Nonstatic Solutions Research Articles

Infinite Degenerate States and Hawking Flux Quantization of Two-Dimensional Black Hole11The project supported by National Natural Science Foundation of China and Fok Ying Tong Education Foundation of China

We further investigate the exactly solvable quantum corrected two-dimensional dilaton-gravity theories. For a fixed choice of boundary conditions, there exist the infinite symmetries on the equations of motion and the constraint equations in such a theory. The generators of these symmetries obey the relations of algebra. They can be used to generate infinite degenerate states of two-dimensional black hole. The existence of the infinite static and non-static solutions results in quantization of the Hawking flux in the procedure of black hole evaporation.

Nonstatic solution of Dilaton-Maxwell compound field and Hawking radiation of its black hole

SINCE Balbinot studied the back reaction of the evaporation on the Hawking temperature of anonstatic radiating black hole by using and generalizing the method of Davies et al.,wideinterest has been aroused in this field.In general,radiation terms with Luminosity Lwere introduced into energy-momentum tensor in the course of deriving evaporating black

Null Fluid Collapse in the Plane Symmetric Anti-de Sitter Spacetime

The stability of the plane anti-de Sitter spacetime and the gravitational collapse in the plane symmetric anti-de Sitter spacetime are investigated. A scalar curvature singularity will be formed at the r=0 plane when the anti-de Sitter spacetime is perturbed by null dust. By employing the method suggested recently by Husain we find a family of non-static exact solution of the null fluid collapse with equation of state P=kρ in the plane anti-de Sitter spacetime. The late time limit of the solutions results in a black plane solution possessing multiple horizon structure.

Non-static non-conformally flat fluid plates of embedding class one

In the present article four non-static perfect fluid solutions have been derived by considering a plane symmetric metric of embedding class one. Out of the solutions so obtained two solutions possess an acceleration free velocity vector field while the other two have flow with acceleration. As far as the authors are aware the solutions with non-vanishing acceleration are new.

Imploding scalar fields

Static spherically symmetric uncoupled scalar space-times have no event horizon and a divergent Kretschmann singularity at the origin of the coordinates. The singularity is always present so that non-static solutions have been sought to see if the singularities can develop from an initially singular free space-time. In flat space-time the Klein-Gordon equation $\Box\ph=0$ has the non-static spherically symmetric solution $\ph=\si(v)/r$, where $\si(v)$ is a once differentiable function of the null coordinate $v$. In particular the function $\si(v)$ can be taken to be initially zero and then grow, thus producing a singularity in the scalar field. A similar situation occurs when the scalar field is coupled to gravity via Einstein's equations; the solution also develops a divergent Kretschmann invariant singularity, but it has no overall energy. To overcome this Bekenstein's theorems are applied to give two corresponding conformally coupled solutions. One of these has positive ADM mass and has the properties: i) it develops a Kretschmann invariant singularity, ii)it has no event horizon, iii)it has a well-defined source, iv)it has well-defined junction condition to Minkowski space-time, v)it is asymptotically flat with positive overall energy. This paper presents this solution and several other non-static scalar solutions. The properties of these solutions which are studied are limited to the following three: i)whether the solution can be joined to Minkowski space-time, ii)whether the solution is asymptotically flat, iii)and if so what the solutions' Bondi and ADM masses are.

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.

Static and nonstatic global string.

Exact gravitational fields due to static and nonstatic cosmic strings arising due to the breaking of a global U(1) symmetry are investigated. The results obtained are compared with that already available in the literature for the static case. One of the nonstatic solutions reduces to an essentially static form under a coordinate transformation while another does not. \textcopyright{} 1996 The American Physical Society.

Rusty scatter branes

We derive double-dimensional reduction/oxidation in a framework where it is applicable to describe general nonstatic (and anisotropic) p-brane solutions. Given this procedure, we are able to relate the dynamical interaction potential for parallel extremal p-branes in D dimensions to that for extremal black holes in D - p dimensions. In particular, we find that to leading order the potential vanishes for all K-symmetric p-branes.

