General relativity,the massless scalar field,and the cosmological constant

For gravity coupled to a neutral, massless scalar field, Wyman suggested a method of solution in power series valid provided the scalar field depends only on time. In this work we generalize his approach to nonzero cosmological constant.     

Spherically symmetric solutions with heat flow in general relativity

Some new solutions of shear-free imperfect fluid spheres with heat flux in the radial direction are obtained. They have isotropic pressure and could be the generalizations of earlier solutions of Nariai and of Banerjee and Banerji for perfect fluid without dissipation.     

On the Casimir energy for a massive quantum scalar field and the cosmological constant

We present a rigorous, regularization-independent local quantum field theoretic treatment of the Casimir effect for a quantum scalar field of mass μ≠0 which yields closed form expressions for the energy density and pressure. As an application we show that there exist special states of the quantum field in which the expectation value of the renormalized energy–momentum tensor is, for any fixed time, independent of the space coordinate and of the perfect fluid form g_μ,νρ with ρ>0, thus providing a concrete quantum field theoretic model of the cosmological constant. This ρ represents the energy density associated to a state consisting of the vacuum and a certain number of excitations of zero momentum, i.e., the constituents correspond to lowest energy and pressure p0.     

Some solutions of the Einstein-Maxwell equations in general relativity

A solution of the Einstein-Maxwell equations corresponding to source-free electromagnetic field plus pure radiation is obtained. The solution is algebraically special. A particular case of the solution is considered which encompasses many known solutions. Among them is a radiating Ruban metric.     

Scalar-tensor cosmologies with a potential in the general relativity limit: Time evolution

We consider Friedmann–Lemaître–Robertson–Walker flat cosmological models in the framework of general Jordan frame scalar-tensor theories of gravity with arbitrary coupling function and potential. For the era when the cosmological energy density of the scalar potential dominates over the energy density of ordinary matter, we use a nonlinear approximation of the decoupled scalar field equation for the regime close to the so-called limit of general relativity where the local weak field constraints are satisfied. We give the solutions in cosmological time with a particular attention to the classes of models asymptotically approaching general relativity. The latter can be subsumed under two types: (i) exponential convergence, and (ii) damped oscillations around general relativity. As an illustration we present an example of oscillating dark energy.     

Exact solutions for the spherically symmetric vacuum field in the general scalar tensor theory

A conformai technique is given for the generation of exact solutions for the spherically symmetric vacuum field in the general Bergmann-Wagoner-Nordtvedt scalar-tensory theory with vanishing cosmological constant. We discuss in particular the solution for Schwinger's theory and for models with ⁿ coupling or with curvature coupling. It appears that all theories with vanishing cosmological term lead to the presence of naked singularities.     

Letter: An Exact Solution for the Fluctuations of an FRW Cosmology with n Scalar Fields, for an Arbitrary Potential

In this work we rigorously study the fluctuations in FRW models coupled with n neutral scalar fields, minimally coupled to the gravitational field. We find the exact solutions and the asymptotic behavior for the fluctuation around the critical point of the background for an arbitrary potential.     

New results in the use of a “reverse engineering” method in cosmologies with scalar field

The method of “reverse engineering” for designing potentials in cosmologies with “quintessence” scalar field is systematically used for several types of cosmologies (through the time behavior of the scale factor). The general recipe is introduced and then applied when matter other than the scalar field is present, and for tachyonic scalar fields. The possibility of using this method for prescribing initial data in numerical simulations in cosmology is investigated.      

Exact classical and quantum solutions for a covariant oscillator near the black hole horizon in Stueckelberg-Horwitz-Piron theory

We found exact solutions for canonical classical and quantum dynamics for general relativity in Horwitz general covariance theory. These solutions can be obtained by solving the generalized geodesic equation and Schrödinger-Stueckelberg-Horwitz-Piron (SHP) wave equation for a simple harmonic oscillator in the background of a two dimensional dilaton black hole spacetime metric. We proved the existence of an orthonormal basis of eigenfunctions for generalized wave equation. This basis functions form an orthogonal and normalized (orthonormal) basis for an appropriate Hilbert space. The energy spectrum has a mixed spectrum with one conserved momentum p according to a quantum number n. To find the ground state energy we used a variational method with appropriate boundary conditions. A set of mode decomposed wave functions and calculated for the Stueckelberg-Schrodinger equation on a general five dimensional blackhole spacetime in Hamilton gauge.     

