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.     

Cosmological electrovac model in Bertotti-Robinson space-time

Cosmological electrovac field equations are studied in Bertotti-Robinson-type space-time, and a class of cosmological solutions is obtained. The nature of the electromagnetic fields and singularities of the solution is studied. A technique is established to generate these solutions from a known vacuum solution with a non-zero cosmological constant.     

Static cylindrically symmetric gravitational field with cosmological constant

We show that a class of solutions for a vacuum cylindrically symmetric gravitational field with nonvanishing cosmological constant reduce to the welknown Levi-Civita metric close to the axis. All the circular geodesics in this generalized vacuum are time like, null or space like depending on the relative magnitudes of the two parameters appearing in the solutions.For other particles moving inZ=constant plane there are some cases where the trapping of timelike and null trajectories occur, while in other cases some of the particles may orbit round the axis in a fixed zone bounded by two limiting radii.     

On birkhoff’s theorem in the bimetric scalar-tensor theory of gravitation

It is shown that in the most general version of the bimetric scalar-tensor theory of gravitation, a spherically symmetric vacuum gravitational field is static if the gravitational scalar does not depend on time. This result is generalized to certain cases in which a source is present, including an electromagnetic field. Both branches of solutions with a variable and a constant scalar field are considered. Translated from Astrofizika, Vol. 40, No. 2, pp. 281–290, April–June, 1997.     

Comment on the GRT-LRS Bianchi type-V solutions

We wish to point out that the locally rotationally symmetric (LRS) Bianchi type-V electromagnetic solutions recently given by Roy and Singh (1983) on the basis of the general theory of relativity (GRT) are wrong. The correct electromagnetic solutions are nothing but the vacuum and stiff matter solutions first given by Ftaclas (1978), which have been generalized by Jantzen (1980) and independently by Lorenz (1981).     

Conformally symmetric Abelian Higgs sunspot and non-metricity of the Sun's spacetime

A U(1)-symmetric Yang-Mills-Higgs (i.e., an Abelian Higgs) sunspot's model is recognized to originate from a massless, complex-valued scalar field coupled minimally to electromagnetic gauge potentials in the background of a (globally)conformally symmetric semi-metric spacetime, whose metric structure is described by the generalized Einstein equations with nonvanishing (positive-valued) cosmological constant. It is shown, in particular, that non-linearity (selfcoupling) of the scalar field appears due to a non-zeroness of the cosmological term, whereas its non-zero vacuum amplitude is induced by the (Ricci scalar) curvature of the Sun's spacetime manifold.     

Thermodynamics of the vacuum

The fact that the energy-momentum tensor has nonzero vacuum expectation value in some space-times (the so-called back reaction) indicates a nontrivial thermodynamics of such vacua. A consequent thermodynamic analysis of the problem in Robertson-Walker space-times shows that, in the generic case, the number of the independent extensives is 2, in spite of the fact that the energy density is completely determined by the time-evolution of the geometry since the preparation of the vacuum state. The appearance of a second independent extensive seems to be in direct connection with the extra entropy term in theGeneralized Second Law of Bekenstein and Hawking.     

An inhomogeneous stiff fluid universe with electromagnetic field in general relativity

An inhomogeneous cylindrically symmetric cosmological model for stiff perfect fluid distribution with electromagnetic field is obtained.F ₁₂ is the non-vanishing component of electromagnetic field tensor. The metric potentials are functions ofx andt both. The behaviour of the electromagnetic field tensor together with geometrical and physical aspects of the model are also examined.     

Cylindrically symmetric cosmologies in Lyra geometry

A class of new exact solutions of the Einstein field equations have been investigated for stationary cylindrically symmetric space-time around a local cosmic string in the theory based on Lyra’s geometry in normal gauge in the presence and absence of an electromagnetic field. The cosmological solutions have been analyzed through various physical and geometrical parameters. It has also been shown that the solutions are space-time inhomogeneous and filled with charged dust.     

Surface vacuum energy and stresses on a brane in AdS space with an application to the brane-world model

The vacuum expectations of the surface energy-momentum tensor generated on a brane in AdS space-time by quantum fluctuations of a scalar field with an arbitrary coupling parameter are studied. It is assumed that the field satisfies mixed boundary conditions on the brane. A generalized zeta function method is used as a regularization procedure. Two regions, located to the left (L-region) and right (R-region) of the brane, are considered. It is shown that the surface energies for both these regions contain pole and finite contributions. Analytic expressions are derived for both parts. When calculating the total surface energy including the contributions from the L- and R-regions, the pole terms add out in odd spatial dimensions. The surface energy-momentum tensor induced by vacuum quantum effects corresponds to the generation of a cosmological constant on the brane. These results are applied to the second Randall-Sundrum model.Translated from Astrofizika, Vol. 48, No. 1, pp. 151–164 (February 2005).     

