Colliding Plane Gravitational Waves Research Articles

Colliding plane gravitational waves of unequal strength

Colliding plane gravitational waves of unequal strength

Colliding gravitational waves and singularities

We have investigated a model of colliding plain gravitational waves, proposed by Szekeres, whose structure of singularities is determined. We have evaluated a total energy of matter as a volume integral of the energy–momentum tensor (EMT), whose contributions arise only at these singularities. The total matter energy is conserved before a collision of two plane gravitational waves but decreases during the collision and becomes zero at the end of the collision. We thus interpret that this model of colliding plane gravitational waves is a space–time describing a pair annihilation of plan gravitational waves. We have also calculated a matter conserved charge proposed by the present author and his collaborators. The matter charge is indeed conserved but is zero due to a cancelation between two plain gravitational waves. This seems natural since nothing remains after a pair annihilation, and gives a hint on a physical interpretation of the conserved charge, which we call the gravitational charge. By modifying the space–time for the pair annihilation, we newly construct two types of a scattering plane gravitational wave and a pair creation of plane gravitational waves, and combining all, a Minkowski vacuum bottle, a Minkowski space–time surrounded by two moving plane gravitational waves.

Electrodynamics effects on colliding gravitational waves background

The degenerate Ferrari-Ibanez solution describes the collision of plane gravitational waves with aligned linear polarization, within the interaction region, the solution is Schwarzschild-like metric, which impels us to be more interesting to analyze the collision process. In this paper, we have considered the electrodynamics effects on the colliding gravitational waves background. Moreover, we have calculated explicitly out the solutions of the electromagnetic waves produced by the plane gravitational wave and the colliding region of plane gravitational waves perturbing a weak magnetic field background. We also work out the solutions of these electromagnetic waves after crossing out a weak magnetic field background.

A continuous Riemann–Hilbert problem for colliding plane gravitational waves

We present the foundations of a new solution technique for the characteristic initial value problem (IVP) of colliding plane gravitational waves. It has extensive similarities to the approach of Alekseev and Griffiths in 2001, but we use an inverse scattering method with a Riemann–Hilbert problem (RHP), which allows for a transformation to a continuous RHP with a solution given in terms of integral equations for non-singular functions. Ambiguities in this procedure lead to the construction of a family of spacetimes containing the solution to the IVP. Therefore the described technique also serves as an interesting solution generating method. The procedure is exemplified by extending the Szekeres class of colliding wave spacetimes with 2 additional real parameters. The obtained solution seems to feature a limiting case of a new type of impulsive waves, which are circularly polarised.

Derivation of nonsingular diagonal metrics describing collision of plane gravitational waves with given initial profiles

The condition obtained by Yurtsever in the problem of a collision of plane gravitational waves is transformed into a form that allows for deriving new solutions without a curvature singularity in the interaction region. The above condition is augmented with a number of restrictions concerning the class of functions describing the initial waves and their behavior on the fronts and focusing surfaces. Two examples of new solutions derived on the basis of the Chandrasekhar-Xantopoulos solution illustrate the technique proposed in this paper.

Role of the initial conditions in the occurrence of singularity at collision of plane gravitational waves with collinear polarization

Collision of plane gravitational waves with collinear polarization is considered. It is demonstrated that if the gravitational wave profiles characterized by the Weyl scalars are continuous functions with possible jump on fronts, the occurrence of a curvature singularity in the region of wave interaction is inevitable. Possible modifications of the initial conditions that eliminate the curvature singularity at collision are discussed.

Role of the initial data in the problem of collision of plane gravitational waves with collinear polarization

The work deals with analysis of a gravitational field near a focusing surface in the interaction region of colliding plane waves with collinear polarization. The profiles of the initial waves are supposed to be arbitrary, satisfying only some smoothness conditions behind their fronts. The asymptotic expansions of the metric coefficients, optical scalars, and tetrad components of the curvature tensor near the focusing surface are derived by a direct analysis of the integral form of the solution of the problem obtained long ago by Szekeres. The approach allows us to obtain rigorously more detailed asymptotic representations of the functions under consideration. The dependence of singularity terms on the functions characterizing the initial waves is explored. Conditions for absence of a true singularity on the focusing surface are discussed.

ON BLACK HOLE CREATION IN PLANCKIAN ENERGY SCATTERING

In a series of papers Amati, Ciafaloni and Veneziano and ’t Hooft conjectured that black holes occur in the collision of two light particles at planckian energies. In this talk based on [10] we discuss a possible scenario for such a process by using the Chandrasekhar-Ferrari-Xanthopoulos duality between the Kerr black hole solution and colliding plane gravitational waves.

DISCONTINUITIES AND COLLISION OF GRAVITATIONAL WAVES IN STRING THEORY

We examine here discontinuities in the metric, the antisymmetric tensor and the dilaton field which are allowed by conformal invariance. We find that the surfaces of discontinuity must necessarily be null and both shock and impulsive waves are allowed. We employ our results for the case of colliding plane gravitational waves and we discuss the SL(2, [Formula: see text]) × SU(2)/[Formula: see text] × [Formula: see text]WZW model in the present perspective. In particular, the singularities encountered in this model may be viewed as the result of the mutual focusing of the colliding waves.