Non-static plane symmetric perfect fluid solutions and Killing symmetries in f(R,T)gravity

In this paper, the non-static solutions for perfect fluid distribution with plane symmetry in f（R, T）gravitational theory are obtained. Firstly, using the Lie symmetries, symmetry reductions are performed for considered vector fields to reduce the number of independent variables. Then,corresponding to each reduction, exact solutions are obtained. Killing vectors lead to different conserved quantities. Therefore, we figure out the Killing vector fields corresponding to all derived solutions. The derived solutions are further studied and it is observed that all of the obtained spacetimes, at least admit to the minimal symmetry group which consists of ?_y, ?_z and-z?_y+ y?_z. The obtained metrics, admit to 3, 4, 6, and 10, Killing vector fields. Conservation of linear momentum in the direction of y and z, and angular momentum along the x axis is provided by all derived solutions.     

Non-existence of a massive scalar field for the Marder universe in Lyra and Riemannian geometries

In this paper, we have studied a massive scalar field for a Marder type universe in the context of Lyra and Riemannian geometries. From the exact solutions obtained we show that the massive scalar field does not survive in Lyra and Riemannian geometries for an anisotropic Marder type universe. Therefore we have solved the massless scalar field problem in Lyra and Riemann geometries for two cases. Also we have obtained vacuum solutions for homogeneous and anisotropic Marder space-time in Lyra geometry and the solutions obtained are compared by considering Lyra and Riemann geometries. Finally, some physical and kinematical properties are discussed by using graphics.     

Exact solutions for the Wick-type stochastic 2-dimensional KdV equations with dissipation

The variable coefficient and Wick-type stochastic 2-dimensional KdV equations with dissipation are investigated. Their exact solutions are showed using the homogeneous balance principle and the Hermite transform in the white noise space.     

Quantum field theory in curved spacetime,the operator product expansion,and dark energy

To make sense of quantum field theory in an arbitrary (globally hyperbolic) curved spacetime, the theory must be formulated in a local and covariant manner in terms of locally measurable field observables. Since a generic curved spacetime does not possess symmetries or a unique notion of a vacuum state, the theory also must be formulated in a manner that does not require symmetries or a preferred notion of a “vacuum state” and “particles”. We propose such a formulation of quantum field theory, wherein the operator product expansion (OPE) of the quantum fields is elevated to a fundamental status, and the quantum field theory is viewed as being defined by its OPE. Since the OPE coefficients may be better behaved than any quantities having to do with states, we suggest that it may be possible to perturbatively construct the OPE coefficients—and, thus, the quantum field theory. By contrast, ground/vacuum states—in spacetimes, such as Minkowski spacetime, where they may be defined—cannot vary analytically with the parameters of the theory. We argue that this implies that composite fields may acquire nonvanishing vacuum state expectation values due to nonperturbative effects. We speculate that this could account for the existence of a nonvanishing vacuum expectation value of the stress-energy tensor of a quantum field occurring at a scale much smaller than the natural scales of the theory. Fourth Award in the 2008 Essay Competition of the Gravity Research Foundation.     

Exact solutions for the flow of non-Newtonian fluid with fractional derivative in an annular pipe

Generally speaking, rheological properties of materials are specified by their so-called constitutive equations. The simplest constitutive equation for a fluid is a Newtonian one, on which the classical Navier-Stokes theory is based. The mechanical behavior of many fluids is well described by this theory. However, there are many rheologically compli- cated fluids such as polymer solutions, blood and heavy oils which are inadequately de- scribed by a Newtonian constitutive equation that does …     

A general method for evaluating the current system and its magnetic field of a plane current sheet, uniform except for a certain area of different uniform conductivity, with results for a square area

Summary We derive a linear Fredholm integral equation of the second kind on an arbitrary closed plane contour which divides an infinite plane current sheet into two regions of different uniform integrated conductivities. This integral equation is satisfield along the above-described contour by a certain combination of the limiting values of the electric potential at both sides of the boundary. This electric potential is due to the currents created in the sheet when a uniform electric field is applied to it. The derived integral equation admits exact solutions in closed form for the cases of circular and elliptical insertions. These solutions are identical with those previously obtained, by other methods, for the same cases. A general method is given for the numerical solution of the integral equation. As an illustration, this method is applied to the case of a square insertion where we used the results of Ashour to obtain numerical estimation for the results of the additional magnetic field on and around the square insertion. To speed up publication, the proofs were not sent to the authors and were supervised by the Scientific Commettee.