Showing papers in "General Relativity and Gravitation in 2005"

Dark energy and viscous cosmology

Abstract: Singularities in the dark energy universe are discussed, assuming that there is a bulk viscosity in the cosmic fluid. In particular, it is shown how the physically natural assumption of letting the bulk viscosity be proportional to the scalar expansion in a spatially flat FRW universe can drive the fluid into the phantom region (w −1) in the non-viscous case.

Cosmography: Cosmology without the Einstein equations

Abstract: How much of modern cosmology is really cosmography? How much of modern cosmology is independent of the Einstein equations? (Independent of the Friedmann equations?) These questions are becoming increasingly germane—as the models cosmologists use for the stress-energy content of the universe become increasingly baroque, it behaves us to step back a little and carefully disentangle cosmological kinematics from cosmological dynamics. The use of basic symmetry principles (such as the cosmological principle) permits us to do a considerable amount, without ever having to address the vexatious issues of just how much “dark energy”, “dark matter”, “quintessence”, and/or “phantom matter” is needed in order to satisfy the Einstein equations. This is the sub-sector of cosmology that Weinberg refers to as “cosmography”, and in this article I will explore the extent to which cosmography is sufficient for analyzing the Hubble law and so describing many of the features of the universe around us.

(Anti-)de Sitter black hole thermodynamics and the generalized uncertainty principle

Abstract: We extend the derivation of the Hawking temperature of a Schwarzschild black hole via the Heisenberg uncertainty principle to the de Sitter and anti-de Sitter spacetimes. The thermodynamics of the Schwarzschild-(anti-)de Sitter black holes is obtained from the generalized uncertainty principle of string theory and non-commutative geometry. This may explain why the thermodynamics of (anti-)de Sitter-like black holes admits a holographic description in terms of a dual quantum conformal field theory, whereas the thermodynamics of Schwarzschild-like black holes does not.

Four-parametric regular black hole solution

Abstract: We present a regular class of exact black hole solutions of the Einstein equations coupled with a nonlinear electrodynamics source. For weak fields the nonlinear electrodynamics becomes the Maxwell theory, and asymptotically the solutions behave as the Reissner–Nordstrom one. The class is endowed with four parameters, which can be thought of as the mass m, charge q, and a sort of dipole and quadrupole moments α and β, respectively. For α≥3, β≥4, and |q|≤2scm the corresponding solutions are regular charged black holes. For α = 3, they also satisfy the weak energy condition. For α = β = 0 we recover the Reissner–Nordstrom singular solution and for α = 3, β = 4 the family includes a previous regular black hole reported by the authors.

Cosmological black holes: A black hole in the Einstein-de Sitter universe

Abstract: As an example of a dynamical cosmological black hole, a spacetime that describes an expanding black hole in the asymptotic background of the Einstein-de Sitter universe is constructed. The black hole is primordial in the sense that it forms ab initio with the big bang singularity and its expanding event horizon is represented by a conformal Killing horizon. The metric representing the black hole spacetime is obtained by applying a time dependent conformal transformation on the Schwarzschild metric, such that the result is an exact solution with a matter content described by a two-fluid source. Physical quantities such as the surface gravity and other effects like perihelion precession, light bending and circular orbits are studied in this spacetime and compared to their counterparts in the gravitational field of the isolated Schwarzschild black hole. No changes in the structure of null geodesics are recorded, but significant differences are obtained for timelike geodesics, particularly an increase in the perihelion precession and the non-existence of circular timelike orbits. The solution is expressed in the Newman-Penrose formalism.

Post-newtonian parameters from alternative theories of gravity

Abstract: Alternative theories of gravity have been recently studied in connection with their cosmological applications, both in the Palatini and in the metric formalism. The aim of this paper is to propose a theoretical framework (in the Palatini formalism) to test these theories at the solar system level and possibly at the galactic scales. We exactly solve field equations in vacuum and find the corresponding corrections to the standard general relativistic gravitational field. On the other hand, approximate solutions are found in matter cases starting from a Lagrangian which depends on a phenomenological parameter. Both in the vacuum case and in the matter case the deviations from General Relativity are controlled by parameters that provide the Post-Newtonian corrections which prove to be in good agreement with solar system experiments.

