Gravitational Waves and Extra Dimensions: A Short Review *

We give a brief review on the recent development of gravitational waves in extra-dimensional theories of gravity. Studying extra-dimensional theories with gravitational waves provides a new way to constrain extra dimensions. After a flash look at the history of gravitational waves and a brief introduction to several major extra-dimensional theories, we focus on the sources and spectra of gravitational waves in extra-dimensional theories. It is shown that one can impose limits on the size of extra dimensions and the curvature of the universe by researching the propagations of gravitational waves and the corresponding electromagnetic waves. Since gravitational waves can propagate throughout the bulk, how the amplitude of gravitational waves decreases determines the number of extra dimensions for some models. In addition, we also briefly present some other characteristics of gravitational waves in extra-dimensional theories.     

Quantization of Gravitational Waves and Squeezing

The question whether gravitational waves are quantised or not can in principle be answered by the help of correlation measurements. If the gravitational waves are quantised and they are generated by the change of the background metrics then they can be squeezed. In a squeezed state there is a correlation between the phase of the wave and the quantum uctuations. It is proposed to analyse the data to be obtained by the gravitational detectors from the point of view of such correlations. Explicit formulae are derived for the squeezing parameters of the quantised gravitational waves. The head on collision of two identical black holes is analysed as a possible source of squeezed gravitational waves.     

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.     

New Effect for Detecting Gravitational Waves by Amplification with Electromagnetic Radiation

The perturbation of Dirac particles moving in a constant magnetic field is calculated for simultaneously incident parallel monochromatic circular polarized electromagnetic and gravitational waves. Resonances are found which depend on the initial energy of the charged particles, the magnetic field, and the frequencies of the incident waves. A suited choice of these parameters allows the selection of only one resonance that is proportional to the product of the squares of the amplitudes of both waves. This effect is valid for all bound systems of Dirac particles interacting simultaneously with electromagnetic and gravitational waves. At least in principle this resonance effect can be used to detect the gravitational waves in the lab. For regions of the universe with strong electromagnetic and gravitational waves and suited magnetic fields this effect may play another important part for the acceleration of charged particles.     

Dispersion of gravitational waves in a relativistic gas

The propagation of gravitational waves in a relativistic gas which is in a static gravitational field in the unperturbed state is considered. The group velocity of the transverse gravitational waves and the decrements of collisional and collisionless damping are calculated.     

Generation of gravitational radiation in dusty plasmas and supernovae

We present a novel nonlinear mechanism for exciting a gravitational radiation pulse (or a gravitational wave) by dust magnetohydrodynamic (DMHD) waves in dusty astrophysical plasmas. We derive the relevant equations governing the dynamics of nonlinearly coupled DMHD waves and a gravitational wave (GW). The system of equations is used to investigate the generation of a GW by compressional Alfvén waves in a type II supernova. The growth rate of our nonlinear process is estimated, and the results are discussed in the context of the gravitational radiation accompanying supernova explosions.     

Gravitational waves from binary black holes

It is almost a century since Einstein predicted the existence of gravitational waves as one of the consequences of his general theory of relativity. A brief historical overview including Chandrasekhar’s contribution to the subject is first presented. The current status of the experimental search for gravitational waves and the attendant theoretical insights into the two-body problem in general relativity arising from computations of gravitational waves from binary black holes are then broadly reviewed.     

Topology change and emergent scale symmetry in compact star matter via gravitational wave detection

Topological structure has been extensively studied and confirmed in highly correlated condensed matter physics. We explore the gravitational waves emitted from binary neutron star mergers using the pseudoconformal model for dense nuclear matter for compact stars. This model considers the topology change and the possible emergent scale symmetry and satisfies all the constraints from astrophysics. We find that the location of the topology change affects gravitational waves dramatically owing to its effect on the equation of state. In addition, the effect of this location on the waveforms of the gravitational waves is within the ability of the on-going and up-coming facilities for detecting gravitational waves, thus suggesting a possible way to measure the topology structure in nuclear physics.     

Response of Charged Particles in a Storage Ring to Gravitational Waves

The influence of gravitational waves on the charged particles in a storage ring is studied. It shows thatthe gravitational waves might be directly detected by monitoring the motion of charged particles in a storage ring. Theangular velocity of the charged particles is continually adjustable by changing the initial energy of particles and thestrength of the magnetic field. This feature is very useful for finding the gravitational waves with different frequencies.     

