General Relativity And Quantum Cosmology

The peculiarities of the inverse square law of Newtonian gravity in standard Big Bang Cosmology are discussed. It is shown that the incorporation of an additive term to Newtonian gravitation, as the inverse Yukawa-like field, allows remove the incompatibility between the flatness of the Universe and the density of matter in the Friedmann equation, provides a new approach for dark energy, and enable theoretical deduce the Hubble-Lemaitre's law. The source of this inverse Yukawa-like field is the ordinary baryonic matter and represents the large-scale contribution of gravity in accordance with the Mach's principle. It's heuristically build from a specular reflection of the Yukawa potential, in agreement with astronomical and laboratory observables, result null in the inner solar system, weakly attractive in ranges of interstellar distances, very attractive in distance ranges comparable to the clusters of galaxies and repulsive in cosmic scales. Its implications in the missing mass of Zwicky, Virial Theorem, Kepler's Third Law in Globular Clusters, rotations curves of galaxies, gravitational redshift and the Jean's mass are discussed. The inclusion of the inverse Yukawa-like field in Newtonian gravitation predicts a graviton mass of at least 10-64 kg and could be an alternative to the paradigm of non-baryonic dark matter concomitant with the observables of the Big Bang.

We provide a new five dimensional black string--like solution by means of the embedding of a four dimensional regular black hole into a compact extra dimension. We enunciate a list of constraints in order to that the five dimensional black string--like solution to be regular, and, following these constraints we construct our solution. Instead of the usual singularity, it is formed a core whose topology corresponds to the product between the de--Sitter core of the four dimensional Hayward solution and S 1 . The horizon has topology S 2 ? S 1 . At infinity of the radial coordinate the regular four dimensional geometry is asymptotically flat, {\it i.e}, at this place the topology of the complete solution corresponds to the product between Minkowski and S 1 . At the induced four dimensional geometry we compute the correct values of temperature and entropy.

The recent opening of gravitational wave astronomy has shifted the debate about black hole mimickers from a purely theoretical arena to a phenomenological one. In this respect, missing a definitive quantum gravity theory, the possibility to have simple, meta-geometries describing in a compact way alternative phenomenologically viable scenarios is potentially very appealing. A recently proposed metric by Simpson and Visser is exactly an example of such meta-geometry describing, for different values of a single parameter, different non-rotating black hole mimickers. Here, we employ the Newman--Janis procedure to construct a rotating generalisation of such geometry. We obtain a stationary, axially symmetric metric that depends on mass, spin and an additional real parameter ??. According to the value of such parameter, the metric may represent a rotating traversable wormhole, a rotating regular black hole with one or two horizons, or three more limiting cases. By studying the internal and external rich structure of such solutions, we show that the obtained metric describes a family of interesting and simple regular geometries providing viable Kerr black hole mimickers for future phenomenological studies.

The Planck or the quantum gravity scale, being 16 orders of magnitude greater than the electroweak scale, is often considered inaccessible by current experimental techniques. However, it was shown recently by one of the current authors that quantum gravity effects via the Generalized Uncertainty Principle affects the time required for free wavepackets to double their size, and this difference in time is at or near current experimental accuracies [1, 2]. In this work, we make an important improvement over the earlier study, by taking into account the leading order relativistic correction, which naturally appears in the systems under consideration, due to the significant mean velocity of the travelling wavepackets. Our analysis shows that although the relativistic correction adds nontrivial modifications to the results of [1, 2], the earlier claims remain intact and are in fact strengthened. We explore the potential for these results being tested in the laboratory.

We investigate bounce solutions for single scalar field theories, with and without Einstein-Hilbert gravity, considering a false vacuum living on flat Euclidean spacetime. We find that, under appropriate conditions, the behaviour of the scalar field far away from the bubble is independent on the form of the potential and it may be determined analytically. In particular, we need the scalar field to be massless, or light, and cubic self-interactions should be small. We mainly discuss Einstein-Hilbert gravity, and, in particular, the case of the Higgs decay, but generalizations to modified gravity are in principle possible. We use our findings to introduce a novel numerical procedure based on minimization, as an alternative to the shooting method.

