Scalar plane waves in general relativity

Condition for invariant spectral degree of coherence of an electromagnetic plane wave on scattering

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.).

Plane walls (including plane domain walls) without reflection symmetry are studied in the framework of Einstein's general relativity. Using the distribution theory, all the Einstein field equations and Bianchi identities are split into two groups: one holding in the regions outside of the wall and the other holding at the wall. The Einstein field equations at the wall are found to take a very simple form, and given explicitly in terms of the discontinuities of the metric coefficients and their derivatives. The Bianchi identities at the wall are also given explicitly. Using the latter, the interaction of a plane wall with gravitational waves and some specific matter fields is studied. In particular, it is found that, when a gravitational plane wave passes through a wall, if the wall has no reflection symmetry, the phenomena, such as reflection, stimulation, or absorption, in general, occur. It is also found that, unlike for gravitational waves, a massless scalar wave or an electromagnetic wave continuously passes through a wall without any reflection. The repulsion and attraction of a plane wall are also studied. It is found that the acceleration of an observer who is at rest relative to the wall usually consists of threemore » parts: one is due to the force produced by the wall, the second is due to the force produced by the space-time curvature, which is zero if the wall has reflection symmetry, and the last is due to the accelerated motion of the wall. As a result, a repulsive (attractive) plane wall may not be repulsive (attractive) at all. Finally, the collision and interaction among the walls are studied.« less

We consider the collisions of plane gravitational and electromagnetic waves with distinct wavefronts and arbitrary polarizations in a Minkowski background. We first present a new, completely geometric formulation of the characteristic initial value problem for solutions in the wave interaction region for which the initial data are those associated with the approaching waves. We present also a general approach to the solution of this problem which enables us in principle to construct solutions in terms of the specified initial data. This is achieved by re-formulating the nonlinear dynamical equations for waves in terms of an associated linear problem on the spectral plane. A system of linear integral ‘evolution’ equations which solve this spectral problem for specified initial data is constructed. It is then demonstrated explicitly how various colliding plane wave spacetimes can be constructed from given characteristic initial data.

It is shown that the solution of Einstein's equations recently found by Kundu can be written in the same form of the Van Stockum solution with the use of an appropriate transformation.

In this work are obtained 5D time‐dependent solutions of Einstein equations, one is obtained by means of equiping a cylindrically symmetry solution (JEKK) with a scalar field, then lifting it to a fifth dimension. The other is obtained transforming the Myers‐Perry solution via Wick rotation. The two solutions can be interpreted as gravitational waves in some cases. The singularities and C‐energy are addressed.

We have investigated a model of colliding plain gravitational waves, proposed by Szekeres, whose structure of singularities is determined. We have evaluated a total energy of matter as a volume integral of the energy–momentum tensor (EMT), whose contributions arise only at these singularities. The total matter energy is conserved before a collision of two plane gravitational waves but decreases during the collision and becomes zero at the end of the collision. We thus interpret that this model of colliding plane gravitational waves is a space–time describing a pair annihilation of plan gravitational waves. We have also calculated a matter conserved charge proposed by the present author and his collaborators. The matter charge is indeed conserved but is zero due to a cancelation between two plain gravitational waves. This seems natural since nothing remains after a pair annihilation, and gives a hint on a physical interpretation of the conserved charge, which we call the gravitational charge. By modifying the space–time for the pair annihilation, we newly construct two types of a scattering plane gravitational wave and a pair creation of plane gravitational waves, and combining all, a Minkowski vacuum bottle, a Minkowski space–time surrounded by two moving plane gravitational waves.

Late-time acceleration with a scalar field source: Observational constraints and statefinder diagnostics

A student-friendly style, over 100 illustrations, and numerous exercises are brought together in this textbook for advanced undergraduate and beginning graduate students in physics and mathematics. Lewis Ryder develops the theory of general relativity in detail. Covering the core topics of black holes, gravitational radiation, and cosmology, he provides an overview of general relativity and its modern ramifications. The book contains chapters on gravitational radiation, cosmology, and connections between general relativity and the fundamental physics of the microworld. It explains the geometry of curved spaces and contains key solutions of Einstein's equations - the Schwarzschild and Kerr solutions. Mathematical calculations are worked out in detail, so students can develop an intuitive understanding of the subject, as well as learn how to perform calculations. The book also includes topics concerned with the relation between general relativity and other areas of fundamental physics. Password protected solutions for instructors are available at www.cambridge.org/9780521845632.

