Colliding Wave Solutions Research Articles

Colliding fields in two-dimensional dilaton gravity background

The ([Formula: see text])-dimensional dilatonic background geometry of [C. Callan, S. Giddings, J. Harvey and A. Strominger, Phys. Rev. D 45 (1992) R1005] admits an infinite class of colliding wave solutions. We give examples from real and ghost fields with bounded/ unbounded profiles. In particular, colliding ghost fields in the “lineland” geometry create particle-like wormholes. Such wormholes, however, collapse to a black hole whenever the supporting ghosts turn off. Lastly, it is shown that the vacuum collision of null fields yields a ghost wormhole which is unstable.

Colliding wave solutions in 2 + 1-dimensions

We identified a new metric that describes both colliding electromagnetic shock waves and scalar waves without cosmological constant in 2 + 1-dimensions. To the future of collision point our metric has spacelike singularity so that the electromagnetic solution differs from its 3 + 1-dimensional counterpart. Our interaction region with scalar waves is related through the Kaluza–Klein argument with the 3 + 1-dimensional Schwarzschild spacetime.

Colliding Wave Solutions in a Symmetric Non-Metric Theory

A method is given to generate the non-linear interaction (collision) of linearly polarized gravity coupled torsion waves in a non-metric theory. Explicit examples are given in which strong mutual focussing of gravitational waves containing impulsive and shock components coupled with torsion waves does not result in a curvature singularity. However, the collision of purely torsion waves displays a curvature singularity in the region of interaction.

Colliding wave solutions from five-dimensional black holes and black p-branes

We consider both the five-dimensional Myers-Perry and Reissner-Nordstrom black holes (BHs) and black p-branes in (4+p)-dimensions. By employing the isometry with the colliding plane waves (CPWs) we generate Cauchy-Horizon (CH) forming CPW solutions. From the five-dimensional vacuum solution through the Kaluza-Klein reduction the corresponding Einstein-Maxwell-dilaton solution is obtained. This CH forming cross polarized solution with the dilaton turns out to be a rather complicated nontype D metric. Since we restrict ourselves to the five-dimensional BHs we obtain exact solutions for colliding 2- and 3-form fields in (p+4)-dimensions for p⩾1. By dualizing these forms we can obtain also colliding (p+1)- and (p+2)-forms which are important processes in the low energy limit of the string theory. All solutions obtained are CH forming, implying that an analytic extension beyond is possible.

Nonsingular colliding wave solutions in Einstein-Maxwell-dilaton-axion theory

The local isometry between black holes and colliding plane waves is employed to derive new colliding wave solutions in the Einstein-Maxwell-dilaton-axion theory. The technique is applied to the asymptotically nonflat linear dilaton black holes. We obtain two new metrics which we label (from the language of black holes) as Kerr and Newman-Unti-Tamburino (NUT) types. The NUT type turns out to be type D while the Kerr type belongs to the general class. Both types share the common feature that, instead of an all encompassing generic singularity, Cauchy horizons develop in the process of collision.

A class of colliding waves in metric-affine gravity, nonmetricity and torsion shock waves

By using our recent generalization of the colliding waves concept to metric–affine gravity theories, and also our generalization of the advanced and retarded time coordinate representation in terms of Jacobi functions, we find a general class of colliding wave solutions with fourth degree polynomials in metric-affine gravity. We show that our general approach contains the standard second degree polynomial colliding wave solutions as a particular case.

Colliding plane waves in terms of Jacobi functions

We present a general class of noncollinear colliding wave solutions of the Einstein–Maxwell equations given in terms of fourth order polynomials, which in turn can be expressed through Jacobi functions depending on generalized advanced and retarded time coordinates. The solutions are characterized by six free parameters. The parameters can be chosen in such a way as to avoid the generic focusing singularity.

Colliding wave solutions, duality, and diagonal embedding of general relativity in two-dimensional heterotic string theory

The non-linear sigma model of the dimensionally reduced Einstein (-Maxwell) theory is diagonally embedded into that of the two-dimensional heterotic string theory. Consequently, the embedded string backgrounds satisfy the (electromagnetic) Ernst equation. In the pure Einstein theory, the Matzner-Misner SL(2, R ) transformation can be viewed as a change of the conformal structure of the compactified flat two-torus, and in particular its integral subgroup SL(2, Z ) acts as the modular transformation. The Ehlers SL(2, R ) and SL(2, Z ) similarly act on another torus whose conformal structure is induced through the Kramer-Neugebauer involution. Either of the Matzner-Misner and the Ehlers SL(2, Z ) can be embedded to a special T-duality, and if the former is chosen, then the Ehlers SL(2, Z ) is shown to act as the S-duality on the four-dimensional sector. As an application we obtain some new colliding string wave solutions by using this embedding as well as the inverse scattering method.

