum by its cosmological average) is invalid. We discuss then how the averaging should be performed correctly and show that, as a consequence, at the classical level the physical masses and geodesics of particles, cosmology, and astrophysics in Palatini modified gravity theories are all indistinguishable from the results of general relativity plus a cosmological constant. Palatini gravity is, however, a different theory from general relativity and predicts different internal structures of particles from the latter. On the other hand, and in contrast to classical particles, the electromagnetic field permeates in the space, and hence a different averaging procedure should be applied here. We show that, in general, Palatini gravity theories would then affect the propagation of photons, thus changing the behavior of a Universe dominated by radiation. Finally, Palatini theories also predict alterations to particle physics laws. For example, they can lead to sensitive corrections to the hydrogen energy levels, the measurements of which could be used to place very strong constraints on the properties of viable Palatini gravity theories.

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 utilize, respectively, a generalization 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/Rb 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.

Diffeomorphism invariance of geometric descriptions of Palatini and Ashtekar gravity

In this paper, we explicitly prove the presymplectic forms of the Palatini and Ashtekar gravity to be zero along gauge orbits of the Lorentz and diffeomorphism groups, which ensures the diffeomorphism invariance of these theories.

Space-time covariant form of Ashtekar’s constraints

The Lagrangian formulation of classical field theories and, in particular, general relativity leads to a coordinate-free, fully covariant analysis of these constrained systems. This paper applies multisymplectic techniques to obtain the analysis of Palatini and self-dual gravity theories as constrained systems, which have been studied so far in the Hamiltonian formalism. The constraint equations are derived while paying attention to boundary terms, and the Hamiltonian constraint turns out to be linear in the multimomenta. The equivalence with Ashtekar’s formalism is also established. The whole constraint analysis, however, remains covariant in that the multimomentum map is evaluated onany space-like hypersurface. This study is motivated by the non-perturbative quantization programme of general relativity.