Gravitational collapse in higher-dimensional charged-Vaidya space-time

We analyze here the gravitational collapse of higher-dimensional charged-Vaidya spacetime. We show that singularities arising in a charged null fluid in higher dimension are always naked violating at least strong cosmic censorship hypothesis (CCH), though not necessarily weak CCH. We show that earlier conclusions on the occurrence of naked singularities in four-dimensional case can be extended essentially in the same manner in 5D case also     

Gravitational interaction and spontaneous breaking of symmetries

An explicit example of spontaneous symmetry breaking due to gravitational interaction is given. It is shown that, in the framework of quantum field theory in curved space-times, the dragging of inertial frame effects lead to a spontaneous symmetry breaking in the ultrarelativistic regime. This situation is compared with those that arise in other interactions. It is pointed out that spinning-up of relativistic configurations is analogous to cooling-down of systems in solid state physics-especially in magnetism-and in high-energy physics. This analogy may turn out to be significant in the investigation of thermodynamical properties of the gravitational field.This essay was awarded the first prize for 1977 by the Gravity Research Foundation.Supported in part by the NSF contract PHY 76-81102 with the University of Chicago.     

Gravitational shock waves

This paper reports on and summarizes some recent progress on gravitational shocks, i.e., discontinuities in the Riemann curvature tensor. It is shown how the constraint equations play a crucial rôle in determining the nature and propagation of the shocks. Existence results are stated and are illustrated by some examples from numerical relativity.     

Spontaneous symmetry breaking in a time-dependent space-time

Spontaneous symmetry breaking of a ⁴ quantum of field theory in a time-dependent space-time, de Sitter space, is discussed in the Schrödinger picture. Instead of the usual cutoff method we use an-regularization procedure to deal with the divergent integrals.     

Gravitational waves from an axi-symmetric source in the Nonsymmetric Gravitational Theory

We examine gravitational waves in an isolated axi-symmetric reflexion symmetric system in the framework of the Nonsymmetric Gravitational Theory (ngt). The vacuum field equations are analyzed and the exact solution for the field variables in the metric tensor are found in the form of expansions in powers of a radial coordinate. We find that when the system radiates, the mass decreases monotonically and the energy flux associated with waves is positive.     

Gravitational waves and astrophysical sources

In linear approximation to general relativity, gravitational waves can be thought of as perturbation of the background metric that propagate at the speed of light. A time-varying quadrupole of matter distribution causes the emission of gravitational waves. Application of Einsteinʼs quadrupole formula to radio binary pulsars has confirmed the existence of gravitational waves and vindicated general relativity to a phenomenal degree of accuracy. Gravitational radiation is also thought to drive binary supermassive black holes to coalescence – the final chapter in the dynamics of galaxy collisions. Binaries of compact stars (i.e., neutron stars and/or black holes) are expected to be the most luminous sources of gravitational radiation. The goal of this review is to provide a heuristic picture of what gravitational waves are, outline the worldwide effort to detect astronomical sources, describe the basic tools necessary to estimate their amplitudes and discuss potential sources of gravitational waves and their detectability with detectors that are currently being built and planned for the future.     

The spontaneous breaking of supersymmetry in curved space-time

The spontaneous breaking of supersymmetry in the presence of a cosmological constant Λ is discussed in a class of theories that includes gauged supergravity and the recently constructed model of N = 1 supergravity coupled to supermatter. The stability of de Sitter, anti-de Sitter and Minkowski vacua in these theories is investigated. Positivity of energy is demonstrated in a model independent way for supersymmetric vacua, even if the scalar potential is unbounded below, and for global minima of the potential for Λ ? 0.Free fields in anti-de Sitter space are considered and the distinction made between the coefficients of quadratic terms in the lagrangian, which vanish for Goldstone scalars, and the physical masses, which give the frequencies and total energies of modes. The number of degrees of freedom depends on gauge invariance, not on the vanishing of mass.The one-loop corrections to the cosmological constant are given for Λ ? 0 and they vanish if the physical masses obey certain sum rules. It is, however, the bilinear coefficients in the N = 1 supergravity-supermatter lagrangian, rather than the physical masses, that satisfy a quadratic sum rule. This sum rule depends on Λ so that a given mass splitting can be obtained for arbitrarily large supersymmetry breaking scales if Λ is sufficiently large and negative.     