Gravitational waves from the Newtonian plus Hénon-Heiles system

We analyze the emission of gravitational waves from a gravitational system described by a Newtonian term plus a Hénon-Heiles term. The main concern is to analyze how the inclusion of the Newtonian term changes the emission of gravitational waves, considering its emission in the chaotic and regular regime.     

Response of Charged Particles in a Storage Ring to Gravitational Waves

The influence of gravitational waves on the charged particles in a storage ring is studied. It shows that the gravitational waves might be directly detected by monitoring the motion of charged particles in a storage ring. The angular velocity of the charged particles is continually adjustable by changing the initial energy of particles and the strength of the magnetic field. This feature is very useful for finding the gravitational waves with different frequencies.     

Some High-Frequency Gravitational Waves Related to Exact Radiative Spacetimes

A formalism is introduced which may describe both standard linearized waves and gravitational waves in Isaacson's high-frequency limit. After emphasizing main differences between the two approximation techniques we generalize the Isaacson method to non-vacuum spacetimes. Then we present three large explicit classes of solutions for high-frequency gravitational waves in particular backgrounds. These involve non-expanding (plane, spherical or hyperbolical), cylindrical, and expanding (spherical) waves propagating in various universes which may contain a cosmological constant and electromagnetic field. Relations of high-frequency gravitational perturbations of these types to corresponding exact radiative spacetimes are described.     

Letter: Some Remarks on Standing Gravitational Waves

An intuitive definition of standing gravitational waves is proposed. Some main classes of exact vacuum solutions are searched for standing gravitational waves, in most cases with a negative result. Only some Einstein–Rosen waves meet the conditions.     

Dynamical Effects of Gravitational Shock Waves

Gravitational shock waves are defined in the framework of space-times with distribution-valued curvature tensors. Then different kinds of motion in the presence of a gravitational shock wave are investigated. In an earlier paper the same investigation was carried out for an ordinary gravitational discontinuity wave. Discontinuity effects due to gravitational shock waves are compared to those due to ordinary waves.     

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.     

On oscillatory wave processes on the surface of massive bodies nonuniform in composition

A set of interrelated nonlinear differential equations describing the simultaneous oscillations of material density (acoustic waves) and gravitational potential is derived in terms of Lagrangean formalism (taking into account the gravitational potential is necessary when massive bodies are considered). The natural frequencies of these oscillations are found. It is shown that, when interacting with the gravitational potential, the spectrum of the surface waves is greatly distorted and depends on the 2D surface wavevector not linearly (as a typical spectrum of phonons in a solid) but quadratically. The concept proposed in this work allows one to detect additional acoustic low-frequency signals due to internal disturbances. It is stated that a separate consideration of acoustic and gravitational waves is incorrect because of the strong correlation between them.     

Massive relic gravitational waves from f(R) theories of gravity: production and potential detection

The production of a stochastic background of relic gravitational waves is well known in various works in the literature, where, by using the so called adiabatically-amplified zero-point fluctuations process, it has been shown how the standard inflationary scenario for the early universe can in principle provide a distinctive spectrum of relic gravitational waves. In this paper, it is shown that, in general, f(R) theories of gravity produce a third massive polarization of gravitational waves and the primordial production of this polarization is analyzed adapting the adiabatically-amplified zero-point fluctuations process at this case. In this way, previous results, where only particular cases of f(R) theories have been analyzed, will be generalized. The presence of the mass could also have important applications in cosmology, because the fact that gravitational waves can have mass could give a contribution to the dark matter of the Universe. An upper bound for these relic gravitational waves, which arises from the WMAP constrains, is also mentioned. At the end of the paper, the potential detection of such massive gravitational waves using interferometers like Virgo and LIGO is discussed.     

Linear gravitational waves and electrodynamic formalism in cosmology

The propagation of linear gravitational waves is studied in open and multiply connected Robertson-Walker cosmologies. In order for the group velocity of the gravitational wave packets to coincide with the speed of light, the linear wave equation must be conformally coupled. This opens the possibility of using the electromagnetic formalism. The gravitational analogue to the electromagnetic field tensor is introduced, and a tensorial counterpart to Maxwell's equations on the spacelike 3-slices is derived. The energy-momentum tensor for linear gravitational waves is constructed without averaging procedures, a strictly positive energy density is obtained, and it is shown that the overall energy of a gravitational pulse scales with the inverse of the expansion factor.     

引力、引力波和引力波的探测

简要地回顾了引力和引力波概念的由来,以及人们为探测引力波所作的各种努力．     

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。