Motivated by the study of physical models associated with General Relativity, we review some finite-dimensional, geometric and covariant formulations that allow us to characterize in a simple manner the symmetries for classical field theory by implementing an appropriate fibre-bundle structure, either at the Lagrangian, the multisymplectic or the polysymplectic levels. In particular, we are able to formulate Noether's theorems by means of the covariant momentum maps and to systematically introduce a covariant Poisson-Hamiltonian framework. Also, by focusing on the space plus time decomposition for a generic classical field theory and its relation to these geometric formulations, we are able to successfully recover the gauge content and the true local degrees of freedom for the theory. In order to illustrate the relevance of these geometric frameworks, we center our attention to the analysis of a model for 3 -dimensional theory of General Relativity that involves an arbitrary Immirzi-like parameter. At the Lagrangian level, we reproduce the field equations of the system which for this model turn out to be equivalent to the vanishing torsion condition and the Einstein equations. We also concentrate on the analysis of the gauge symmetries of the system in order to obtain the Lagrangian covariant momentum map associated with the theory and, consequently, its corresponding Noether currents. Next, we aim our attention to describing how the gauge symmetries of the model yield covariant canonical transformations on the covariant multimomenta phase-space, thus giving rise to the existence of a covariant momentum map. Besides, we analyze the physical system under consideration within the De Donder-Weyl canonical theory implemented at the polysymplectic level, thus establishing a relation from the covariant momentum map to the conserved currents of the theory.

In this note we characterize 1+n doubly twisted spacetimes in terms of `doubly torqued' vector fields. They extend Bang-Yen Chen's characterization of twisted and generalized Robertson-Walker spacetimes with torqued and concircular vector fields. The result is a simple classification of 1+n doubly-twisted, doubly-warped, twisted and generalized Robertson-Walker spacetimes.

The stability of the recently proposed static solutions for boson stars is analyzed. These solutions of Einstein-Klein-Gordon (EKG) equations arise from considering the interaction of a real scalar field with matter. We assume that the inclusion of the scalar field in addition with matter, allows to justify that stability implies that the total mass of the solution should grow when the initial condition for the density of matter at the origin is also increased. Employing numerical values for the static boson star based on a linear relation between the source and the energy density and between this and the pressure, we found the relation that linked the the scalar field at the origin with the matter energy density (MED) in the same point. We also determine the behavior of the total mass (TM) with the matter energy density in the origin, by also obtaining through this and the weak energy condition, two possible ranges for stable solutions of static boson stars.

We propose a unified version of hoop conjecture valid for various black holes and horizonless compact stars. This conjecture is expressed by the mass to circumference ratio 4? M in /C�? , where C is the circumference of the smallest ring that can engulf the object in all azimuthal directions and M in is the mass within the engulfing sphere.

In this paper, we investigate the Weak Cosmic Censorship Conjecture in nearly extremal Kerr black hole by absorbing particles . In previous work, they ignore the process of black hole absorbing particles. They assume the whole particle can be absorbed and the overspinning occurs. However, it is questionable whether the whole particle can be absorbed. Therefore, we will investigate it in this paper. We consider the absorption process of a particle with finite size. During this absorption process, the black hole's parameters will change. This change will prevent the rest part of particle enter black hole. We show the part entering black hole can not overspin a nearly extremal Kerr black hole. Different from Sorce and Wald, we solve the overspinning problem for Kerr black hole without radiation effect or self-force effect. Further, we use this process to a general black hole. Under three assumptions, we show if Weak Cosmic Censorship Conjecture is valid for an extremal black hole by absorbing a particle, it will be valid for the corresponding nearly extremal black hole. In many situation, the extremal black holes satisfy Weak Cosmic Censorship Conjecture and the corresponding nearly extremal black holes don't satisfy it. Therefore, if those black holes satisfy three assumptions, these violations may be solved by absorption process.