Modifcations to gravitational waves due to matter shells

As detections of gravitational waves (GWs) mount, the need to investigate various effects on the propagation of these waves from the time of emission until detection also grows. We investigate how a thin low density dust shell surrounding a gravitational wave source affects the propagation of GWs. The Bondi-Sachs (BS) formalism for the Einstein equations is used for the problem of a gravitational wave (GW) source surrounded by a spherical dust shell. Using linearised perturbation theory, we and the geometry of the regions exterior to, interior to and within the shell. We and that the dust shell causes the gravitational wave to be modified both in magnitude and phase, but without any energy being transferred to or from the dust. This finding is novel. In the context of cosmology, apart from the gravitational redshift, the effects are too small to be measurable; but the effect would be measurable if a GW event were to occur with a source surrounded by a massive shell and with the radius of the shell and the wavelength of the GWs of the same order. We extended our investigation to astrophysical scenarios such as binary black hole (BBH) mergers, binary neutron star (BNS) mergers, and core collapse supernovae (CCSNe). In these scenarios, instead of a monochromatic GW source, as we used in our initial investigation, we consider burst-like GW sources. The thin density shell approach is modified to include thick shells by considering concentric thin shells and integrating. Solutions are then found for these burst-like GW sources using Fourier transforms. We show that GW echoes that are claimed to be present in the Laser Interferometer Gravitational-Wave Observatory (LIGO) data of certain events, could not have been caused by a matter shell. We do and, however, that matter shells surrounding BBH mergers, BNS mergers, and CCSNe could make modifications of order a few percent to a GW signal. These modifications are expected to be measurable in GW data with current detectors if the event is close enough and at a detectable frequency; or in future detectors with increased frequency range and amplitude sensitivity. Substantial use is made of computer algebra in these investigations. In setting the scene for our investigations, we trace the evolution of general relativity (GR) from Einstein's postulation in 1915 to vindication of his theory with the confirmation of the existence of GWs a century later. We discuss the implications of our results to current and future considerations. Calculations of GWs, both analytical and numerical, have normally assumed their propagation from source to a detector on Earth in a vacuum spacetime, and so discounted the effect of intervening matter. As we enter an era of precision GW measurements, it becomes important to quantify any effects due to propagation of GWs through a non-vacuum spacetime Observational confirmation of the modification effect that we and in astrophysical scenarios involving black holes (BHs), neutron stars (NSs) and CCSNe, would also enhance our understanding of the details of the physics of these bodies.

Type II Vacuum Spacetime Admitting Closed Timelike Curves

We present a cyclic symmetry type II vacuum spacetime admitting closed timelike curves (CTCs) which appear after a certain instant of time, i.e., a time-machine spacetime. The various authors in past have considered the 2D and 4D flat generalization of Misner space, but in the present work, we have considered the curved spacetime generalzations of 4D Misner space, and is asymptotically flat radially

Static Spherically Symmetric Black Holes in Weak f(T)-Gravity

With the advent of gravitational wave astronomy and first pictures of the “shadow” of the central black hole of our milky way, theoretical analyses of black holes (and compact objects mimicking them sufficiently closely) have become more important than ever. The near future promises more and more detailed information about the observable black holes and black hole candidates. This information could lead to important advances on constraints on or evidence for modifications of general relativity. More precisely, we are studying the influence of weak teleparallel perturbations on general relativistic vacuum spacetime geometries in spherical symmetry. We find the most general family of spherically symmetric, static vacuum solutions of the theory, which are candidates for describing teleparallel black holes which emerge as perturbations to the Schwarzschild black hole. We compare our findings to results on black hole or static, spherically symmetric solutions in teleparallel gravity discussed in the literature, by comparing the predictions for classical observables such as the photon sphere, the perihelion shift, the light deflection, and the Shapiro delay. On the basis of these observables, we demonstrate that among the solutions we found, there exist spacetime geometries that lead to much weaker bounds on teleparallel gravity than those found earlier. Finally, we move on to a discussion of how the teleparallel perturbations influence the Hawking evaporation in these spacetimes.

The first-order symmetry operator on gravitational perturbations in the 5D Myers–Perry spacetime with equal angular momenta

It has been revealed that the first-order symmetry operator for the linearized Einstein equation on a vacuum spacetime can be constructed from a Killing–Yano 3-form. This might be used to construct all or part of the solutions to the field equation. In this paper, we perform a mode decomposition of a metric perturbation on the Schwarzschild spacetime and the Myers–Perry spacetime with equal angular momenta in 5 dimensions, and investigate the action of the symmetry operator on specific modes concretely. We show that, on such spacetimes, there is no transition between the modes of a metric perturbation by the action of the symmetry operator, and it ends up being the linear combination of the infinitesimal transformations of isometry.

Cosmic acceleration via space-time-matter theory

We consider the space-time-matter theory (STM) in a 5D vacuum spacetime with a generalized FLRW metric to investigate the late-time acceleration of the universe. For this purpose, we derive the 4D induced field equations and obtain the evolution of the state parameter with respect to the redshift. Then, we show that with consideration of the extra dimension scale factor to be a linear function of redshift, this leads to a model which gives an accelerating phase in the universe. Moreover, we derive the geodesic deviation equation in the STM theory to study the relative acceleration of the parallel geodesics of this spacetime, and also, obtain the observer area-distance as a measurable quantity to compare this theory with two other models.

Asymptotically flat vacuum solution in modified theory of Einstein’s gravity

A number of recent observations have suggested that the Einstein’s theory of general relativity may not be the ultimate theory of gravity. The f(R) gravity model with R being the scalar curvature turns out to be one of the best bet to surpass the general relativity which explains a number of phenomena where Einstein’s theory of gravity fails. In the f(R) gravity, behaviour of the spacetime is modified as compared to that of given by the Einstein’s theory of general relativity. This theory has already been explored for understanding various compact objects such as neutron stars, white dwarfs etc. and also describing evolution of the universe. Although researchers have already found the vacuum spacetime solutions for the f(R) gravity, yet there is a caveat that the metric does have some diverging terms and hence these solutions are not asymptotically flat. We show that it is possible to have asymptotically flat spherically symmetric vacuum solution for the f(R) gravity, which is different from the Schwarzschild solution. We use this solution for explaining various bound orbits around the black hole and eventually, as an immediate application, in the spherical accretion flow around it.

Generating elastic solutions of the Einstein field equations from the Schwarzschild vacuum solution

The problem of generating solutions of the Einstein field equations with an elastic energy–momentum tensor from the Schwarzschild vacuum solution by means of conformal transformations is analyzed. Applying the formulation of relativistic elasticity, suitable conformal factors are obtained for static and non-static elastic spacetime configurations and particular solutions are presented. This work shows that the technique used here permits generating new elastic matter solutions from a vacuum spacetime.