Quantum string theory in curved space-times

A general method to quantize strings in curved space-times is exposed. It treats the space-time metric exactly and the string excitations small as compared with the energy scale of the geometry. The method is applied to cosmological (de Sitter) and black-hole (Schwarzschild) geometries. The critical dimension decreases in one for de Sitter and stays unaltered for black-holes as compared with flat space-time values. Bogoliubov transformations in the context of string theory are derived and the Bogoliubov coefficients describing elastic and inelastic scattering and excitation of modes are computed explicitely. The string-black-hole cross section is derived and a pair mode creation phenomena is found. The quantization and scattering of strings in shockwave geometries (ultrarelativistic boosted black-holes or Aichelburg-Sexl space time) is found to be exactly solvable.     

Gravitational stability of dark energy in galaxies and clusters of galaxies

We analyze the behavior of the scalar field as dark energy of the Universe in a static world of galaxies and clusters of galaxies. We find the analytical solutions of evolution equations of the density and velocity perturbations of dark matter and dark energy, which interact only gravitationally, along with the perturbations of metric in a static world with background Minkowski metric. It was shown that quintessential and phantom dark energy in the static world of galaxies and clusters of galaxies is gravitationally stable and can only oscillate by the influence of self-gravity. In the gravitational field of dark matter perturbations, it is able to condense monotonically, but the amplitude of density and velocity perturbations on all scales remains small. It was also illustrated that the “accretion” of phantom dark energy in the region of dark matter overdensities causes formation of dark energy underdensities-the regions with negative amplitude of density perturbations of dark energy.     

A primordial cosmological scenario with two scalar fields and matter

The presence of matter in its different forms in a hexadimensional space-time, where gravitation is coupled to a conformal field, generates a class of cosmological solutions with very peculiar features: the initial proper distance between any two points of the space-time is infinite, following successive contraction and expansion phases in the evolution of the Universe. This behaviour defines a Anti-Big Bang Singular Cosmology. In this article we analyze this primordial cosmological scenario considering different matter forms and the effects of a Conformal Transformation on the metric.     

Plane-symmetric vacuum in self-creation cosmology

Vacuum field equations for the static and non-static plane-symmetric metric are obtained in self-creation theory of gravitation proposed by Barber (1982). It is shown that, in both static and non-static cases, the only plane-symmetric solution in vacuum is the empty flat space-time of Einstein's theory. It is observed that this result is quite different from that of the Brans-Dicke and other scalar-tensor theories of gravitation.     

Schwarzschild black hole in dark energy background

In this paper we present an exact solution of Einstein’s field equations describing the Schwarzschild black hole in dark energy background. It is also regarded as an embedded solution that the Schwarzschild black hole is embedded into the dark energy space producing Schwarzschild-dark energy black hole. It is found that the space-time geometry of Schwarzschild-dark energy solution is non-vacuum Petrov type D in the classification of space-times. We study the energy conditions (like weak, strong and dominant conditions) for the energy-momentum tensor of the Schwarzschild-dark energy solution. We also find that the energy-momentum tensor of the Schwarzschild-dark energy solution violates the strong energy condition due to the negative pressure leading to a repulsive gravitational force of the matter field in the space-time. It is shown that the time-like vector field for an observer in the Schwarzschild-dark energy space is expanding, accelerating, shearing and non-rotating. We investigate the surface gravity and the area of the horizons for the Schwarzschild-dark energy black hole.     

Relation between physical and metric field in general relativity and cosmology

By assuming that the whole matter of the Universe possesses a dilatational degree of freedom, we attempted to show the equivalence between the curvedmetric of space-time and the flat metric of dilated space-time. In the framework of this procedure we supposed that the metrical field and the physical space and time change their roles. The basic result suggests that gravitation and dilatation are interrelated phenomena. In addition we discuss the possibility of the Universe which is of a hybrid type: it possesses at the same time properties of the evolutionary and stationary Universe. Finally, we discuss the lenghtening of day in time as an example which can support our ideas. There was suggested that this phenomenon appears partly as cosmological manifestation.     

Concerning the instantaneous mass and the extent of an expanding universe

In this article we want to answer the cosmologically relevant question what, with some good semantic and physical reason, could be called the massM _u of an infinitely extended, homogeneously matter‐filled and expanding universe. To answer this question we produce a space‐like sum of instantaneous cosmic energy depositions surrounding equally each spacepoint in the homogeneous universe. We calculate the added‐up instantaneous cosmic energy per volume around an arbitrary space point in the expanding universe. To carry out this sum we use as basic metrics an analogy to the inner Schwarzschild metric applied to stars, but this time applied to the spacepoint‐related universe. It is then shown that this leads to the added‐up proper energy within a sphere of a finite outer critical radius defining the point‐related infinity. As a surprise this radius turns out to be reciprocal to the square root of the prevailing average cosmic energy density. The equivalent mass of the universe can then also be calculated and, by the expression which is obtained here, shows a scaling with this critical radius of this universe, a virtue of the universe which was already often called for in earlier works by E. Mach, H. Thirring and F. Hoyle and others. This radius on the other hand can be shown to be nearly equal to the Schwarzschild radius of the so‐defined mass M _u of the universe. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Energy distribution of a stationary beam of light

