Self-consistent solutions of the semi-classical back-reaction equations with cosmological constant spatial curvature and perfect fluid

Exact solutions of the semi-classical Einstein equations with cosmological constant for conformally invariant free quantum fields in a general Robertson-Walker metric are found when a classical perfect fluid is present. There exist a one-parameter family of time-symmetric bouncing solutions that avoid the singularity and a one-parameter family which does not have particles horizons. The de Sitter solution is found to be stable, while the Einstein universe is unstable.     

Vaidya black hole in non-stationary de Sitter space: Hawking’s temperature

In this paper we present a class of non-stationary solutions of Einstein’s field equations describing embedded Vaidya-de Sitter black holes with a cosmological variable function Λ(u). The Vaidya-de Sitter black hole is interpreted as the radiating Vaidya black hole is embedded into the non-stationary de Sitter space with variable Λ(u). The energy-momentum tensor of the Vaidya-de Sitter black hole is expressed as the sum of the energy-momentum tensors of the Vaidya null fluid and that of the non-stationary de Sitter field, and satisfies the energy conservation law. We study the energy conditions (like weak, strong and dominant conditions) for the energy-momentum tensor. We find the violation of the strong energy condition due to the negative pressure and leading to a repulsive gravitational force of the matter field associated with Λ(u) in the space-time. We also find that the time-like vector field for an observer in the Vaidya-de Sitter space is expanding, accelerating, shearing and non-rotating. It is also found that the space-time geometry of non-stationary Vaidya-de Sitter solution with variable Λ(u) is Petrov type D in the classification of space-times. We also find the Vaidya-de Sitter black hole radiating with a thermal temperature proportional to the surface gravity and entropy also proportional to the area of the cosmological black hole horizon.     

Gravitational collapse in generalized Vaidya space-time for Lovelock gravity theory

In this work, we have assumed the generalized Vaidya solution in Lovelock theory of gravity in (n+2)-dimensions. It has been shown that Gauss-Bonnet gravity, dimensionally continued Lovelock gravity and pure Lovelock gravity can be constructed by suitable choice of parameters. We have investigated the occurrence of singularities formed by the gravitational collapse in above three particular forms of Lovelock theory of gravity. The dependence of the nature of singularity on the existence of radial null geodesic for Vaidya space-time has been specially considered. In all the three models, we have shown that the nature of singularities (naked singularity or black hole) completely depend on the parameters. Choices of various parameters are shown in tabular form. In Gauss-Bonnet gravity theory, it can be concluded that the possibility of naked singularity increases with increase in dimensions. In dimensionally continued Lovelock gravity, the naked singularity is possible for odd dimensions for several values of parameters. In pure Lovelock gravity, only black hole forms due to the gravitational collapse for any values of parameters. It has been shown that when accretion is taking place on a collapsing object, it is highly unlikely to get a black hole. Finally on considering the phantom era in the expanding universe it is observed that there is no possibility of formation of a black hole if we are in the Gauss-Bonnet gravity considering the accreting procedure upon a collapsing object.     

A new independent limit on the cosmological constant/dark energy from the relativistic bending of light by Galaxies and clusters of Galaxies

We derive new limits on the value of the cosmological constant, Λ, based on the Einstein bending of light by systems where the lens is a distant galaxy or a cluster of galaxies. We use an amended lens equation in which the contribution of Λ to the Einstein deflection angle is taken into account and use observations of Einstein radii around several lens systems. We use in our calculations a Schwarzschild–de Sitter vacuole exactly matched into a Friedmann–Robertson–Walker background and show that a Λ-contribution term appears in the deflection angle within the lens equation. We find that the contribution of the Λ-term to the bending angle is larger than the second-order term for many lens systems. Using these observations of bending angles, we derive new limits on the value of Λ. These limits constitute the best observational upper bound on Λ after cosmological constraints and are only two orders of magnitude away from the value determined by those cosmological constraints.     

Strange star model with Tolmann IV type potential

We report a general solution in one of the gravitational potentials to the Einstein system in static spherically symmetric spacetime, modeling anisotropic strange quark matter by imposing a linear barotropic equation of state. The model generated by choosing Tolmann IV form for the gravitational potential is shown to contain the previously known anisotropic dark energy star model of Lobo (Class. Quantum Gravity 23:1525, 2006) and isotropic models of de Sitter and Einstein. Moreover, the model is shown to be physically admissible and corroborate with experimental observations on strange star candidates such as SAX J1808.4-3658 and 4U 1820-30.     

