Topological defect solutions in the spherically symmetric space-time admitting conformal motion

In this paper, we have examined strings with monopole and electric field and domain walls with matter and electric field in the spherically symmetric space-time admitting a one-parameter group of conformal motions. For this purpose, we have solved Einstein's field equations for a spherically symmetric space-time via conformal motions. Also, we have discussed the features of the obtained solutions.     

New solutions for charged spheres in general relativity

Exact solutions of the Einstein-Maxwell field equations are obtained for the case of static and spherically symmetric distribution of charged matter. The solutions are obtained through the extension of a method originally used for neutral configurations and are conveniently matched to the Reissner-Nordstrom exterior metric. The physical plausability of the solutions is discussed and it is shown that some of them reduce in appropriate limits to known neutral or charged solutions.     

A class of exact strange quark star model

Static spherically symmetric space-time is studied to describe dense compact star with quark matter within the framework of MIT Bag Model. The system of Einstein’s field equations for anisotropic matter is expressed as a new system of differential equations using transformations and it is solved for a particular general form of gravitational potential with parameters. For a particular parameter, as an example, it is shown that the model satisfies all major physical features expected in a realistic star. The generated model also smoothly matches with the Schwarzschild exterior metric at the boundary of the star. It is shown that the generated solutions are useful to model strange quark stars.     

Stationary and static axisymmetric perfect fluid solutions

Using a certain formalism for the stationary axisymmetric problem with source a rigidly rotating perfect fluid it is shown that under specific assumptions, covariantly imposed, the field equations are reduced to a system of two ordinary second order differential equations. Two known metrics are special solutions of this system. In addition two static axisymmetric perfect fluid solutions, with a spherically symmetric limit, are derived explicitly.     

Spherically Symmetric Solutions of Einstein's Vacuum Equations in Five Dimensions

Multi-dimensional spherically symmetric spacetimes are of interest in the study of higher-dimensional black holes (and solitons) and higher-dimensional cosmological models. In this paper we shall present a comprehensive investigation of solutions of the five-dimensional spherically symmetric vacuum Einstein field equations subject only to the condition of separability in the radial coordinate (but not necessarily in the remaining two coordinates). A variety of new solutions are found which generalize a number of previous results. The properties of these solutions are discussed with particular attention being paid to their possible astrophysical and cosmological applications. In addition, the four-dimensional properties of matter can be regarded as geometrical in origin by a reduction of the five-dimensional vacuum field equations to Einstein's four-dimensional theory with a non-zero energy-momentum tensor constituting the material source; we shall also be interested in the induced matter associated with the new five-dimensional solutions obtained.     

Are all static black hole solutions spherically symmetric?

The static black hole solutions to the Einstein-Maxwell equations are all spherically symmetric, as are many of the recently discovered black hole solutions in theories of gravity coupled to other forms of matter. However, counterexamples demonstrating that static black holes need not be spherically symmetric exist in theories, such as the standard electroweak model, with electrically charged massive vector fields. In such theories, a magnetically charged Reissner-Nordström solution with sufficiently small horizon radius is unstable against the development of a nonzero vector field outside the horizon. General arguments show that, for generic values of the magnetic charge, this field cannot be spherically symmetric. Explicit construction of the solution shows that it in fact has no rotational symmetry at all.This essay received the second award from the Gravity Research Foundation, 1995-Ed.     

Cosmological shock waves in general relativity

The problem of finding spherically symmetric self-similar solutions of Einstein's field equations with a barotropic perfect fluid, which can be joined through a shock wave to some cosmological models, is considered. It is found that such solutions comprise an expanding shell of matter surrounding a horizon with an interior singularity.     