Aguirregabiria et al. showed that Einstein, Landau and Lifshitz, Papapetrou, and Weinberg energy-momentum complexes coincide for all Kerr-Schild metric. Bringely used their general expression of the Kerr-Schild class and found energy and momentum densities for the Bonnor metric. In this paper the latter results are obtained without using Aguirregabiria et al results. This also supports Aguirregabiria et al results as well as Cooperstock hypothesis. We obtain further the energy distribution of the space-time under consideration.     

Gravitational energy, momentum and angular momentum of Schwarzschild Anti-de Sitter space-times in the teleparallel equivalent of general relativity

We give a class of spherically symmetric-Anti de Sitter (Ads), exact solution in the teleparallel equivalent of general relativity (TEGR). The solution depends on an arbitrary function F(R)\mathcal{F}(R) and reproduce the metric of Schwarzschild Ads space-time. In the context of the Hamiltonian formulation of the TEGR we compute the gravitational energy of this class. The calculation is carried out by means of an expression for the energy of the gravitational field that naturally arises from the integral form of the constraint equations of the formalism. We show that the form of the energy depends on the arbitrary function. We make a constrain on this arbitrary function to give the correct form of energy.     

Nonlinear gravidynamics: Energy-momentum tensor of collapsar field

In the bounds of a theoretical scheme treating consistently gravitational interaction as dynamical (gauge) field in flat space-time, an expression was obtained for the density of energy-momentum-tension of gravitational field in vacuum around a collapsed object. A case was studied of an interacting static spherically-symmetric field of a collapsar in vacuum with taking into account of input of all the possible components (spin states of virtual gravitons) into the energy for the symmetric tensor of second rank _ik . The radius of the sphere filled by matter for the collapsar of massM may achieve values up toGM/c ².     

Non,thermal Cosmic Gravitational Radiation and Redshift Fluctuations

Intergalactic gravitational radiation fields with wavelengths in the range of 1 to 10³ Megaparsecs have remarkable observational effects if the energy density of the fields becomes comparable to the equivalent “critical” cosmological matter density χo = 3H₀². In this case the perturbation in the space-time metric caused by the radiation field is high enough to change the frequency and to shift the path of light rays of extragalactic objects in a random manner by observable amounts. The present paper discusses the wave spectrum as a function of cosmic time and gives a statistical treatment of the redshift fluctuations.     

Non-vacuum static cylindrically symmetric solution and energy distribution in f(R) gravity

In this paper, we investigate static cylindrically symmetric solution in metric f(R) gravity by taking matter in the form of dust. The assumption of constant Ricci scalar curvature is taken to find the solution. The energy distribution of this solution is explored by applying Landau-Lifshitz energy-momentum complex. In addition, we explore the stability as well as constant scalar curvature conditions for some viable f(R) models along with their energy distribution. It is interesting to mention here that these models satisfy the above mentioned conditions.     

Relativistic parametric embedding class I solutions of cold stars in Karmarkar space-time continuum

The aim of this paper is to explore a new parametric class of relativistic solutions to the Einstein field equations describing a spherically symmetric, static distribution of anisotropic fluid spheres to study the behavior of some of the cold stars in the setting of Karmarkar space-time continuum. We develop models of stellar objects for a range of parameter values of n and analyze their behavior through graphical representation. For each of these models, we have found that the metric potentials are well behaved inside the stellar interior and the physical parameters such as density, radial and tangential pressures, red-shift, radial speed, radial pressure density ratio and energy conditions display a continuous decrease from the center to surface of the stars whereas the mass, anisotropy, adiabatic indexes and compactification factor show a monotonous increase which imply that the proposed solution satisfy all the physical aspects of a realistic stellar objects. The stability of the solutions are verified by examining various stability aspects, viz., Zeldovich criteria, causality condition, Bondi condition, equilibrium condition (TOV-equation) and stable static criteria in connection to their cogency.     

Plane symmetric solutions to the Einstein’s field equations with dark energy

In this paper, we solve the Einstein’s field equations for the space-time described by a special plane symmetric metric with dark energy, and the exact solutions which offer an alternative and complementary approach to study cosmological models are obtained. The dark energy is given by either the quintessence or the modified Chaplygin gas. We show the models are isotropic and analyze the expansion scalar and the deceleration parameter of the models.     