Gravitational wave imprint of new symmetry breaking

It is believed that there are more fundamental gauge symmetries beyond those described by the Standard Model of particle physics. The scales of these new gauge symmetries are usually too high to be reachable by particle colliders. Considering that the phase transition (PT) relating to the spontaneous breaking of new gauge symmetries to the electroweak symmetry might be strongly first order, we propose considering the stochastic gravitational waves (GW) arising from this phase transition as an indirect way of detecting these new fundamental gauge symmetries. As an illustration, we explore the possibility of detecting the stochastic GW generated from the PT of begin{document}$ {bf{B}}-{bf{L}}$end{document} in the space-based interferometer detectors. Our study demonstrates that the GW energy spectrum is reachable by the LISA, Tianqin, Taiji, BBO, and DECIGO experiments only for the case where the spontaneous breaking of begin{document}$ {bf{B}}-{bf{L}}$end{document} is triggered by at least two electroweak singlet scalars.     

Gravitational waves without gravitons

The radiation connection induced on an isotropic hypersurface of a Lorentz manifold is described. Consequences for the energy tensor in Einstein field equation are analyzed. A cosmological interpretation is proposed.     

Gravitational waves in the general theory of relativity

The problem of gravitational radiation is discussed with the help of the Rodichev energy-momentum tensor. An invariant criterion is formulated for finding radiation in a space without sources. In general, the question of the presence of radiation in a system is resolved by a local study of the behavior of the energy-momentum tensor in the comoving tetrad. The results are applied to the study of certain exact solutions of the Einstein equations.     

Gravitational waves in the general theory of relativity

The methods and capabilities of the invariant theory of gravitational radiation derived previously are demonstrated for an exact solution of the Kaigorodov type III. Analysis of this solution shows that it describes gravitational radiation with sources.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 11, pp. 121–125, November, 1969.In conclusion, we thank V. I. Rodichev for constant interest in this study.     

Gravitational plane waves in Einstein-aether theory

In this paper, we systematically study spacetimes of gravitational plane waves in Einstein-aether theory. Due to the presence of the timelike aether vector field, now the problem in general becomes overdetermined. In particular, for the linearly polarized plane waves, there are five independent vacuum Einstein-aether field equations for three unknown functions. Therefore, solutions exist only for particular choices of the four free parameters \(c_{i}\)’s of the theory. We find that there exist eight cases, in two of which any form of gravitational plane waves can exist, similar to that in general relativity, while in the other six cases, gravitational plane waves exist only in particular forms. Beyond these eight cases, solutions either do not exist or are trivial (simply representing a Minkowski spacetime with a constant or dynamical aether field).     

Gravitational waves from seismic sources

A fast moving mass radiates part of its energy through gravitational waves. It is possible to consider hurricanes and earthquakes as terrestrial sources of quadrupole gravitational waves. These phenomena have the necessary parameters for the generation of gravitational waves: large quadrupole moments m/r² and also energies and masses moving with large velocities. Estimates indicate a possibility of observing gravitons from the source of a strong earthquake. Local changes in the earth's gravistatic field and the generation of a gravidynamic field during earthquakes will cause variations in the trajectories of the moon and artificial satellites. A mathematical theory of trajectories, containing gravitons, will enable us to fix the graviton according to data from trajectory measurements.Published as a matter for discussion.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 41–46, June, 1974.The author is grateful to Prof. A. A. Sokolov of the Moscow State University for discussing the material expounded here and for interesting remarks.     

Gravitational interaction of plane neutrino waves

An exact solution is found for the gravitational equations corresponding to a space-time containing interacting plane neutrino waves. The waves propagate along congruences of isotropic geodesics with rotation. The rate of rotation of each of the congruences is proportional to the intensity of the oncoming wave.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 51–52, June, 1980.     

The space-time pattern of price waves

We investigate the way price fluctuations are transmitted between spatially separated markets. More specifically we show that the correlation patterns of wheat prices exhibit definite regularities some of which appear to be at variance with intuitive reasoning. Such patterns can be explained in the framework of a wave propagation model based on the so-called spatial arbitrage assumption. In 19th century France the velocity of price waves was of the order of 100 km/month. The economic implications of such an order of magnitude are discussed. In the concluding section we emphasize that what gives this problem its importance is its relative “simplicity”, a word for which we propose an operational definition. Received 1 September 1998 and Received in final form 3 October 1998