Metric conditions for clusters in hierarchical cosmologies

Algebraic conditions on the continuity of the components of the metric tensor are employed to get an approximate metric in four limiting forms relevant to a condensation in an expanding Einstein/de Sitter substratum. The metric of the condensation is in general spherically-symmetric, nonstatic and asymptotically flat, passing over into the usual Friedmann solution at large distances and late times. The line-element derived supersedes an earlier incorrect formulation of the problem by Einstein and Straus. The metric is applicable in particular to clusters of galaxies, wich cannot avoid being involved in the expansion of the Universe for the density-distributions relevant to average loose clusters as presently observed. It is likely that all clusters, including compact ones, are in a state of dynamical evolution, a conclusion which may remove the missing mass problem. The results found agree, in this respect, with recent work by Noerdlinger and Petrosian, and give effective Hubble parmeters for systems in an expanding substratum.     

Gravitational collapse, black holes and naked singularities

This article gives an elementary review of gravitational collapse and the cosmic censorship hypothesis. Known models of collapse resulting in the formation of black holes and naked singularities are summarized. These models, when taken together, suggest that the censorship hypothesis may not hold in classical general relativity. The nature of the quantum processes that take place near a naked singularity, and their possible implication for observations, is briefly discussed.     

Generalized de Sitter solution in multi-dimensional cosmology with static internal spaces

A multi-dimensional cosmological model with space-time consisting of n(n ≥ 2) Einstein spaces M_i is investigated in the presence of a cosmological constant λ and a homogeneous minimally coupled free scalar field. A generalized de Sitter solution was found for λ > 0 and a Ricci-flat external space for the case of static internal spaces with fine tuning of parameters.     

Dynamical evolution of an unstable gravastar with zero mass

Using the conventional gravastar model, that is, an object constituted by two components where one of them is a massive infinitely thin shell and the other one is a de Sitter interior spacetime, we physically interpret a solution characterized by a zero Schwarzschild mass. No stable gravastar is formed and it collapses without forming an event horizon, originating what we call a massive non-gravitational object. The most surprise here is that the collapse occurs with an exterior de Sitter vacuum spacetime. This creates an object which does not interact gravitationally with an outside test particle and it may evolve to a point-like topological defect.     

Black hole solutions in warped DGP brane world

Using the effective gravitational field equations in the warped DGP brane-world scenario (Maeda et al. in Phys. Rev. D 68:024033, 2003), we study spherically symmetric vacuum (static black hole) solutions on the brane. Working with a conformally flat bulk, we have obtained an exact Schwarzschild–de Sitter black hole solution similar to the standard solution in the presence of a cosmological constant, which confirms the idea that an extra term in the effective vacuum field equations on the warped DGP brane can play the role of a positive cosmological constant.     

Exact Boltzmann-Gas Filled Bianchi Type V Space-Times

Bianchi type V cosmological models are studied that contain a relativistic ideal Boltzmann gas. The effect of a cosmological constant upon the space-time geometry is also considered. In both high and low temperature limit the general solution of the Einstein gravitational field equations can be expressed in an exact closed parametric form. At final stages, depending on the presence or absence of the cosmological constant, cosmologies are driven to an isotropic inflationary open de Sitter type Universe or to an isotropic open Friedmann era.     

Exact Nonbarotropic Bianchi Type I Universe

Bianchi type I cosmological models are studied that contain a nonbarotropic relativistic Boltzmann gas. The effect of a cosmological constant is considered too. In the limit of small temperatures the general solution of the Einstein gravitational field equations can be expressed in an exact closed parametrical form. At final stages, depending on the presence or absence of the cosmological constant, cosmologies are driven to an isotropic inflationary de Sitter Universe or to an isotropic Friedmann era. This revised version was published online in July 2006 with corrections to the Cover Date.     

Hawking’s radiation in non-stationary rotating de Sitter background

Hawking’s radiation effect of Klein-Gordon scalar field, Dirac particles and Maxwell’s electromagnetic field in the non-stationary rotating de Sitter cosmological space-time is investigated by using a method of generalized tortoise co-ordinates transformation. The locations and the temperatures of the cosmological horizons of the non-stationary rotating de Sitter model are derived. It is found that the locations and the temperatures of the rotating cosmological model depend not only on the time but also on the angle. The stress-energy regularization techniques are applied to the two dimensional analog of the de Sitter metrics and the calculated stress-energy tensor contains the thermal radiation effect.     

