Wormhole with varying cosmological constant

It has been suggested that the cosmological constant is a variable dynamical quantity. A class of solution has been presented for the spherically symmetric space time describing wormholes by assuming the erstwhile cosmological constant Λ to be a space variable scalar, viz., Λ = Λ (r) . It is shown that the averaged null energy condition (ANEC) violating exotic matter can be made arbitrarily small.     

Existence of Noncompact Static Spherically Symmetric Solutions of Einstein SU(2)-Yang–Mills Equations

We consider static spherically symmetric solutions of the Einstein equations with cosmological constant Λ coupled to the SU(2)-Yang–Mills equations that are smooth at the origin r=0. We prove that all such solutions have a radius r _c at which the solution in Schwarzschild coordinates becomes singular. However, for any positive integer N, there exists a small positive Λ _N such that whenever 0<Λ<Λ _N , there exist at least N distinct solutions for which the singularity is only a coordinate singularity and the solution can be extended to r≥r _c . Received: 5 June 2000 / Accepted: 13 March 2001     

A nonstatic plane symmetric solution of Einstein's field equations for zero-rest mass scalar fields

An exact solution of Einstein's field equations of general relativity is given for a plane symmetric zero-rest-mass scalar field in the nonstatic case. The solution generalizes Singh's solution, which itself extends Taub's empty space-time.     

Cylindrically symmetric Brans-Dicke fields. III

In the previous work I and II, we have obtained a class of exact solutions for the Brans-Dicke scalar-tensor theory for Einstein-Rosen nonstatic cylindrically symmetric metric when only scalar field is present and then in presence of source-free electromagnetic field. In the present work we have developed a more general sets of solutions from those given in I and II under the unit transformation by Morganstern [Phys. Rev. D 3 (1971), 2946]. These have been found to be the solutions of the Brans-Dicke scalar-tensor theory for the most general cylindrically symmetric metric of Marder.     

Exact solution of Poincaré gauge field equations of gravity with torsion

Under empty, static, and spherically symmetric conditions we find an exact metric solution of the Poincaré gauge field equations. The Schwarzschild metric solution is contained in the solution and we also obtain new gauge correction termsr ^–1 andr ² lnr.     

Static and time-dependent solutions of Einstein-Maxwell-Yukawa fields

An exact solution of Einstein-Maxwell-Yukawa field equations has been obtained in a space-time with a static metric. A critical analysis reveals that the results previously obtained by Patel [9], Singh [10], and Taub [11] are particular cases of our solution. The singular behavior of the solutions has also been discussed in this paper. Further, extending the technique developed by Janis et al. [12], for static fields, to the case of nonstatic fields, an exact time-dependent axially symmetric solution of EMY fields has been obtained. Our solution in the nonstatic case is nonsingular in the sense of Bonnor [15] and presents a generalization of the results obtained by Misra [7] to the case when a zero-mass scalar field coexists with a source free electromagnetic field.     

The absence of the Kerr black hole in the Hořava–Lifshitz gravity

We show that the Kerr metric does not exist as a fully rotating black hole solution to modified Hořava–Lifshitz (HL) gravity with Λ _W =0 and λ=1. We do this by showing that the Kerr metric does not satisfy the full equations derived from modified HL gravity.     

A class of exact solutions for coupled electromagnetic and scalar fields for Einstein-Rosen metric. Part IA

In the previous work [1] we have obtained a class of exact solutions for the nonstatic cylindrically symmetric Einstein-Rosen metric in the presence of combined electromagnetic and zero-rest-mass scalar meson fields. But, these solutions are restricted because of assuming certain conditions on the scalar field. The present work deals with all the solutions obtained in the previous paper without any such restriction. The class of exact solutions obtained thus is more general than that given in [1].     

Some exact solutions of F(R) gravity with charged (a)dS black hole interpretation

In this paper we obtain topological static solutions of some kind of pure F(R) gravity. The present solutions are two kind: first type is uncharged solution which corresponds with the topological (a)dS Schwarzschild solution and second type has electric charge and is equivalent to the Einstein-Λ-conformally invariant Maxwell solution. In other word, starting from pure gravity leads to (charged) Einstein-Λ solutions which we interpreted them as (charged) (a)dS black hole solutions of pure F(R) gravity. Calculating the Ricci and Kreschmann scalars show that there is a curvature singularity at r = 0. We should note that the Kreschmann scalar of charged solutions goes to infinity as r → 0, but with a rate slower than that of uncharged solutions.     

Spherically symmetric conformally flat distributions of charged dust and zero-mass scalar fields

The problem of charged dust distribution in the presence of zero-mass scalar field for a spherically symmetric conformally flat metric has been investigated. Exact solutions are obtained in the comoving coordinate system for the static model as well as for the nonstatic model. It has been shown that in the nonstatic model the electromagnetic field and dust distribution cannot survive when the scalar field is taken to be a function of timet only. Physical interpretation of the solutions has been investigated.     

SO q (4) quantum mechanics

In this paper we extend our previously discovered exact solution for an SU(2) Yang-Mills-Higgs theory, to the general group SU(N+1). Using the first-order formalism of Bogomolny, an exact, spherically symmetric solution for the gauge and scalar fields is found. This solution is similar to the Schwarzschild solution of general relativity, in that the gauge and scalar fields become infinite on a spherical shell of radiusr ₀=K. However in the Schwarzschild case the singularity at the event horizon is a coordinate singularity while for the present solution the singularity is a true singularity. It is speculated that this solution may give a confinement mechanism for non-Abelian gauge theories, since any particle which carries the SU(N+1) charge would become permanently trapped inside the regionr<r ₀.     