Inhomogeneous perfect fluid cosmologies in (4+1) dimensions

Exact solutions are obtained in (4+1) dimensions for plane symmetric and cylindrically symmetric inhomogeneous spacetimes. In the former case the three space depends on time only while the metric corresponding to the extra dimension is dependent on space as well as time coordinates. The cylindrically symmetric nonstatic solutions for the perfect fluid have no singularity near the axis, but show big bang type of singularity in the finite past. One of the classes of such solutions satisfies the barotropic equation of state of the form ρ=ep. Static solutions with cylindrically symmetric solutions are also obtained in 5 dimensions.

Plane-symmetric mesonic viscous fluid cosmological model

Exact nonstatic solutions to Einstein field equations are obtained for the plane symmetric spacetime filled with viscous perfect fluid in the presence of attractive scalar fields. Some physical and geometrical properties of the model are studied. The solutions characterize strong interaction of elementary particles.

A radiating dyon solution

We give a non-static exact solution of the Einstein-Maxwell equations (with null fluid), which is a non-static magnetic charge generalization to the Bonnor-Vaidya solution and describes the gravitational and electromagnetic fields of a non-rotating massive radiating dyon. In addition, using the energy-momentum pseudotensors of Einstein and Landau and Lifshitz we obtain the energy, momentum, and power output of the radiating dyon and find that both prescriptions give the same result.

TACHYON EFFECTS ON THE TWO-DIMENSIONAL BLACK HOLE GEOMETRY

We study solutions of the tree level string effective action in the presence of the tachyon mode. In the case of static fields we find numerically that the full system has a black hole solution with the tachyon regular at the horizon. We also find a nonstatic exact solution of the equations of motion having a black hole structure with a past singularity.

Mathematical investigation of bode's law and quantilization of gravity

A non-static General Relativistic mathematical solution for the gravitational field around a star is obtained. From this mathematical solution, the orbits of the planets around the Sun are calculated and compared with Bode's law and the mean distances of the orbits, the origin of the Moon is deduced, and a theory for quantilization of gravity is concluded.

PLANE SYMMETRIC VISCOUS-FLUID COSMOLOGICAL MODELS WITH HEAT FLUX

A class of nonstatic inhomogeneous plane-symmetric solutions of Einstein field equations is obtained. The source for these solutions is a viscous fluid with heat flow. The fluid flow is irrotational and it has nonzero expansion, shear and acceleration. All these solutions have a big-bang singularity. The matter-free limit of the solutions is the well-known Kasner vacuum solution. Some physical features of the solutions are briefly discussed.

Radiation collapse and gravitational waves in three dimensions.

Two nonstatic solutions for three-dimensional gravity coupled to matter fields are given. One describes the collapse of radiation that results in a black hole. This is the three-dimensional analogue of the Vaidya metric, and is used to construct a model for mass inflation. The other describes plane gravitational waves for coupling to a massless scalar field.

A NONSTATIC PLANE-SYMMETRIC SOLUTION OF EINSTEIN EQUATIONS WITH A SPECIAL SCALAR FIELD

A nonstatic solution of plane-symmetric metric generated by a special scalar field V = V(t-z) has been obtained. The global properties, such as its symmetries, singularities, are also investigated.

Conformally flat solutions to the Einstein-Maxwell equations

The integration of the Einstein-Maxwell equations for an anisotropic charged fluid sphere acting as a source of the Reissner-Nordstrom metric is considered, under the assumption of a conformally flat interior metric. The solutions asymptotically tend to static configurations. In the isotropic pressure limiting case, the non-static solutions are found to be incompatible with charged models.

Nonstatic solutions of Kazner type in the relativistic theory of gravitation

A nonstatic solution of Kazner type to the system of equations (1)–(2) satisfying all requirements of the relativistic theory of gravitation is constructed.

On space-time interpretation of the coset models in D<26 critical string theory

Abstract Manifest expressions for the 3D string metric-dilaton backgrounds corresponding to the (anti-) de Sitter coset models introduced previously are obtained in the leading order approximation. They may be interpreted as non-static cosmological solutions in D =3 critical string theory. A generalization to D >3 space-time dimension is discussed.

Cosmological mesonic viscous fluid model

A class of exact nonstatic solutions is obtained for Einstein field equations in a closed elliptic Robertson-Walker spacetime filled with viscous perfect fluid in the presence of attractive scalar fields. The solutions characterize strong interaction of elementary particles. It is also shown that the massive graviton possesses zero spin.