Friedmann cosmology with decaying vacuum density

Abstract: Among the several proposals to solve the incompatibility between the observed small value of the cosmological constant and the huge value obtained by quantum field theories, we can find the idea of a decaying vacuum energy density, leading from high values at early times of universe evolution to the small value observed nowadays. In this paper we consider a variation law for the vacuum density recently proposed by Schutzhold on the basis of quantum field estimations in the curved, expanding background, characterized by a vacuum density proportional to the Hubble parameter. We show that, in the context of an isotropic and homogeneous, spatially flat model, the corresponding solutions retain the well established features of the standard cosmology, and, in addition, are in accordance with the observed cosmological parameters. Our scenario presents an initial phase dominated by radiation, followed by a dust era long enough to permit structure formation, and by an epoch dominated by the cosmological term, which tends asymptotically to a de Sitter universe. Taking the matter density equals to half of the vacuum energy density, as suggested by observation, we obtain a universe age given by Ht = 1.1, and a decelerating parameter equals to −1/2.

Compact anisotropic spheres with prescribed energy density

Abstract: New exact interior solutions to the Einstein field equations for anisotropic spheres are found. We utilise a procedure that necessitates a choice for the energy density and the radial pressure. This class contains the constant density model of Maharaj and Maartens (Gen. Rel. Grav. 21, 899–905 (1989)), and the variable density model of Gokhroo and Mehra (Gen. Rel. Grav. 26, 75–84 (1994)), as special cases. These anisotropic spheres match smoothly to the Schwarzschild exterior and gravitational potentials are well behaved in the interior. A graphical analysis of the matter variables is performed which points to a physically reasonable matter distribution.

Smarr's formula for black holes with non-linear electrodynamics

Abstract: It is known that for nonlinear electrodynamics the First Law of Black Hole Mechanics holds, however the Smarr’s formula for the total mass does not. In this contribution we discuss the point and determine the corresponding expressions for the Bardeen black hole solution that represents a nonlinear magnetic monopole. The same is done for the regular black hole solution derived by Ayon–Beato and Garcia [1], showing that in the case that variations of the electric charge are involved, the Smarr’s formula is no longer valid.

Gravity from local Lorentz violation

Abstract: In general relativity, gravitational waves propagate at the speed of light, and so gravitons are massless. The masslessness can be traced to symmetry under diffeomorphisms. However, another elegant possibility exists: masslessness can instead arise from spontaneous violation of local Lorentz invariance. We construct the corresponding theory of gravity. It reproduces the Einstein-Hilbert action of general relativity at low energies and temperatures. Detectable signals occur for sensitive experiments, and potentially profound implications emerge for our theoretical understanding of gravity.

Greybody factors of charged dilaton black holes in 2 + 1 dimensions

Abstract: We have studied the scalar perturbation of charged dilaton black holes in 2+1 dimensions. The black hole considered here is a solution to the low-energy string theory in 2+1 dimensions. The exact decay rates and the grey body factors for the massless minimally coupled scalar is computed for both the charged and the uncharged dilaton black holes. The charged and the uncharged black hole show similar behavior for grey body factors, reflection coefficients and decay rates.

WANDs of the black ring

Abstract: Necessary conditions for various algebraic types of the Weyl tensor in higher dimensions are determined. These conditions are then used to find Weyl aligned null directions for the black ring solution. It is shown that the black ring solution is algebraically special, of type Ii, while locally on the horizon the type is II. One exceptional subclass – the Myers-Perry solution – is of type D.

Noether symmetry in the higher order gravity theory

Abstract: We explore the conditions for the existence of Noether symmetries for higher order gravity theory, after introducing an auxiliary variable, which gives the correct quantum description of the theory. It turns out that the application of Noether theorem in higher order theory of gravity is a powerful tool to find the solution of the field equations. A few such physically reasonable solutions like power law inflation are presented.

Energy conditions, traversable wormholes and dust shells

Abstract: Firstly, we review the pointwise and averaged energy conditions, the quantum inequality and the notion of the “volume integral quantifier,” which provides a measure of the “total amount” of energy condition violating matter. Secondly, we present a specific metric of a spherically symmetric traversable wormhole in the presence of a generic cosmological constant, verifying that the null and the averaged null energy conditions are violated, as was to be expected. Thirdly, a pressureless dust shell is constructed around the interior wormhole spacetime by matching the latter geometry to a unique vacuum exterior solution. In order to further minimize the usage of exotic matter, we then find regions where the surface energy density is positive, thereby satisfying all of the energy conditions at the junction surface. An equation governing the behavior of the radial pressure across the junction surface is also deduced. Lastly, taking advantage of the construction, specific dimensions of the wormhole, namely, the throat radius and the junction interface radius, and estimates of the total traversal time and maximum velocity of an observer journeying through the wormhole, are also found by imposing the traversability conditions.

Acceleration of the Universe with a simple trigonometric potential

Abstract: In this paper, we investigate the quintessence model with a minimally coupled scalar field in the context of recent supernovae observations. By choosing a particular form of the deceleration parameter q, which gives an early deceleration and late time acceleration for the dust dominated model, we show that this sign flip in q can be obtained by a simple trigonometric potential. The early matter dominated model expands with q = 1/2 as desired and enters a negative q phase quite late during the evolution.