The scalar and Einstein field equations are considered in the general symmetric comoving system. The self-gravitational interaction of the scalar field is expressed by identifying the energy momentum tensor with the one canonically associated to the scalar field. It is shown that the scalar field can depend only on the radial and time variables and that the energy momentum tensor is implicitly conserved. Two classes of solutions are then studied. A first class, that contains the static case previously considered and the complete time-dependent case, is determined by a priori assuming the unknown functions to depend on one only variable. This class is meaningful essentially for massless field. A second class of solutions refers to the a priori assumption that the scalar field alone depends on r or on t. In both cases some comments are developed for the massive scalar field and for a large class of massless fields we are able to determine the solutions.

We consider the coupling of quantum massless and massive scalar particles with exact gravitational plane waves. The cross section for scattering of the quantum particles by the waves is shown to coincide with the classical cross section for scattering of geodesics. The expectation value of the scalar field stress tensor between scattering states diverges at the points where classical test particles focus after colliding with the wave. This indicates that back-reaction effects cannot be ignored for plane waves propagating in the presence of quantum particles and that classical singularities are likely to develop.

A little known embedding theorem due to Campbell1 is discussed and employed to establish the local embedding of four-dimensional gravitational and electromagnetic plane waves in five-dimensional Ricci-flat spaces. In general, this theorem can be employed as a way of relating n-dimensional gravity to (n+1)-dimensional vacuum theories.

We discuss the conditions under which plane electromagnetic and gravitational waves can be amplified by a rotating black hole due to superradiant scattering. We show, in particular, that amplification can occur for low-frequency waves with an incidence angle parametrically close to 0 (or $\pi$) with respect to the black hole spin axis and with a parametrically small left (or right) polarization. This is the case of the radiation emitted by a spinning electric/magnetic dipole or gravitational quadrupole orbiting a black hole companion at large radius and co-rotating with the latter. This can yield observable effects of superradiance, for example, in neutron star-stellar mass black hole binaries, as well as in triple systems composed by a compact binary orbiting a central supermassive black hole. Due to superradiance, the total source luminosity in these systems exhibits a characteristic orbital modulation that may lead to significant observational signatures, thus paving the way for testing, in the near future, one of the most peculiar predictions of general relativity.

Solution of Einstein's equations for a line-mass of perfect fluid

As gravitational wave astronomy prepares for the first detections of gravitational waves from compact-object binary inspirals, theoretical work is required on the study of (i) gravitational-wave sources, (ii) the signals emitted by those sources, and (iii) the searches for those signals in detector data. This thesis describes work on all three fronts. (i) We discuss intermediate-mass-ratio inspirals (IMRIs) of black holes or neutron stars into intermediate-mass black holes (IMBHs) that could be detected with Advanced LIGO. We analyze different mechanisms of IMRI formation and compute IMRI event rates of up to tens of events per year for Advanced LIGO. We study the spin evolution of IMBHs that grow through a series of minor mergers. We explore how a deviation of an IMRI's central body from a Kerr black hole influences geodesics, including the possibility of chaotic orbital dynamics. We also address the scientific consequences of extreme-mass-ratio inspiral (EMRI) detections by LISA for astrophysics and general relativity, and the difficulties associated with detecting and analyzing EMRI signals. (ii) We study the periodic standing-wave approximation (PSWA), which can potentially provide accurate waveforms in the last inspiral cycles of a comparable-mass black-hole binary. Using a simple model, we find that the solution to Einstein's equations for inspiraling black holes can be recovered to a high accuracy by the addition a perturbative radiation-reaction field to the standing-wave, noninspiraling solution. (iii) We demonstrate the utility of searching for and analyzing tracks in time-frequency spectrograms of a gravitational-wave signal as a means of estimating the parameters of a massive black-hole binary inspiral, as observed by LISA.