Geometrization of linear perturbation theory for diffeomorphism-invariant covariant field equations. II. Basic gauge-invariant variables with applications to de sitter space-time

In a companion paper, a systematic treatment of linearized perturbations and a new geometric definition of gauge-invariant variables, based on the theory of vector bundles and applicable to the case of an arbitrary system of covariant field equations, were carefully presented. One of the purposes of the present paper is to specify a necessary and sufficient condition that a given, finite set of gaugeinvariant variables, denoted collectively by ω and referred to as the complete set of basic variables, can be used to extract the equivalence classes of perturbations from ω in a unique way. The above set is complete because it has the following property: a knowledge of ω is all one needs in the sense that ifx represents an arbitrary point of the “space-time” manifoldX andG denotes any gauge-invariant tensor field onX, then the value ofG atx∈X is uniquely specified by giving the germs of basic gauge-invariant variables atx∈X. Arguments are proposed that ω also has a stronger property which is more immediately useful: anyG is obtainable directly from the basic variables through purely algebraic and differential operations. These results are of practical interest, and one concrete setting where one is led to the explicit definition of ω occurs when considering the infinitesimal perturbation of the metric tensor itself (pure gravity) defined on a fixed background de Sitter space-time and obeying the linearized empty-space Einstein equations with nonnegative cosmological constant Λ; the case Λ=0 corresponds to linear perturbation theory in Minkowski space-time.     

Scalar field counterexamples to the cosmic censorship hypothesis

The applications of spherically symmetric solutions of the massless scalar Einstein equations to cosmic censorship are discussed. A new nonstatic solution to these equations is given. The Vaidya form of Wyman's solution is constructed and is shown to obey reasonable energy conditions.     

Plane Symmetric Vacuum Bianchi Type <Emphasis Type="Italic">III</Emphasis> Cosmology in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) Gravity

The main purpose of this paper is to study the exact solution of Bianchi type III spacetime in the context of metric f(R) gravity. The field equations are solved by taking expansion scalar θ proportional to shear scalar σ which gives C=A ⁿ , where A and C are the metric coefficients. The physical behavior of the solution has been discussed using some physical quantities. Also, the function of the Ricci scalar is evaluated.     

Static spherically symmetric solutions in general projective relativity

Static spherically symmetric solutions have been obtained for general projective relativity withn=0 andn0 both in isotropic and curvature coordinates. In curvature coordinates, only a restricted exact solution is possible. However, an approximate solution can always be obtained following a method similar to Vanden Bergh. In these spacetimes there is no horizon, but only a naked singularity atr=0. Thus there are no black holes. It is shown that there is no solution in static, spherically symmetric, conformally flat spacetime.     

Three dimensional black hole coupled to the Born-Infeld electrodynamics

A nonlinear charged version of the (2+1)-anti de Sitter black hole solution is derived. The source to the Einstein equations is a Born-Infeld electromagnetic field, which in the weak field limit becomes the (2+1)-Maxwell field. The obtained Einstein-Born-Infeld solution for certain range of the parameters (mass, charge, cosmological and the Born-Infeld constants) represent a static circularly symmetric black hole. Although the covariant metric components and the electric field do not exhibit a singular behavior at r=0 the curvature invariants are singular at that point.     

An Exact Inflationary Solution to Non-Minimally Coupling

We find a new exact inflationary solution to non-minimally coupled scalar field from a specific H(φ). The inflation is driven by the evolution of the scalar field with a new inflation potential. The spectral index of the scalar density fluctuations n _s is consistent with the result of WMAP3 for the power-law flat ΛCDM model. Our solution relaxes the constraint to the quartic coupling constant, e.g. when ξ=10³, λ≤8.9×10⁻¹¹.     

Can electro-magnetic field,anisotropic source and varying Λ be sufficient to produce wormhole spacetime?

It is well known that solutions of general relativity which allow for traversable wormholes require the existence of exotic matter (matter that violates weak or null energy conditions (WEC or NEC)). In this article, we provide a class of exact solution for Einstein-Maxwell field equations describing wormholes assuming the erstwhile cosmological term Λ to be space variable, viz., Λ=Λ(r). The source considered here not only a matter entirely but a sum of matters i.e. anisotropic matter distribution, electromagnetic field and cosmological constant whose effective parts obey all energy conditions out side the wormhole throat. Here violation of energy conditions can be compensated by varying cosmological constant. The important feature of this article is that one can get wormhole structure, at least theoretically, comprising with physically acceptable matters.     

A class of generalised Robinson-Trautman solutions in non-comoving coordinates

A new class of algebraically special solutions is found for Einstein's equations based on the generalised Robinson-Trautman formulation introduced by Wainwright. The solution metrics depend on all four spacetime coordinates t,x,y and r, and in the x,y subspace are either spherically symmetric (parameter K ₀ > 0) or spatially flat (K ₀ = 0). The inhomogeneous spacetimes, of Petrov type II, have singularities at t = 0 and r = 0. The source is a stiff perfect fluid that expands with shear and acceleration but without rotation. The dynamical configuration in the era t ∼ 0 depends directly on a function h(x,y) of the metric. Trapped surfaces are found, associated with the singularity r = 0, which is shown to be censored.