Numerical modeling of black holes as sources of gravitational waves in a nutshell

These notes summarize basic concepts underlying numerical relativity and in particular the numerical modeling of black hole dynamics as a source of gravitational waves. Main topics are the 3+1 decomposition of general relativity, the concept of a well-posed initial value problem, the construction of initial data for general relativity, trapped surfaces and gravitational waves. Also, a brief summary is given of recent progress regarding the numerical evolution of black hole binary systems.     

A non-covariant theory of gravitation,I

Homogeneous isotropic models of the universe, based on the general theory of relativity, lead to the existence of a preferred frame of reference, which is similar to the absolute space of, Newton, and a preferred time coordinate, which resembles the absolute time of Newton. These concepts seem to be in contradiction to the principle of covariance on which the general relativity theory is based. A theory of gravitation is therefore proposed which uses the world picture of general relativity but is not covariant. In the three crucial tests, the proposed theory gives the same results as the general relativity theory. However, in contrast to general relativity, the present theory predicts the emission of gravitational waves by spherically symmetric systems, and gravitational waves are found, in general, to have both transverse and longitudinal components.     

Gravitation and mass decrease

Consequences in physical theory of assuming the general relativistic time transformation for the de Broglie frequencies of matter, v = E/h = mc²/h, are investigated in this paper. Experimentally it is known that electromagnetic waves from a source in a gravitational field are decreased in frequency, in accordance with the Einstein general relativity time transformation. An extension to de Broglie frequencies implies mass decrease in a gravitational field. Such a decrease gives an otherwise missing energy conservation for some processes; also, a physical alteration is then associated with change in gravitational potential. Further, the general relativity time transformation that is the source of gravitational action in the weak field (Newtonian) approximation then has a physical correlate in the proposed gravitational mass loss. Rotational motion and the associated equivalent gravitational-field mass loss are considered; an essential formal difference between metric (gravitational) mass loss and special relativity mass increase is discussed. For a spherical, nonrotating mass collapsed to its Schwarzschild radius the postulated mass loss is found to give a 25% decrease in the mass acting as origin of an external gravitational field.     

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 confrontation between general relativity and experiment

We review the experimental evidence for Einstein’s general relativity. Tests of the Einstein equivalence principle support the postulates of curved space-time and bound variations of fundamental constants in space and time, while solar system experiments strongly confirm weak-field general relativity. The binary pulsar provides tests of gravitational wave damping and of strong-field general relativity. Future experiments, such as the gravity probe B gyroscope experiment, a satellite test of the equivalence principle, and tests of gravity at short distance to look for extra spatial dimensions could further constrain alternatives to general relativity. Laser Interferometric Gravitational Wave Observatories on Earth and in space may provide new tests of scalar-tensor gravity and graviton-mass theories via the properties of gravitational waves.     

Flux of momentum ofN-bodies system by gravitational waves

The energy and angular momentum carried by gravitational waves of anN-body system has been extensively studied by the author. In this paper the linear momentum, within general relativity, is investigated by studying waves emitted from a source consisting ofN-particles moving under their own gravitation.     

Energy-momentum tensor inN=1 supergravity

The classical energy momentum tensor of gravitational waves inN=1 supergravity theory is obtained in analogy with the definition of the same quantity in general relativity.     

Interaction of plane gravitational waves with variable polarization

A solution is obtained in the paper, in the general theory of relativity, for the interaction of plane gravitational waves with variable polarization, by the application of Geroch's method to Szekeres' problem of the interaction of plane linearly polarized gravitational waves. An analysis is carried out of the solution obtained.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 79–84, September, 1979.The author thanks Yu. G. Sbytov and Professor D. D. Ivanenko for attention to the work.     

Gravitational waves generated during inflation from a 5D vacuum theory of gravity in a de Sitter expansion

In this Letter we study the generation of gravitational waves during inflation from a 5D vacuum theory of gravity. Within this formalism, on an effective 4D de Sitter background, we recover the typical results obtained with 4D inflationary theory in general relativity, for the amplitude of gravitational waves generated during inflation. We also obtain a range of values for the amplitude of tensor to scalar ratio which is in agreement with COBE observations.     

Gravitational wave due to explosion of SN 1987A

Observations of the gravitational waves from the explosion of SN 1987A are shown to be more consistent with a new special relativistic theory of gravitation than with predictions of general relativity.     

