Gravitational Shock Waves Research Articles

Particle creation in a colliding plane wave spacetime: Wave packet quantization.

We use wave packet mode quantization to compute the creation of massless scalar quantum particles in a colliding plane wave spacetime. The background spacetime represents the collision of two gravitational shock waves followed by trailing gravitational radiation which focus into a Killing-Cauchy horizon. The use of wave packet modes simplifies the problem of mode propagation through the different spacetime regions which was previously studied with the use of monochromatic modes. It is found that the number of particles created in a given wave packet mode has a thermal spectrum with a temperature which is inversely proportional to the focusing time of the plane waves and which depends on the mode trajectory.

Reduction of space–time by a constraint for C(0) metrics

It is shown how a constraint imposed by the physical relevance of the solutions reduces the dimension of space–time. The C(0) metric given by Nutku is used to describe gravitational shock waves and the trivial case is looked at. It is found that imposing triviality on the solutions reduces the dimension of space–time by one.

Erratum: Gravitational Faraday rotation induced from interacting gravitational plane waves

The polarization of gravitational plane waves is studied. In particular, it is found that each interacting gravitational plane wave can be split into two parts: the shock part and the impulsive part. The plane of the polarization for the plane gravitational shock waves usually gets rotated due to two kinds of interaction: one is the nonlinear interacton between the oppositely moving plane gravitational shock waves, and the other is the interaction between the gravitational shock wave and the matter fields which are present. The change of polarization due to the nonlinear interaction is exactly a gravitational analogue of Faraday rotation, but with the oppositely moving gravitational shock wave as the magnetic field and medium. The effect of the above two kinds of interaction on the impulsive gravitational plane waves is different from that on the shock waves. Only the interaction between the impulsive gravitational wave and the matter fields can change the polarization of the impulsive wave.

Gravitational shock waves and quantum fields in de Sitter space.

We analyze the particle creation of gravitational shock waves in de Sitter space. Our main result is that if the quantum matter vacuum state is the Euclidean vacuum state, the waves propagate without dissipation produced by particle creation.

Curved-spacetime metric generated by Planckian energy string collisions

We study Planckian energy string collisions in flat spacetime as the scattering of a string in the effective curved background produced by the others as the impact parameter $b$ decreases. We find the effective energy-density distribution $\ensuremath{\sigma}(\ensuremath{\rho})\ensuremath{\sim}\mathrm{exp}{\frac{{\ensuremath{-}\ensuremath{\rho}}^{2}}{{\ensuremath{\Delta}}^{2}}}$, generated by these collisions. Two different regimes can be studied: intermediate impact parameters ${x}^{d}<<b<<\sqrt{{\ensuremath{\alpha}}^{\ensuremath{'}}\mathrm{ln}s}\ensuremath{\simeq}\frac{\ensuremath{\Delta}}{2}$ (${x}^{d}$ characterizing the string fluctuations) and large impact parameters $b>>\sqrt{{\ensuremath{\alpha}}^{\ensuremath{'}}\mathrm{ln}s}\ensuremath{\simeq}\frac{\ensuremath{\Delta}}{2}>>{x}^{d}$. The effective metric generated by these collisions for large $b$ is a gravitational shock wave of profile $f(\ensuremath{\rho})\ensuremath{\sim}p{\ensuremath{\rho}}^{4\ensuremath{-}D}$, i.e., the Aichelburg-Sexl (AS) geometry for a pointlike particle of momentum $p$. For intermediate $b$, $f(\ensuremath{\rho})\ensuremath{\sim}q{\ensuremath{\rho}}^{2}$, corresponding to an extended source of momentum $q$. The scattering matrix in this geometry and its implications for the string collision process are analyzed. We show that the poles $iGs=n$, $n=0,1,2,\dots{}$, characteristic of the scattering by the AS geometry are absent here, due to the extended nature of the effective source.

Quantum fluctuations of a spherical gravitational shock wave

The author shows that quantum fluctuations, in particular vacuum polarization, vanish in the background of the spherical shock wave solution of the Einstein field equations, recently found by Nutku (1991). This result is due to the smoothness properties of the new solution.

