Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userRainbow scattering of gravitational plane waves by a compact body
56
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We study the time-independent scattering of a planar gravitational wave propagating in the curved spacetime of a compact body with a polytropic equation of state. We begin by considering the geometric-optics limit, in which the gravitational wave propagates along null geodesics of the spacetime; we show that a wavefront passing through a neutron star of tenuity $R/M = 6$ will be focussed at a cusp caustic near the stars surface. Next, using the linearized Einstein Field Equations on a spherically-symmetric spacetime, we construct the metric perturbations in the odd and even parity sectors; and, with partial-wave methods, we numerically compute the gravitational scattering cross section from helicity-conserving and helicity-reversing amplitudes. At long wavelengths, the cross section is insensitive to stellar structure and, in the limit $M omega rightarrow 0$, it reduces to the known low-frequency approximation of the black hole case. At higher frequencies $M omega gtrsim 1$, the gravitational wave probes the internal structure of the body. In essence, we find that the gravitational wave cross section is similar to that for a massless scalar field, although with subtle effects arising from the non-zero helicity-reversing amplitude, and the coupling in the even-parity sector between the gravitational wave and the fluid of the body. The cross section exhibits emph{rainbow scattering} with an Airy-type oscillation superposed on a Rutherford cross section. We show that the rainbow angle, which arises from a stationary point in the geodesic deflection function, depends on the polytropic index. In principle, rainbow scattering provides a diagnostic of the equation of state of the compact body; but, in practice, this requires a high-frequency astrophysical source of gravitational waves.
rate research
Read More
We investigate the wave effects of gravitational waves (GWs) using numerical simulations with the finite element method (FEM) based on the publicly available code {it deal.ii}. We robustly test our code using a point source monochromatic spherical wave. We examine not only the waveform observed by a local observer but also the global energy conservation of the waves. We find that our numerical results agree very well with the analytical predictions. Based on our code, we study the scattering of GWs by compact objects. Using monochromatic waves as the input source, we find that if the wavelength of GWs is much larger than the Schwarzschild radius of the compact object, the amplitude of the total scattered GWs does not change appreciably due to the strong diffraction effect, for an observer far away from the scatterer. This finding is consistent with the results reported in the literature. However, we also find that, near the scatterer, not only the amplitude of the scattered waves is very large, comparable to that of the incident waves, but also the phase of the GWs changes significantly due to the interference between the scattered and incident waves. As the evolution of the phase of GWs plays a crucial role in the matched filtering technique in extracting GW signals from the noisy background, our findings suggest that wave effects should be taken into account in the data analysis in the future low-frequency GW experiments, if GWs are scattered by nearby compact objects in our local environment.
The geometry of twisted null geodesic congruences in gravitational plane wave spacetimes is explored, with special focus on homogeneous plane waves. The role of twist in the relation of the Rosen coordinates adapted to a null congruence with the fundamental Brinkmann coordinates is explained and a generalised form of the Rosen metric describing a gravitational plane wave is derived. The Killing vectors and isometry algebra of homogeneous plane waves (HPWs) are described in both Brinkmann and twisted Rosen form and used to demonstrate the coset space structure of HPWs. The van Vleck-Morette determinant for twisted congruences is evaluated in both Brinkmann and Rosen descriptions. The twisted null congruences of the Ozsvath-Schucking,`anti-Mach plane wave are investigated in detail. These developments provide the necessary geometric toolkit for future investigations of the role of twist in loop effects in quantum field theory in curved spacetime, where gravitational plane waves arise generically as Penrose limits; in string theory, where they are important as string backgrounds; and potentially in the detection of gravitational waves in astronomy.
We give a higher even dimensional extension of vacuum colliding gravitational plane waves with the combinations of collinear and non-collinear polarized four-dimensional metric. The singularity structure of space-time depends on the parameters of the solution.
We give an account of the gravitational memory effect in the presence of the exact plane wave solution of Einsteins vacuum equations. This allows an elementary but exact description of the soft gravitons and how their presence may be detected by observing the motion of freely falling particles. The theorem of Bondi and Pirani on caustics (for which we present a new proof) implies that the asymptotic relative velocity is constant but not zero, in contradiction with the permanent displacement claimed by Zeldovich and Polnarev. A non-vanishing asymptotic relative velocity might be used to detect gravitational waves through the velocity memory effect, considered by Braginsky, Thorne, Grishchuk, and Polnarev.
The behaviour of a test electromagnetic field in the background of an exact gravitational plane wave is investigated in the framework of Einsteins general relativity. We have expressed the general solution to the de Rham equations as a Fourier-like integral. In the general case we have reduced the problem to a set of ordinary differential equations and have explicitly written the solution in the case of linear polarization of the gravitational wave. We have expressed our results by means of Fermi Normal Coordinates (FNC), which define the proper reference frame of the laboratory. Moreover we have provided some gedanken experiments, showing that an external gravitational wave induces measurable effects of non tidal nature via electromagnetic interaction. Consequently it is not possible to eliminate gravitational effects on electromagnetic field, even in an arbitrarily small spatial region around an observer freely falling in the field of a gravitational wave. This is opposite to the case of mechanical interaction involving measurements of geodesic deviation effects. This behaviour is not in contrast with the principle of equivalence, which applies to arbitrarily small region of both space and time.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
