Gravitational plane waves in Einstein-aether theory

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.

A number of exact solutions of Einstein's equations are obtained, which describe the collisions between one scalar plane wave and one scalar, neutrino, electromagnetic or gravitational plane wave.

Gravitational waves can act like gravitational lenses, affecting the observed positions, brightnesses, and redshifts of distant objects. Exact expressions for such effects are derived here in general relativity, allowing for arbitrarily-moving sources and observers in the presence of plane-symmetric gravitational waves. At least for freely falling sources and observers, it is shown that the commonly-used predictions of linear perturbation theory can be generically overshadowed by nonlinear effects; even for very weak gravitational waves, higher-order perturbative corrections involve secularly-growing terms which cannot necessarily be neglected when considering observations of sufficiently distant sources. Even on more moderate scales where linear effects remain at least marginally dominant, nonlinear corrections are qualitatively different from their linear counterparts. There is a sense in which they can, for example, mimic the existence of a third type of gravitational wave polarization.

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.

Compact orbiting binaries like the black hole binary system observed in GW150914 carry large amount of orbital angular momentum. The post-ringdown compact object formed after merger of such a binary configuration has only spin angular momentum, and this results in a large orbital angular momentum excess. One significant possibility is that the gravitational waves generated by the system carry away this excess orbital angular momentum. An estimate of this excess is made. Arguing that plane gravitational waves cannot possibly carry any orbital angular momentum, a case is made in this paper for gravitational wave beams carrying orbital angular momentum, akin to optical beams. Restricting to certain specific beam-configurations, we predict that such beams may produce a new type of strain, in addition to the longitudinal strains measured at aLIGO for GW150914 and GW170817. Current constraints on post-ringdown spins, derived within the plane-wave approximation of gravitational waves, therefore stand to improve. The minimal modification that might be needed on a laser-interferometer detector (like aLIGO or VIRGO) to detect such additional strains is also briefly discussed.

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 study the classical and quantum dynamics of strings near spacetime singularities. We deal with singular gravitational plane waves of arbitrary polarization and arbitrary profile functions W1(U) and W2(U), whose behaviour for U to 0 is W1(U)= alpha 1/ mod U mod ( beta 1), W2(U)= alpha 2/ mod U mod ( beta 2) (U being a null variable). In these spacetimes, the string dynamics is exactly (and explicitly) solvable even at the spacetime singularities. The string behaviour depends crucially on whether both parameters beta 1 and beta 2 are smaller or larger than two. When beta 1>or=2 and/or beta 2>or=2, the string does not cross the singularity U = 0 but goes off to infinity in a given direction alpha depending on the polarization of the gravitational wave. The string time evolution is fully determined by the spacetime geometry, whereas the overall sigma -dependence is fixed by the initial string state. The proper length at fixed tau to 0 (U to 0) stretches infinitely. For beta 1<2 and beta 2<2, the string passes smoothly through the spacetime singularity and reaches the U>0 region. In this case, outgoing operators make sense and we find the explicit transformation relating in and out operators. For the quantum string states, this implies spin polarization rotations and particle transmutations. The expectation values of the outgoing mass and mode number operators are computed and the excitation of the string modes after the crossing of the spacetime singularity is analysed.

Gravitational wave (GW) observations of coalescing compact binaries will be unique probes of strong-field, dynamical aspects of relativistic gravity. We present a short review of various schemes proposed in the literature to test general relativity (GR) and alternative theories of gravity using inspiral waveforms. Broadly these schemes may be classified into two types: model dependent and model independent. In the model dependent category, GW observations are compared against a specific waveform model representative of a particular theory or a class of theories such as scalar-tensor theories, dynamical Chern–Simons theory and massive graviton theories. Model independent tests are attempts to write down a parametrized gravitational waveform where the free parameters take different values for different theories and (at least some of) which can be constrained by GW observations. We revisit some of the proposed bounds in the case of downscaled LISA configuration (eLISA) and compare them with the original LISA configuration. We also compare the expected bounds on alternative theories of gravity from ground-based and space-based detectors and find that space-based GW detectors can test GR and other theories of gravity with unprecedented accuracies. We then focus on a recent proposal to use singular value decomposition of the Fisher information matrix to improve the accuracies with which post-Newtonian theory can be tested. We extend those results to the case of space-based detector eLISA and discuss its implications.