The Three-Arm Michelson-Fabry-Perot Detector for Gravitational Waves

A three-arm Michelson-Fabry-Perot detector for gravitational waves is designed.It consists of three MichelsonFabry-Perot interferometers,one for each pair of arms.The new detector can be used to confirm whether the gravitational waves are in general relativity polarization states and to set the strong constraints on non-GR gravitational wave polarization states.By the new detectors,the angular resolution of sources can be improved significantly.With the new detector,it is easier to search for and confirm a gravitational wave signal in the observation data.     

Astrophysics from data analysis of spherical gravitational wave detectors

The direct detection of gravitational waves will provide valuable astrophysical information about many celestial objects. Also, it will be an important test to general relativity and other theories of gravitation. The gravitational wave detector SCHENBERG has recently undergone its first test run. It is expected to have its first scientific run soon. In this work the data analysis system of this spherical, resonant mass detector is tested through the simulation of the detection of gravitational waves generated during the inspiralling phase of a binary system. It is shown from the simulated data that it is not necessary to have all six transducers operational in order to determine the source’s direction and the wave’s amplitudes.     

Strong gravitational waves in semiclosed electromagnetic universes. Statement and analysis of the problem in terms of the method of spin coefficients

The problem of integration is discussed for a complete system of Newman-Penrose equations for electrovacuum spaces of the general theory of relativity with nonzero cosmological constant. In terms of the method of spin coefficients, we formulate conditions on the electromagnetic and gravitational field variables, which distinguish a special class of Riemann spaces corresponding to strong gravitational waves in semiclosed Universes of Bertotti-Robinson type.Translated from Izvestiya Vysshikh Uchebnykh Zavederiii, Fizika, No. 11, pp. 74–78, November, 1987.     

On the gravitational wave induced oscillations of viscoelastic bodies

An equation for the propagation of oscillations in a viscoelastic solid, induced by gravitational waves, is derived here. A linearized version of a relativistically invariant constitutive equation of integral type is employed in connection with the appropriately linearized field equations of general relativity. This theory could be applied for a more realistic design of gravitational wave detectors.     

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).     

Gravity from local Lorentz violation

In general relativity, gravitational waves propagate at the speed of light, and so gravitons are massless. The masslessness can be traced to symmetry under diffeomorphisms. However, another elegant possibility exists: masslessness can instead arise from spontaneous violation of local Lorentz invariance. We construct the corresponding theory of gravity. It reproduces the Einstein-Hilbert action of general relativity at low energies and temperatures. Detectable signals occur for sensitive experiments, and potentially profound implications emerge for our theoretical understanding of gravity. Third Award in the 2005 Essay Competition of the Gravity Research Foundation, 2005. - Ed.     

空间引力波探测计划-LISA系统设计要点

为了验证广义相对论,世界各国竞相开展了空间引力波探测方面的研究。本文以欧洲空间引力波探测LISA(Laser Interferometer Space Antenna)计划为例,根据基线设计,对LISA系统有效载荷及主要组件的设计进行了分析和阐述。LISA主要探测和研究低频引力波辐射,其工作频段为10^-3~1 Hz,工作距离为5×10⁶ km,预计能探测到双致密星系统以及星系合并引起的超大质量并合等波源,测距精度达到pm量级。以上研究希望能对我国未来的空间引力波探测计划有一定启示。     

Interaction of plane electromagnetic-gravitational waves

The solution in the general theory of relativity of the problem of the interaction of plane electromagnetic-gravitational waves is derived in this paper by means of an electromagnetic generalization of the problem of the collision of plane gravitational pulses. It is shown that the interaction of waves leads to a physical singularity on a spacelike hypersurface.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 65–70, October, 1978.In conclusion, the author thanks Professor D. D. Ivanenko for his comments.     

Longitudinal Wave Propagation in Relativistic Two-Fluid Plasmas Around Reissner-Nordström Black Hole

The 3+1 spacetime formulation of general relativity is used to investigate the transverse waves propagating in a plasma influenced by the gravitational field of Reissner-Nordström black hole, as explained in an earlier paper, to take account of relativistic effects due to the event horizon. Here, a local approximation is used to investigate the one-dimensional radial propagation of longitudinal waves. We derive the dispersion relation for these waves and solve it numerically for the wave number k.     

Action of weak plane gravitational waves on a system of two connected masses

Based on the monad method of assignment of frames of reference and definitions of observables in the general theory of relativity, an analysis is carried out of the physical interpretation of Weber's formula for the oscillations of elastically connected masses under the action of weak plane gravitational waves.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 81–86, February, 1979.