Gravitational Collapse with Heat Flux and Gravitational Waves

In this paper, we investigated the cylindrical gravitational collapse with heat flux by considering the appropriate geometry of the interior and exterior spacetimes. For this purpose, we matched collapsing fluid to an exterior containing gravitational waves.The effects of heat flux on gravitational collapse are investigated and matched with the results obtained by Herrera and Santos (Class. Quantum Gravity 22:2407, 2005).     

Resonant Scattering of Gravitational Waves with Electromagnetic Waves

A certain class of exact solutions of Einstein Maxwell spacetime in general relativity is discussed to demonstrate that at the level of theory, when certain parametric resonance condition is met, the interaction of electromagnetic field with a gravitational wave will display certain Lyapunov instability and lead to exponential amplification of a gravitational wave train described by certain Newman–Penrose component of the Weyl curvature. In some way akin to a free electron laser in electromagnet...     

Gravitational Waves in Matter

The theory of gravitational waves in matter is given. This covers the questions of constitutive relation, number of independent polarizations, index of refraction, reflection and refraction at an interface, etc. The theory parallels the familiar optics of electromagnetic waves in material media, but there are some striking differences. The use of the Campbell-Morgan formalism in which the gauge-invariant tidal force dyads E and B rather than the gauge-dependent metric perturbations are the unknowns is essential. The main justification of the theory at the moment is as a theoretical exercise worth doing. The assumption: size L of the medium gravitational wave length (infinite medium) rules out application to the already well-understood detection problem, but there may be an application to gravitational wave propagation through molecular gas clouds of galactic or inter-galactic size.     

Strongly Focused Gravitational Waves

This paper contains a new proof of the formation of trapped spheres, in vacuum spacetimes, by the focusing of gravitational waves, from generic data. The first such result was obtained by Christodoulou (Zurich: Eur Math Soc, 2009). We exploit the same physical mechanism, but give a logically independent construction of these spacetimes.     

Cosmology with Gravitational Waves: A Review

Standard sirens have been the central paradigm in gravitational-wave cosmology so far. From the gravitational wave signature of compact star binaries, it is possible to measure the luminosity distance of the source directly, and if additional information on the source redshift is provided, a measurement of the cosmological expansion can be performed. This review article discusses several methodologies that have been proposed to use gravitational waves for cosmological studies. Methods that use only gravitational-wave signals and methods that use gravitational waves in conjunction with additional observations such as electromagnetic counterparts and galaxy catalogs will be discussed. The review also discusses the most recent results on gravitational-wave cosmology, starting from the binary neutron star merger GW170817 and its electromagnetic counterpart and finishing with the population of binary black holes, observed with the third Gravitational-wave Transient Catalog GWTC–3.     

Non-Conservative Gravitational Equations

We propose a theory of gravity based on the interaction of the gauge field representing gravitation with a suitable vector substratum (physical vacuum). To build up the new theory, we exploit the formalism of the Symbolic Gauge Theory, an application to gauge theories of the General System Logic Theory, which results from the fusion of three mathematical structures, the logical theory of systems, the categorial algebra and the Lie algebra. The coupling of gravity to the substratum implies the nonconservation of the energy-momentum tensor. The derivative coupling term is approximated to the first order, and a Schwarzschild-like solution of the corresponding nonconservative gravitational equations is obtained. It is shown that, in this approximation, the main effect of the new theory is to introduce an extra-mass term in the standard Schwarzschild metric. The application of such a result to perihelion shifts and light deflection yields results comparable to those obtained in General Relativity. Gravitational-wave solutions of the new equations are derived in the weak field approximation. It is shown that our nonconservative theory of gravity implies a cosmological model with a locally varying, non-zero cosmological constant.     

High-Frequency Gravitational Waves in Electromagnetic Waveguides

The interaction between a very-high-frequency gravitational wave (VHFGW) and an electromagnetic wave (EMW) in a rectangular waveguide is discussed in the weak field limit. The background EMW is assumed to be initially in the TE₁₀ mode along the waveguide. It is then shown that a VHFGW, having the same frequency and direction of propagation of the EMW, induces through the waveguide a TE mode with a frequency doubled when compared to the original EMW frequency. In that respect, the GW acts similar to a non-linear medium, giving rise to a Second Harmonic Generation (SHG) effect.     

Gravitational Waves and Black Holes

In these lectures general relativity is outlined as the classical field theory of gravity, emphasizing physical phenomena rather than formalism. Dynamical solutions representing traveling waves as well as stationary fields like those of black holes are discussed. Their properties are investigated by studying the geodesic structure of the corresponding space-times, as representing the motion of point-like test particles. The interaction between gravitational, electro-magnetic and scalar fields is also considered.     

Gravitational Waves and Discontinuous Motions

The mathematical theory of gravitational wave-fronts is revisited with the help of orthogonal decomposition techniques. Thus many important well known results about gravitational waves in empty space are readily obtained in the local geometry framework and in general coordinates. Then different kinds of motion in the presence of a wave are investigated. Our study shows that a discontinuity effect, in traversing the wave-front, arises in the motion. The importance of this effect increases with the complexity of the considered particle. No essential discontinuity is present in simple motions such as that of a point particle and, differently from what usually believed, that of a dust of particles governed by the geodesic deviation equation.     

On Gravitational Energy in Newtonian Theories

There are well-known problems associated with the idea of (local) gravitational energy in general relativity. We offer a new perspective on those problems by comparison with Newtonian gravitation, and particularly geometrized Newtonian gravitation (i.e., Newton–Cartan theory). We show that there is a natural candidate for the energy density of a Newtonian gravitational field. But we observe that this quantity is gauge dependent, and that it cannot be defined in the geometrized (gauge-free) theory without introducing further structure. We then address a potential response by showing that there is an analogue to the Weyl tensor in geometrized Newtonian gravitation.     

Carmeli's Gravitational Field Equations

Carmeli has proposed spinorial field equations in curved space-time to describe gravitation. In this paper we give the relationship between these equations and the standard Einstein gravitational field equations. In particular we show that all solutions to Einstein's equations are solutions to Carmeli's equations, but not vice versa.     

The Use of Gravitational Lenses for Testing Gravitational Theories

The possibility of using gravitational lenses to test gravitational theories is discussed. Relations for gravity ray deflection, rotation of polarization, and shift of the signal arrival time are derived by means of a parametrized post-newtonian formalism for small-sized massive objects.     

Gravitational Waves from a Pseudo-Newtonian Kerr Field with Halos

A close relation between gravitational waveforms and the types of trajectories in a superposed field between a pseudo-Newtonian Kerr black hole and quadrupolar halos is shown in detail. The gravitational waveforms emitted from circular, KAM tori and chaotic orbits must be periodic, quasiperiodic and stochastic, respectively. The chaotic motion can maximally enhance both the amplitudes and the energy emission rates of the waves.     

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.