Interior Weyl-type Solutions to the Einstein-Maxwell Field Equations

Static solutions of the electro-gravitationalfield equations exhibiting a functional relationshipbetween the electric and gravitational potentials arestudied. General results for these metrics are presented which extend previous work of Majumdar. Inparticular it is shown that for any solution of thefield equations exhibiting such a Weyl-typerelationship, there exists a relationship between thematter density, the electric field density and the chargedensity. It is also found that the Majumdar conditioncan hold for a bounded perfect fluid only if the matterpressure vanishes (that is, charged dust). Byrestricting to spherically symmetric distributions ofcharged matter a number of exact solutions are presentedin closed form which generalise the Schwarzschildinterior solution. Some of these solutions exhibitfunctional relations between the electric andgravitational potentials different to the quadratic oneof Weyl. All the non-dust solutions are well-behavedand, by matching them to the Reissner-Nordstromsolution, all of the constants of integration areidentified in terms of the total mass, total charge andradius of the source. This is done in detail for anumber of specific examples. These are also shown tosatisfy the weak and strong energy conditions and manyother regularity and energy conditions that may berequired of any physically reasonable matterdistribution.     

Static conformally flat solutions in a general scalar-tensor theory of gravitation

Explicit field equations in the general scalar-tensor theory of gravitation proposed by Nordtvedt are obtained with the aid of a static spherically symmetric conformally flat metric. Exact static solutions of Nordtvedt-Barker field equations both in vacuum and in the presence of a source-free electromagnetic field are presented and studied. It is shown that there are no spherically symmetric static conformally flat solutions of Nordtvedt-Barker field equations representing perfect fluid distribution with disordered radiation obeying the equation of state=3p, except for the trivial empty flat space-time of Einstein's theory.     

Regular models with quadratic equation of state

We provide new exact solutions to the Einstein–Maxwell system of equations which are physically reasonable. The spacetime is static and spherically symmetric with a charged matter distribution. We utilise an equation of state which is quadratic relating the radial pressure to the energy density. Earlier models, with linear and quadratic equations of state, are shown to be contained in our general class of solutions. The new solutions to the Einstein–Maxwell are found in terms of elementary functions. A physical analysis of the matter and electromagnetic variables indicates that the model is well behaved and regular. In particular there is no singularity in the proper charge density at the stellar centre unlike earlier anisotropic models in the presence of the electromagnetic field.     

On the occurrence of naked singularity in spherically symmetric gravitational collapse

Generalizing earlier results of [1], we analyze here the spherically symmetric gravitational collapse of a matter cloud with a general form of matter for the formation of a naked singularity. It is shown that this is related basically to the choice of initial data to the Einstein field equations, and would therefore occur in generic situations from regular initial data within the general context considered here, subject to the matter satisfying the weak energy condition. The condition on initial data which leads to the formation of black hole is also characterized.     

Extremality of mass in the bimetric theory of gravitation

In the bimetric theory of gravitation, the static spherically symmetric case involving matter characterized by density and pressure is considered. It is found that the condition that the mass be stationary under small variations of the field variables (including the density) for a fixed number of baryons leads to the field equations and to the equilibrium condition. If one considers only solutions of the field equations, then the mass for a fixed baryon number is stationary (one can expect it to be extremal in most cases) if the equilibrium condition holds.Dedicated to Achille Papapetrou on the occasion of his retirement.     

On Singularities of General Relativity and Gravitational Equations of Fourth Order

Comparing Einstein's gravitational equations and equations containing fourth-order derivative corrections we discuss some aspects of singularities of spherically symmetric static vacuum solutions from the point of view, first, of the coupling to non-gravitational matter and, second, of the Einsteinian classical particle programme.     