A superdense star model as charged analogue of Schwarzschild?s interior solution

Abstract: A charged analogue of Schwarzschild’s interior solution has been derived by considering the non-gravitational energy density to be constant along with a special choice of electric intensity. The charged fluid sphere so obtained is seen to be more general than that of P.S. Florides and joins smoothly with the Reissner-Nordstrom metric at the pressure-free interface. Also the new charged fluid sphere is capable of representing a superdense star with surface density of 2×1014 g cm−3 which can occupy maximum mass 1.502408 times the solar mass. In the process of deriving the solution, the authors have also come across A. L. Mehra’s gaseous charged fluid model which is found to be unphysical as it has negative pressure at least at the center of the model.

On static spherically symmetric solutions of the vacuum Brans-Dicke theory

Abstract: It is shown that among the four classes of the static spherically symmetric solutions of the vacuum Brans-Dicke theory of gravity only two are really independent. Further, by matching exterior and interior (due to physically reasonable spherically symmetric matter source) scalar fields it is found that only the Brans class I solution with a certain restriction on the solution parameters may represent an exterior metric for a nonsingular massive object. The physical viability of the black hole nature of the solution is investigated. It is concluded that no physical black hole solution different from the Schwarzschild black hole is available in the Brans-Dicke theory.

The similarity hypothesis in general relativity

Abstract: Self-similar models are important in general relativity and other fundamental theories. In this paper we shall discuss the “similarity hypothesis”, which asserts that under a variety of physical circumstances solutions of these theories will naturally evolve to a self-similar form. We will find there is good evidence for this in the context of both spatially homogenous and inhomogeneous cosmological models, although in some cases the self-similar model is only an intermediate attractor. There are also a wide variety of situations, including critical phenomena, in which spherically symmetric models tend towards self-similarity. However, this does not happen in all cases and it is important to understand the prerequisites for the conjecture.

A Vaidya-type radiating solution in Einstein-Gauss-Bonnet gravity and its application to braneworld

Abstract: We consider a Vaidya-type radiating spacetime in Einstein gravity with the Gauss-Bonnet combination of quadratic curvature terms. Simply generalizing the known static black hole solutions in Einstein-Gauss-Bonnet gravity, we present an exact solution in arbitrary dimensions with the energy-momentum tensor given by a null fluid form. As an application, we derive an evolution equation for the “dark radiation” in the Gauss-Bonnet braneworld.

Non-spherical sources of static gravitational fields: Investigating the boundaries of the no-hair theorem

Abstract: A new, globally regular model describing a static, non spherical gravitating object in General Relativity is presented. The model is composed by a vacuum Weyl–Levi-Civita special field – the so called gamma metric – generated by a regular static distribution of mass-energy. Standard requirements of physical reasonableness such as, energy, matching and regularity conditions are satisfied. The model is used as a toy in investigating various issues related to the directional behavior of naked singularities in static spacetimes and the black hole (Schwarzschild) limit.

A model to explain varying Λ, G and σ 2 simultaneously

Abstract: Models with varying cosmic parameters, which were earlier regarded constant, are getting attention. However, different models are usually invoked to explain the evolution of different parameters. We argue that whatever physical process is responsible for the evolution of one parameter, should also be responsible for the evolution of others. This means that the different parameters are coupled together somehow. Based on this guiding principle, we investigate a Bianchi type I model with variable Λ and G, in which Λ, G and the shear parameter σ2, all are coupled. It is interesting that the resulting model reduces to the FLRW model for large t with G approaching a constant.

Does inflation provide natural initial conditions for the universe

Abstract: If our universe underwent inflation, its entropy during the inflationary phase was substantially lower than it is today. Because a low-entropy state is less likely to be chosen randomly than a high-entropy one, inflation is unlikely to arise through randomly-chosen initial conditions. To resolve this puzzle, we examine the notion of a natural state for the universe, and argue that it is a nearly-empty spacetime. If empty space has a small vacuum energy, however, inflation can begin spontaneously in this background. This scenario explains why a universe like ours is likely to have begun via a period of inflation, and also provides an origin for the cosmological arrow of time.

Is brane cosmology predictable

Abstract: The creation of the inflationary brane universe in 5d bulk Einstein and Einstein-Gauss-Bonnet gravity is considered. We demonstrate that the emerging universe is ambiguous due to arbitrary function dependence of the junction conditions (or freedom in the choice of boundary terms). We argue that some fundamental physical principle (which may be related with AdS/CFT correspondence) is necessary in order to fix the 4d geometry in a unique way.