Planckian-energy scattering, colliding plane gravitational waves and black hole creation

In a series of papers Amati, Ciafaloni and Veneziano and 't Hooft conjectured that black holes occur in the collision of two light particles at Planckian energies. In this paper we discuss a possible scenario for such a process by using the Chandrasekhar-Ferrari-Xanthopoulos duality between the Kerr black hole solution and colliding plane gravitational waves. We clarify issues arising in the definition of transition amplitude from a quantum state containing only usual matter without black holes to a state containing black holes. Collision of two plane gravitational waves producing a space-time region that is locally isometric to an interior of black hole solution is considered. The phase of the transition amplitude from plane waves to white and black holes is calculated by using the Fabbrichesi, Pettorino, Veneziano and Vilkovisky approach. An alternative extension beyond the horizon in which the space-time again splits into two separating gravitational waves is also discussed. Such a process is interpreted as the scattering of plane gravitational waves through the creation of virtual black and white holes.

On stiff fluids and colliding plane gravitational waves coupled with fluid motions

It is shown how two different but related potentials arise for stiff fluids in space-times with two commuting space-like Killing vectors. This is applied to the generation of stiff fluid or scalar field solutions from vacuum solutions in the colliding plane wave problem, and it is indicated how large families of new solutions can be obtained.

Colliding plane gravitational waves with colinear polarization

The colliding plane wave problem is considered using an unconventional coordinate system. This permits a complete solution to be explicitly stated for the general case of arbitrary approaching waves with constant and aligned polarization.

THE EFFECT OF POLARIZATION OF COLLIDING PLANE GRAVITATIONAL WAVES ON FOCUSING SINGULARITIES

A five-parameter class of colliding plane gravitational wave solutions is obtained by using the soliton technique of Belinsky and Zakharov, which includes most of the important known solutions. A four-parameter subclass of the solutions can be considered as a noncollinear generalization of the famous Szekeres family of colliding collinear polarization plane gravitational wave solutions. The effect of polarization of colliding plane gravitational waves on the formation and nature of singularities is, in turn, investigated.

Curvature-singularity-free solutions for colliding plane gravitational waves with broken u-v symmetry.

We discuss the most general solution describing the collision of plane gravitational waves with constant polarization. Among these solutions there is an infinite-dimensional family of metrics free of curvature singularities and analytically extendable across the ``focusing'' hypersurface. These regular solutions describe collisions between two incoming plane waves with different amplitudes for which u-v symmetry is broken. Boundary conditions on the null hypersurfaces u=0, v=0 are discussed and it is shown that any solution describing the scattering of plane gravitational waves with constant polarization has to include at least two solitary terms each of which stabilizes the behavior of the gravitational field on the null boundaries.

New family of exact solutions for colliding plane gravitational waves.

We construct an infinite-parameter family of exact solutions to the vacuum Einstein field equations describing colliding gravitational plane waves with parallel polarizations. The interaction regions of the solutions in this family are locally isometric to the interiors of those static axisymmetric (Weyl) black-hole solutions which admit both a nonsingular horizon, and an analytic extension of the exterior metric to the interior of the horizon. As a member of this family of solutions we also obtain, for the first time, a colliding plane-wave solution where both of the two incoming plane waves are purely anastigmatic, i.e., where both incoming waves have equal focal lengths.

The effect of sources on horizons that may develop when plane gravitational waves collide

Colliding plane gravitational waves that lead to the development of a horizon and a subsequent time-like singularity are coupled with an electromagnetic field, a perfect fluid (whose energy density, ∊ , equals the pressure, p ), and null dust (consisting of massless particles). The coupling of the gravitational waves with an electromagnetic field does not affect, in any essential way, the development of the horizon or the time-like singularity if the polarizations of the colliding gravitational waves are not parallel. If the polarizations are parallel, the space-like singularity which occurs in the vacuum is transformed into a horizon followed by a three-dimensional time-like singularity by the merest presence of the electromagnetic field. The coupling of the gravitational waves with an ( ∊ = p )-fluid and null dust affect the development of horizons and singularities in radically different ways: the ( ∊ = p )-fluid affects the development decisively in all cases but qualitatively in the same way, while null dust prevents the development of horizons and allows only the development of space-like singularities. The contrasting behaviours of an ( ∊ = p )-fluid and of null dust in the framework of general relativity is compared with the behaviours one may expect, under similar circumstances, in the framework of special relativity.

Colliding plane gravitational waves: A class of nondiagonal soliton solutions.

Using the inverse scattering method we construct a general class of nondiagonal solutions of the vacuum Einstein field equations describing the collision of two plane-fronted impulsive gravitational waves accompanied with gravitational shock waves with the same front. It is a two-parameter class of solutions: the first represents the angle between the directions of polarization of the two waves; the second determines the wave profile.

Colliding plane gravitational waves

Exact solutions of Einstein's field equations for colliding gravitational pp waves are analysed and reviewed using a new approach. A general method is given for deriving solutions in which the approaching waves have constant aligned polarisation. Two new solutions are presented.

Comment on "Collision of plane gravitational waves without singularities"

An incorrect paper was published by B. J. Stoyanov carrying the title above. Here we shall point out a coordinate transformation whereby ''the new exact solution'' of his paper is recognized as a Kasner universe. Further, we shall show that Stoyanov's interpretation of the Kasner solution as colliding plane gravitational waves runs into the difficulty that the Einstein field equations are not satisfied everywhere.

Comment on colliding plane gravitational waves

It is shown that a theorem proved on colliding plane gravitational waves is not correct.