Neutron stars in Scalar-Tensor-Vector Gravity

Scalar-Tensor-Vector Gravity (STVG), also referred as Modified Gravity (MOG), is an alternative theory of the gravitational interaction. Its weak field approximation has been successfully used to describe Solar System observations, galaxy rotation curves, dynamics of clusters of galaxies, and cosmological data, without the imposition of dark components. The theory was formulated by John Moffat in 2006. In this work, we derive matter-sourced solutions of STVG and construct neutron star models. We aim at exploring STVG predictions about stellar structure in the strong gravity regime. Specifically, we represent spacetime with a static, spherically symmetric manifold, and model the stellar matter content with a perfect fluid energy-momentum tensor. We then derive the modified Tolman–Oppenheimer–Volkoff equation in STVG and integrate it for different equations of state. We find that STVG allows heavier neutron stars than General Relativity (GR). Maximum masses depend on a normalized parameter that quantifies the deviation from GR. The theory exhibits unusual predictions for extreme values of this parameter. We conclude that STVG admits suitable spherically symmetric solutions with matter sources, relevant for stellar structure. Since recent determinations of neutron stars masses violate some GR predictions, STVG appears as a viable candidate for a new gravity theory.     

Spherically Symmetric Static Solutions of the Einstein Equations with Elastic Matter Source

The Einstein equations for a spherically symmetric static distribution of elastic matter are examined. The existence of regular solutions near the center is proven under a fairly mild hypothesis on the constitutive equation. These solutions are uniquely determined by the choice of central pressure and constitutive equation. It is also shown for a Hookean elastic material that these solutions can be integrated outward till the radial pressure vanishes, thus one can join an exterior Schwarzschild metric to obtain a maximal solution of the Einstein equations.     

Spherically symmetric nonstatic perfect fluid solutions with shear

In this paper we investigate solutions of Einstein's field equations for the spherically symmetric perfect fluid case with shear and with vanishing acceleration. If these solutions have shear, they must necessarily be nonstatic. We examine the integrable cases of the field equations systematically. Among the cases with shear we find three known classes of solutions. The fourth class of solutions with shear leads to a generalized Emden-Fowler equation. This equation is discussed by means of Lie's method of point symmetries.     

Matching Spherical Dust Solutions to Construct Cosmological Models

Conditions for smooth cosmological models are set out and applied to inhomogeneous spherically symmetric models constructed by matching together different Lemaître–Tolman–Bondi solutions to the Einstein field equations. As an illustration the methods are applied to a collapsing dust sphere in a curved background. This describes a region which expands and then collapses to form a black hole in an Einstein de Sitter background. We show that in all such models if there is no vacuum region then the singularity must go on accreting matter for an infinite LTB time.     

Is the universe homogeneous and isotropic in the time when quark-gluon plasma exists?

In this study, quark and strange quark matter which exist in the first seconds of the early Universe have been studied in the context of general relativity to be able to obtain space–time geometry of first seconds of the early Universe. For this purpose, Einstein’s field equations for quark and strange quark matter in the non static spherically symmetric space–time have been solved by using experimental result that anisotropy parameter of quark matter is very small. We have concluded from obtained solutions that the space–time structure of first seconds of the Early Universe is homogeneous and isotropic. Also we have concluded that the color interactions of the quarks may be origin of primordial magnetic field in the early universe.     

On static spherically symmetric solutions of the vacuum Brans-Dicke theory

It is shown that among the four classes of the static spherically symmetric solutions of the vacuum Brans-Dicke theory of gravity only two are really independent. Further, by matching exterior and interior (due to physically reasonable spherically symmetric matter source) scalar fields it is found that only the Brans class I solution with a certain restriction on the solution parameters may represent an exterior metric for a nonsingular massive object. The physical viability of the black hole nature of the solution is investigated. It is concluded that no physical black hole solution different from the Schwarzschild black hole is available in the Brans-Dicke theory.     

Black holes in static vacuum space-times

An extension of Israel's theorem on the regularity of Killing horizons is proven. Well behaved asymptotically flat vacuum solutions of the Einstein equations which represent the exterior of a non-rotating black hole are considered. It is shown that the black hole has spherical topology and that the equipotential surfaces g ₀₀=constant are non-intersecting two-spheres. The solutions must therefore be members of the one-parameter family of spherically symmetric Schwarzschild solutions.This work has been carried out under a NATO Research Fellowship.