MASS AND ENERGY-MOMENTUM TENSOR OF QUANTUM STRINGS IN GRAVITATIONAL SHOCK-WAVES

We investigate at the quantum level the nonlinear transformation relating the string operators (zero modes and oscillators) and Fock space states before and after the collision with gravitational shock waves. This throws light on the rôle of the space–time geometry in this problem. We do all the treatment for a general shock wave space–time of any localized source. We compute the exact expectation values of the total number (N) and mass ( M 2) operators and show that they are finite, which generalize our previous results in the Aichelburg–Sexl geometry. We study the energy-momentum tensor of the string and compute the exact expectation values of all its components. We analyze vacuum polarization and quadratic fluctuations. All these physical magnitudes are finite. We express all of them in terms of exact integral representations in which the role of the real pole singularities characteristic of the tree level string spectrum (real mass resonances) are clearly exhibited. The presence of such poles is not at all related to the structure of the space–time geometry (which may or may not be singular).

Chemistry in the Early Universe

Galaxies and the first stars in the universe formed billions of years ago as a result of the cooperative effects of gravitational collapse and nonequilibrium chemistry. Gravity drew the primordial gas together into lumps; the formation of the first molecules in the universe, simple diatomic molecules like H2, H2+, HD, HeH+, LiH, and LiH+, may then have ensured that the heat generated by gravitational collapse and shock waves was radiated away rapidly enough to allow the gravitational collapse and fragmentation of these gaseous lumps to proceed to the point of forming stars and galaxies. We briefly mention a few of the latest studies of this primordial chemistry, including that in the evolving intergalactic medium (IGM) in a Cold Dark Matter (CDM) model cosmology and that in radiative shocks in the early universe.

Strings in gravitational shock wave backgrounds

In this paper and the subsequent one, the quantum scattering of particles by a gravitational shock wave (GSW) is computed within the framework of string theory. The exact string equations of motion and constraints in the GSW background are reviewed for the light-cone gauge. In addition, the ambiguity in the solution for the longitudinal coordinate is solved. The light-cone solution is generalized to an arbitrary covariant gauge. This general solution turns out to be completely explicit and not much more involved than the solution for the light-cone gauge. The extension of the string solution to the case of a GSW generated by an arbitrary ultrarelativistic source is also presented.

Quantum string scattering by gravitational shock waves

The two-point amplitude, A 2( k 2, k 1), describing the scattering of the lowest string excitation (the tachyon) by a gravitational shock wave (GSW) is computed. For this purpose, we use the appropriate vertex operator in the GSW background. We explicitly evaluate A 2( k 2, k 1) for large impact parameters q. It is given by the Coulombian amplitude plus string corrections of order s q ( s = ( k 1 + k 2) 2), for large q. These string corrections produce an infinite sequence of imaginary poles in s, the semi-infinite sequence of Coulomb poles noticed by 't Hooft always remaining present.

Gravitational Faraday rotation induced from interacting gravitational plane waves.

The polarization of gravitational plane waves is studied. In particular, it is found that each interacting gravitational plane wave can be split into two parts: the shock part and the impulsive part. The plane of the polarization for the plane gravitational shock waves usually gets rotated due to two kinds of interaction: one is the nonlinear interacton between the oppositely moving plane gravitational shock waves, and the other is the interaction between the gravitational shock wave and the matter fields which are present. The change of polarization due to the nonlinear interaction is exactly a gravitational analogue of Faraday rotation, but with the oppositely moving gravitational shock wave as the magnetic field and medium. The effect of the above two kinds of interaction on the impulsive gravitational plane waves is different from that on the shock waves. Only the interaction between the impulsive gravitational wave and the matter fields can change the polarization of the impulsive wave.

Gravitational shock waves generated by extended sources: ultrarelativistic cosmic strings, monopoles and domain walls

We study the gravitational shock waves generated by ultrarelativistic extended sources, mainly when cosmic strings (local, global, spinning and superconducting) and other topological defects (monopoles and domain walls) are boosted and become ultrarelativistic. In this limit, the sources travel at the speed of light and the physical parameters (mass, charges and spin) must be taken γ-dependent [ γ = (1 - v 2) − 1 2 ] and must vanish in an appropriated way. The scattering matrices of Klein-Gordon fields in these geometries are computed and the low- and high-energy behaviour analysed. Comparison with the scattering by point-like sources (Aichelburg-Sexl geometry for which the S-matrix has coulombian type poles) is made. For extended as well as point-like sources, the ultrarelativistic limit and the weak-field limit (or large-distance behaviour) of the geometry give the same scattering matrices.