The Friedmann universe and the world potential

In Section 1 of the paper the energy equation of the Friedmann universe, when matter dominates over radiation, is discussed. It is known that the value of the world potential is constant everywhere in the Universe, despite the pulsation motion of the Universe or a possible transformation of pulsation energy into matter or vice versa. The condition for the Universe being closed is deduced. Furthermore, the possibility to define the mass-energy of the Universe is discussed; and the conclusion is arrived at that the mass-energy of the Universe relative to an observer in the non-metric space outside the Universe is equal to zero; i.e. the Universe originated as a vacuum fluctuation. Finally, the view-point of an external observer is described. Such an observer can claim that our closed Universe is a black hole in a non-metric empty space. Besides, the differences between such a black hole and the astrophysical black holes are indicated.In Section 2 the origin of the gravitational force retarding the expansion is discussed, using the properties of the relativistic gravitational potential. In contradiction to Section 1, the view-point of an inner observer (inside the Universe) is used here. It is concluded that the boundary of the closed Universe is an unlocalizable potential barrier.In Section 3 of the paper the apparent discrepancy between Mach's principle and the general theory of relativity is resolved. The solution is based on the fact that, for the Euclidean open universe, the concept of mass is related to the potential of the background equal to –1, but the concept of the mass-energy is related to the zero-potential of the non-metric background. Because the universe is open and a potential barrier (a boundary of the universe) can be localized-i.e. is geometrically existing — by solution of the field equation, we have to refer to the background with zero-potential. The principal idea of the solution is then that the zero-density means the density of mass-energy, when simultaneously the mass density is equal to the critical value for which the Robertson-Walker metric becomes the Euclidean metric of the Minkowski (i.e., flat) space-time. Further a generalization of Newton's law of inertia is formulated, and the properties of nullgeodesics are touched upon. As a conclusion it is stated that this paper and the two previous ones (see Voráek, 1979a, b)de facto express Mach's principle.     

Self-gravitating fluid in a conformally-flat space-time

The Einstein field equations for an irrotational perfect fluid with pressurep, equal to energy density are studied when the space-time is conformally flat. The coordinate transformation to co-moving coordinates is discussed. The energy and Hawking-Penrose inequalities are studied. Static and non-static solutions of the field equations are obtained. It is interesting to note that in the static case the only spherically-symmetric conformally flat solution for self-gravitating fluid is simply the empty flat space-time of general relativity.     

On the Hubble Law in a Nonexpanding Nonstationary Universe with Cosmological Constant

A nonsingular, homogeneous, isotropic cosmological model with cosmological constant in flat space-time theory of gravitation is studied. The second law of thermodynamics yields a nonexpanding (nonstationary) universe without entropy production. At the beginning of the universe radiation, matter and vacuum energy given by the cosmological constant are zero and then emerge from gravitational energy. In the course of time the energy of radiation and matter decrease whereas the vacuum energy increases forever. Light emitted from a distant galaxy loses energy on his way to the observer producing the observed redshift. The velocity of light in the past is greater than the present one. This may explain superluminal velocities but only for large redshifts. The sum of the density parameters of matter, radiation and vacuum energy is a little greater than one. All the matter can be baryonic. There is no age problem of the universe. This revised version was published online in July 2006 with corrections to the Cover Date.     

Non-Existence Of <Emphasis Type="Italic">N</Emphasis>-Dimensional Static Plane Symmetric Solutions In Bimetric Relativity Theory

A problem of static plane symmetric metric in the perfect fluid, the mesonic massive scalar field and in their coupling is studied in Rosen’s (1973) bimetric theory of relativity. It was found that the matter field like either perfect fluid or mesonic massive scalar field or their coupling does not survive in bimetric theory of gravitation when the space–time is governed by n-dimensional static plane symmetric metric.     

Distance in the space of energetically bounded Keplerian orbits

In this paper we derive an explicit, analytic formula for the geodesic distance between two points in the space of bounded Keplerian orbits in a particular topology. The specific topology we use is that of a cone passing through the direct product of two spheres. The two spheres constitute the configuration manifold for the space of bounded orbits of constant energy. We scale these spheres by a factor equal to the semi-major axis of the orbit, forming a linear cone. This five-dimensional manifold inherits a Riemannian metric, which is induced from the Euclidean metric on \mathbbR⁶{\mathbb{R}^6}, the space in which it is embedded. We derive an explicit formula for the geodesic distance between any two points in this space, each point representing a physical, gravitationally bound Keplerian orbit. Finally we derive an expression for the Riemannian metric that we used in terms of classical orbital elements, which may be thought of as local coordinates on our configuration manifold.     

Relativistic modeling of the neutron star in Vela X-1 via Bardeen space-time satisfying the embedding condition

In this paper, we present two new exact and analytic solutions of the Einstein–Maxwell field equations describing compact anisotropic charged stars satisfying the Karmarkar condition in the background of Bardeen black hole geometry. The solutions are composed of two parts: The inner region of the star is described by class I Karmarkar space-time, while exterior of the star is characterized by both the Bardeen and the Reissner–Nordstrom space-times. Physical analysis of the matter and thermodynamical variables show that the models are well-behaved. For our parametric set of values, we conclude that the Bardeen black hole metric can be used as an alternate to the exterior Reissner–Nordstrom metric.