Singularities and cosmic censorship

We give an elementary overview of the subject of gravitational collapse in classical general relativity. Recent theoretical evidence for the formation of black-holes and naked singularities is summarised.     

Plane symmetric gravitational collapse and linear equation of state

This paper examines the gravitational collapse in plane symmetry with a perfect fluid using a linear equation of state p=kρ. We find a class of collapse models satisfying the Einstein field equations and also the regularity as well as energy conditions. For a given initial data, the outcome of the collapse turns out to be a black membrane or a naked singularity depending upon the equation of state parameter. We conclude that this parameter plays a crucial role in determining the final fate of the collapse.     

The post-collapse equilibrium structure of cosmological haloes in a low-density universe

An analytical model is presented for the post-collapse equilibrium structure of virialized objects that condense out of a low-density cosmological background universe, either matter-dominated or flat with a cosmological constant. This generalizes the model we derived previously for an Einstein–de Sitter (EdS) universe. The model is based upon the assumption that cosmological haloes form from the collapse and virialization of 'top-hat' density perturbations, and are spherical, isotropic and isothermal. This leads to the prediction of a unique, non-singular, truncated isothermal sphere (TIS), a particular solution of the Lane–Emden equation (suitably modified when Λ≠0) . The size and virial temperature are unique functions of the mass and redshift of formation of the object for a given background universe. The central density is roughly proportional to the critical density of the universe at the epoch of collapse. This TIS model is in good agreement with observations of the internal structure of dark-matter-dominated haloes on scales ranging from dwarf galaxies to X-ray clusters. It also reproduces many of the average properties of haloes in simulations of the cold dark matter (CDM) model to good accuracy, suggesting that it is a useful analytical approximation for haloes that form from realistic initial conditions. Our TIS model matches the density profiles of haloes in CDM N -body simulations outside the innermost region, while avoiding the steep central cusp of the latter which is in apparent conflict with observations. The TIS model may also be relevant to non-standard CDM models, such as that for self-interacting dark matter, recently proposed to resolve this conflict.     

Exact Bianchi Type-I Cosmological Micro Model in Modified Theory of General Relativity

An anisotropic, homogeneous Bianchi type-I cosmological micro model is obtained in Barber's modified theory of general relativity. Some properties of the model are discussed. Further, it is found that this theory leads to Einstein theory as the coupling parameterλ → 0 in micro level (i.e., quantum level) in general. This revised version was published online in July 2006 with corrections to the Cover Date.     

Extragalactic research in Europe and the United States in the early 20th century

While the theoretical foundations of modern relativistic cosmology were laid, to a large extent, by European researchers like Einstein, de Sitter, Friedmann, Lemaître, and others, observational cosmology was (and to a large extent, still is) dominated by US astronomers, working at Lick and Mt. Wilson observatories. From today's viewpoint, Hubble appears to dwarf all his – national and international – peers. However, Keeler and Curtis, Fath and Slipher carried put pioneering work in the US, as did Wolf, Wirtz, Lundmark, de Sitter in Europe, both by observation and by statistical analysis of data. European extragalactic research during the early 20th century is outlined and compared with studies in the United States. Reasons for the small impact of European research are a mixture of deliberate and accidental neglect and suppression, as well as the lack of technical and organizational infrastructure, which was especially noticeable after World War I.     

Energy–Momentum In The Viscous Kasner-Type Universe In Teleparallel Gravity

Using the teleparallel gravity versions of the Einstein and Landau–Lifshitz’s energy and/or momentum complexes, I obtain the energy and momentum of the universe in viscous Kasner-type cosmological models. The energy and momentum components (due to matter plus field) are found to be zero and this agree with a previous work of Rosen and Johri et al., who investigated the problem of the energy in Friedmann–Robertson–Walker (FRW) universe. The result that the total energy and momentum components of the universe in these models is zero same as Bergmann–Thomson’s energy–momentum and props the viewpoint of Tryon. Rosen found that the energy of the FRW space–time is zero, which agrees with the studies of Tryon. PACs Numbers: 04.20.-q; 04.50.+h An erratum to this article is available at .