Starting from the polarized Gowdy model in Ashtekar variables, the Killing equations characteristic for plane-fronted parallel gravitational waves are introduced in part as a set of first-class constraints, in addition to the standard ones of General Relativity. These constraints are expressed in terms of quantities that have an operator equivalent in Loop Quantum Gravity, making plane wave space-times accessible to loop quantization techniques.

Exact Plane Gravitational Waves and Electromagnetic Fields

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.

We study spin and flavor oscillations of astrophysical neutrinos under the influence of external fields in curved spacetime. First, we consider spin oscillations in case of neutrinos gravitationally scattered off a rotating supermassive black hole surrounded by a thin magnetized accretion disk. We find that the gravitational interaction only does not result in the spin-flip of scattered ultrarelativistic neutrinos. Realistic magnetic fields lead to the significant reduction of the observed flux of neutrinos possessing reasonable magnetic moments. Second, we study neutrino flavor oscillations in stochastic gravitational waves (GWs). We derive the effective Hamiltonian for neutrinos interacting with a plane GW having an arbitrary polarization. Then, we consider stochastic GWs with arbitrary correlators of amplitudes. The equation for the density matrix for neutrino oscillations is solved analytically and the probabilities to detect certain neutrino flavors are derived. We find that the interaction of neutrinos, emitted by a core-collapsing supernova, with the stochastic GW background results in the several percent change of the neutrino fluxes. The observability of the predicted effects is discussed.

In general relativity (GR), linearized gravitational waves propagating in empty Minkowski spacetime along a fixed spatial direction have the property that the wave front is the Euclidean plane. Beyond the linear regime, exact plane waves in GR have been studied theoretically for a long time and many exact vacuum solutions of the gravitational field equations are known that represent plane gravitational waves. These have parallel rays and uniform wave fronts. It turns out, however, that GR also admits exact solutions representing gravitational waves propagating along a fixed direction that are nonplanar. The wave front is then nonuniform and the bundle of rays is twisted. We find a class of solutions representing nonplanar unidirectional gravitational waves and study some of the properties of these twisted waves.

We consider a class of Lorentz-violating theories of gravity involving a timelike unit vector field (the aether) coupled to a metric, two examples being Einstein-aether theory and Ho\v{r}ava gravity. The action always includes the Ricci scalar of the metric and the invariants quadratic in covariant derivatives of the aether, but the theories differ in how the aether is constructed from other fields, and whether those fields are varied in the action. Fields that are not varied define background structures breaking diffeomorphsim invariance, including threadings, folations, and clocks, which generally produce novel degrees of freedom arising from the violation of what would otherwise be initial value constraints. The principal aims of this paper are to survey the nature of the theories that arise, and to understand the consequences of breaking diffeomorphism invariance in this setting. In a companion paper [arXiv:1504.03305], we address some of the phenomenology of the "ponderable aether" case in which the presence of a background clock endows the aether with a variable internal energy density that behaves in some respects like dark matter.

Gravitational radiation arising during the formation of a protoneutron star is studied. Here it is mainly large-scale nonuniformities that develop inside the star. The entropy and density profiles of such nonuniformities resemble the "mushroom cloud" of a nuclear explosion. A bubble of hot neutron matter floats to the surface of the star, like the "mushroom cloud" of an explosion in the earth's atmosphere. Depending on the symmetry of the problem, from two to six bubbles can float upward at the same time. The characteristic masses of such bubbles are 0.01M ⊗ and the radial velocities reach ∼0.1c. The energy radiated in the form of gravitational waves in one cycle of bubbles floating to the surface is ∼10−2 M ⊗ c 2−10−10 M ⊗ c 2. Such cycles occur repeatedly as the neutron star cools. This phase can last up to seconds. The total energy radiated in the form of gravitational radiation can reach 10−1 M ⊗ c 2.