Gravitational radiation from cosmic string splitting on a Friedmann-Robertson-Walker background

We present exact solutions of Einstein's equations that may be interpreted as representing the splitting of a primordial cosmic string imbedded in a perfect fluid Friedmann-Robertson-Walker (FRW) cosmology. The splitting leads to the creation of a ‘bubble’ whose boundary is given by a gravitational shock wave, expanding from the point of splitting, associated to the motion of the free ends of the string. Inside the bubble we have a perturbed FRW metric. This perturbation is largest near the string ends, producing a sort of ‘wake’ along the path of the free ends, but decreases rapidly with time and the metric approaches the FRW regime locally everywhere inside the bubble. Similar results are shown to hold also for flat vacuum de Sitter space-times.

Space time singularities in string theory and string propagation through gravitational shock waves

A comment on the Letter by G. T. Horowitz and A. R. Steif, Phys. Rev. Lett. 64, 260 (1990).

Horowitz and Steif reply.

Horowitz et al. answer the questions raised by de Vega et al. on propagation of quantized string in a gravitational shock waves.(AIP)Received 25 June 1990DOI:https://doi.org/10.1103/PhysRevLett.65.1518©1990 American Physical Society

Quantum string propagation through gravitational shock waves

We study the propagation of quantum closed strings in gravitational shock wave space-times. We find the exact expressions of the expectation values of the total number operator 〈 N〉 and of the mass square operator 〈 M 2〉 and analyze their properties. We show that they are both finite and that strings propagate consistently through gravitational shock waves. Exact integral representations for 〈 N〉 and 〈 M 2〉 are found in which the presence of the real mass resonances characteristic of tree string amplitudes is exhibited. The issue of space-time singularities is briefly discussed.

The ultrarelativistic limit of the Kerr-Newman geometry and particle scattering at the Planck scale

We study the effect of the spin in the scattering of ultra-high energetic particles. We find the ultrarelativistic limit of the boosted Kerr-Newman geometry. This represents the gravitational shock wave of a particle travelling at the speed of light with quantum numbers given by kinetic ( p), electromagnetic and color ( p b ) and spin ( a) momenta [mass, charges and spin vanish as m-γ −1p, b=γ − 1 2 p b and s=apγ −1(γ −1= 1 −v 2) ]. We find the exact S-matrix describing the scattering of a neutral masive field with this shock wave geometry. Finally, we discuss briefly the relation of this process with that of the scattering of strings.

Gravitational shock waves of ultra-high energetic particles on curved spacetimes

We generalize the Dray and 't Hooft procedure to generate gravitational shock waves superimposed on curved background solutions of the vacuum Einstein equations in order to include sources and a non-zero cosmological constant for the backgrounds, and a charge for the shock waves (all that in D dimensions). We apply this generalization to the study of the gravitational shock wave of ultrarelativistic particles with kinetic and electromagnetic momenta p and p e in static spherically symmetric spacetimes and its effect on shifting the event horizon (the terms with p and p e give rise to different shifts). Examples of these shock waves on the Reissner-Nordstrom and the Schwarzschild-de Sitter (and Schwarzschild-anti de Sitter) spacetimes are considered.

Distinct family of colliding gravitational waves in general relativity.

We present a new family of exact solutions for the Einstein equations that describes colliding gravitational shock waves with cross polarization. In the limit of single polarization it reduces to a family that, up to a transformation of its metric functions, is distinct from the well-known Szekeres family. Furthermore, this family of solutions does not belong to the largest family found recently by Ferrari, Iban\ifmmode \tilde{}\else \~{}\fi{}ez, and Bruni.

Quantum field theory in a gravitational shock wave background

A scalar massless non-interacting quantum field theory on an arbitrary gravitational shock wave background is exactly solved. S-matrix and expectation values of the energy-momentum tensor are computed for an arbitrary polarized sourceless gravitational shock wave and for a homogeneous infinite planar shell shock wave, all performed in any number of space-time dimensions. Expectation values of the energy density in scattering states exhibit a singularity which lies exactly at the location of the curvature singularity found in the infinite shell collision.