Infinite-dimensional family of colliding wave solutions with variable polarization

The authors construct an infinite-dimensional family of solutions to Einstein's field equations representing collisions between plane gravitational waves with variable polarization. The boundary conditions on the null hypersurfaces are studied and presented as a set of algebraic conditions for the constant coefficients of the Legendre functions. The behaviour of the gravitational field near the focusing two-surface is also analysed and some of the issues related to the strong cosmic censorship conjecture are briefly discussed.

Colliding wave solutions of the Einstein–Maxwell field equations

A large family of solutions of the vacuum Einstein equations [J. Math. Phys. 32, 723 (1991)] is generalized to the electrovac case. The new solutions are shown to possess Killing–Cauchy horizons when one of the parameters n is set equal to 3, 1, −1 or −3.

Colliding gravitational plane waves with noncollinear polarizations

A method devised recently by Hauser and Ernst [J. Math. Phys. 31, 871 (1990)] is exploited to deduce an elegant generalization of the FIB/EGH family of colliding wave solutions [J. Math. Phys. 29, 681 (1988)] involving five parameters plus a real analytic function ψ0(z,ρ). All metrical and curvature quantities are evaluated explicitly, and solutions in which curvature singularities are avoidable are identified.

Colliding wave generalization of the Ferrari-Ibañez solution in the Einstein-Maxwell theory

A four-parameter class of colliding wave solutions of the Einstein-Maxwell equations is presented. It generalizes the vacuum Ferrari-Ibañez metric.

A family of electrovac colliding wave solutions of Einstein’s equations

Beginning with any colliding wave solution of the vacuum Einstein equations, a corresponding electrified colliding wave solution can be generated through the use of a transformation due to Harrison [J. Math. Phys. 9, 1744 (1968)]. The method, long employed in the context of stationary axisymmetric fields, is equally applicable to colliding wave solutions. Here it is applied to a large family of vacuum metrics derived by applying a generalized Ehlers transformation to solutions published recently by Ernst, García, and Hauser (EGH) [J. Math. Phys. 28, 2155, 2951 (1987); 29, 681 (1988)]. Those EGH solutions were themselves a generalization of solutions first derived by Ferrari, Ibañez, and Bruni [Phys. Rev. D 36, 1053 (1987)]. Among the electrovac solutions that are obtained is a charged version of the Nutku–Halil [Phys. Rev. Lett. 39, 1379 (1977)] metric that possesses an arbitrary complex charge parameter.

Generalization of the Hauser-Ernst formalism for two-dimensional reduced Einstein abelian gauge field equations

Recently the Hauser-Ernst formalism has played an important role in the discussion of the Virasoro symmetry in the two-dimensional reduced gravity theory. In this Letter we generalize the Hauser-Ernst formalism to the Einstein abelian gauge field equations when the spacetime possesses two commuting Killing vectors. Using this formalism, it is effective to investigate the Kac-Moody symmetry and, in particular, the Virasoro symmetry, which can be used to induced new solutions from the old one. We then provide an example concerning the derivation of a six-parameter generalization of a three-parameter family of colliding wave solutions found by Ernst, García and Hauser.

The S̄(a,b,c/m) metrics interpreted as colliding wave solutions

It is shown that the class of solutions S̄(a,0,−1/1), a real slice of the ‘‘complexified’’ Plebański S(a,b,c/m) metrics, is interpretable as colliding wave solutions and, for a=−s2, coincides precisely with the Ferrari–Ibañez colliding wave metrics.

Colliding gravitational plane waves with noncollinear polarization. III

The Hauser–Ernst homogeneous Hilbert problem (HHP) approach, formerly used in connection with the derivation of stationary axisymmetric fields, is here adapted to the derivation of colliding gravitational plane wave solutions of the vacuum Einstein equations. Proceeding from Kasner metrics, and using a double-Harrison transformation, the HHP approach yields a three-parameter generalization of a two-parameter family of colliding wave solutions found recently by Ferrari, Ibañez, and Bruni. In the present paper we provide the details concerning the derivation of this new family of solutions, and we set the stage for future applications of the HHP approach in connection with gravitational waves.