A bianchi type-III cosmological model in Brans-Dicke theory for vacuum field

An exact solution of Brans-Dicke (B-D) field equations for the metric tensor of a spatially homogeneous Bianchi type-III configuration has been obtained for vacuum field. It is shown that in the limiting case the solution reduces to that of Einstein field equations in vacuum.     

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.     

Quantum Vacuum Effects in the Gravitational Field of a Global Monopole

A study is made of the vacuum expectation values for the energy-momentum tensor of a massive scalar field that satisfy a Robin mixed boundary condition on a spherical surface with a background gravitational field from a D+1-dimensional global monopole. Expressions are derived for the Wightman function, vacuum expectation of the square of the field, vacuum energy density, and the radial and azimuthal pressures inside the spherical surface. The regularization procedure involves using the generalized Abel-Plana formula for series in terms of the zeroes of cylindrical functions. This formula makes it possible to separate the part owing to the gravitational field of a global monopole without boundaries from the vacuum expectation and to represent the parts induced by the boundary in the form of exponentially converging integrals which are especially convenient for numerical calculations. The asymptotic behavior of the vacuum averages is studied at the center of the sphere and near its surface. It is shown that for small values of the parameter describing the solid-angle deficit in the geometry of a global monopole, the vacuum stresses induced by the boundary are highly anisotropic.     

Cosmological viscous fluid models in the presence of electromagnetic field and zero-mass scalar field

The problem of electromagnetic field interacting with viscous fluid without and with zero-mass scalar field has been studied. It has been shown that electromagnetic field cannot interact with viscous fluid for spherically-symmetric Robertson-Walker metric. Exact solutions corresponding to the problem of electromagnetic field interactions in presence of viscous fluid and zero-mass scalar field have been obtained subject to various physical conditions. It presents a scope for the study of imperfect fluid FRW models showing the existence of the electromagnetic field due to the presence of zero-mass scalar field.     

Exact Brans-Dicke cosmologies with a cosmological constant

We present the general Brans-Dicke-Friedmann-Robertson-Walker (k=0) vacuum solutions with a cosmological constant. The space-times considered here are the generalizations of the de Sitter models of the general theory of relativity.     

Duality rotations and type D solutions of Einstein-Born-Infeld theory

Within the non-linear electrodynamics of Born-Infeld type, constrained by the condition that admits the freedom of the duality rotations the explicit type D solutions, which generalize the charged Taub-NUT metric with cosmological constant, are constructed. The obtained type D solution exhausts all solutions within the considered class, assumed that the real eigenvectors of the electromagnetic field are aligned along the geodesic and shear-free principa null directions.     

A Class of higher dimensional spherically symmetric cosmological model in Lyra geometry

Exact analytical solutions are obtained for a higher dimensional spherically symmetric inhomogeneous metric in presence of a mass-less scalar field with a flat potential within the framework of Lyra geometry. Assuming a homogeneous scalar field, we have shown that the metric can be reduced to a generalized FRW type.     

Birkhoff's theorem in a conformally-invariant scalar field theory

A result having formal similarity to Birkhoff's theorem in general relativity is proved, both in vacuum as well as in the presence of electromagnetic fields, in a conformally-invariant scalar field theory with trace-free energy-momentum tensor for the special case when the scalar field is independent of time.     

Inhomogeneous perfect fluid universe with electromagnetic field

Cylindrically symmetric inhomogeneous cosmological model for perfect fluid distribution with electromagnetic field is obtained. The source of the magnetic field is due to an electric current produced along the z-axis. F ₁₂ is the non-vanishing component of electromagnetic field tensor. To get the deterministic solution, it has been assumed that the expansion θ in the model is proportional to the shear σ. Physical and geometric aspects of the models are also discussed in presence and absence of magnetic field.      

Space-Time Geometry of Quark and Strange Quark Matter

We study quarkand strangequarkmatter in the contextof generalrelativity.For this purpose,we solve Einstein's field equations for quark and strange quark matter in spherical symmetric space-times. We analyze strange quark matter for the different equations of state (EOS) in the spherical symmetric space-times,thus we are able to obtain the space-time geometries of quark and strange quark matter. Also,we discuss the features of the obtained solutions. The obtained solutions are consistent with the results of Brookhaven Laboratory,i.e. the quark-gluon plasma has a vanishing shear (i.e. quark-gluon plasma is perfect).