Dimensions and units in electrodynamics

Abstract: We sketch the foundations of classical electrodynamics, in particular the transition that took place when Einstein, in 1915, succeeded to formulate general relativity. In 1916 Einstein demonstrated that, with a choice of suitable variables for the electromagnetic field, it is possible to put Maxwell’s equation into a form that is covariant under general coordinate transformations. This unfolded, by basic contributions of Kottler, Cartan, van Dantzig, Schouten & Dorgelo, Toupin & Truesdell, and Post, to what one may call premetric classical electrodynamics. This framework will be described shortly. An analysis is given of the physical dimensions involved in electrodynamics and subsequently the question of units addressed. It will be pointed out that these results are untouched by the generalization of classical to quantum electrodynamics (QED). We compare critically our results with those of L.B. Okun which he had presented at a recent conference.

Rotating metrics admitting non-perfect fluids

Abstract: In this paper an application of Newman-Janis algorithm in spherically symmetric metrics with the functions M(u,r) and e(u,r) has been discussed. After the transformation of the metric via this algorithm, these two functions M(u,r) and e(u,r) will be transformed to depend on the three variables u,r,θ. With these functions of three variables, all the Newman–Penrose (NP) spin coefficients, the Ricci as well as the Weyl scalars have been calculated from the Cartan’s structure equations. Using these NP quantities, we first give examples of rotating solutions of Einstein’s field equations like Kerr–Newman, rotating Vaidya solution and rotating Vaidya–Bonnor solution. It is found that the technique developed by Wang and Wu can be used to give further examples of embedded rotating solutions, that the rotating Kerr–Newman solution can be combined smoothly with the rotating Vaidya solution to derive the Kerr–Newman–Vaidya solution, and similarly, Kerr–Newman–Vaidya–Bonnor solution of the field equations. It has also shown that the embedded universes like Kerr–Newman de Sitter, rotating Vaidya–Bonnor–de Sitter, Kerr–Newman–Vaidya–de Sitter can be derived from the general solutions with Wang–Wu function. All rotating embedded solutions derived here can be written in Kerr–Schild forms, showing the extension of Xanthopoulos’s theorem. It is also found that all the rotating solutions admit non-perfect fluids.

Exact solutions of the Einstein-Maxwell equations with closed timelike curves

Abstract: We examine two electrovac spacetimes, the Kerr-Newman solution and another due to Perjes, which represent single charged, rotating, magnetic objects. Both contain regions with closed timelike curves (CTC), but these regions would be covered by the sources in any physical realisation of the spacetimes, so the CTC would not be detectable. We then study a stationary solution referring to two charged, rotating, magnetic objects. In general there is a region of CTC between the objects no matter how far apart they are. In this case the region would not be covered by the sources, and CTC would be detectable in principle.

Exact uncertainty approach in quantum mechanics and quantum gravity

Abstract: The assumption that an ensemble of classical particles is subject to nonclassical momentum fluctuations, with the fluctuation uncertainty fully determined by the position uncertainty, has been shown to lead from the classical equations of motion to the Schrodinger equation. This ‘exact uncertainty’ approach may be generalised to ensembles of gravitational fields, where nonclassical fluctuations are added to the field momentum densities, of a magnitude determined by the uncertainty in the metric tensor components. In this way one obtains the Wheeler-DeWitt equation of quantum gravity, with the added bonus of a uniquely specified operator ordering. No a priori assumptions are required concerning the existence of wave functions, Hilbert spaces, Planck's constant, linear operators, etc. Thus this approach has greater transparency than the usual canonical approach, particularly in regard to the connections between quantum and classical ensembles. Conceptual foundations and advantages are emphasised.

Near extremal Schwarzschild-de Sitter black hole area spectrum from quasi-normal modes

Abstract: Using the quasi-normal modes frequency of near extremal Schwar-zschild-de Sitter black holes, we obtain area and entropy spectrum for the black hole horizon. By using Bohr-Sommerfeld quantization for an adiabatic invariant I = ∫dEω(E), where E is the energy of the system and ω(E) is the vibrational frequency, we arrive at an equally spaced mass spectrum. In the other terms, we extend directly the Kunstatter’s approach kun [6] to determine mass and entropy spectrum of near extremal Schwarzschild-de Sitter black holes which are asymptotically de Sitter rather than asymptotically flat. We show the mass and area spectrum is equally spaced only for a fixed l. For different l there are multiplets with different values of spacing.

Global existence of solutions for the relativistic Boltzmann equation with arbitrarily large initial data on a Bianchi Type I space-time

Abstract: We prove, for the relativistic Boltzmann equation on a Bianchi Type I space-time, a global existence and uniqueness theorem, for arbitrarily large initial data.