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Over a four-dimensional manifold M, a neighbourhood U of a point p ∈ M can be mapped to a subset Ψ(U ) of R 4 . (Only two dimensions are shown.)
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The existence of gravitational radiation is a natural prediction of any relativistic description of the gravitational interaction. In this chapter, we focus on gravitational waves, as predicted by Einstein's general theory of relativity. First, we introduce those mathematical concepts that are necessary to properly formulate the physical theory, su...
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... such that, at every point, it is possible to define a local neighbourhood that is isomorphic to an open set of R 4 . Loosely speaking, this means that for a "sufficiently small" part of M, it is possible to assign four numbers, called coordinates, to every point p. Therefore, a coordinate system (or chart) over an open subset U of M is a map (see Fig. ...
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We model the scalar waves produced during the ringdown stage of binary black hole coalescence in Einstein scalar Gauss-Bonnet (EsGB) gravity, using numerical relativity simulations of the theory in the decoupling limit. Through a conformal coupling of the scalar field to the metric in the matter-field action, we show that the gravitational waves in...
Citations
... In a curved space with a Peres [6,7] type of cylindrically symmetric metric ...
The proposed modications of the Einstein-Maxwell equations include: (1) the addition of a scalar term to the electromagnetic side of the equation rather than to the gravitational side, (2) the introduction of a 4-dimensional, nonlinear electromagnetic constitutive tensor, (3) the addition of curvature terms arising from the non-metric components of a general symmetric connection and (4) the addition of a non-isotropic pressure tensor. The scalar term is dened by the condition that a spherically symmetric particle be force-free and mathematically well-behaved everywhere. The constitutive tensor introduces two structure elds; one contributes to the mass and the other contributes to the angular momentum. The additional curvature terms couple both to particle solutions and to localized electromagnetic and gravitational wave solutions. The pressure term is needed for the most general spherically symmetric, static metric. It results in a distinction between the Schwarzschild mass and the inertial mass.
... Einstein's field equation compares the energy distribution of an object with its disruption of spacetime, thus, disturbances in the physical nature of a gravitational body will have an influence in its space-time distortion, generating the so called gravitational waves, which propagate through space-time and can be measured. The amplitude of the GWs, also referred to as space-time strain (h) can be modelled as a function of the quadrupole moment acceleration (Q ij ) of the source body, the distance between source and GW position (r) and the gravitational (G) and speed of light (c) constants to obtain the Quadrupole formula [5] h(r, t) = − 4G c 4 ...
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The characterisation and testing of space instruments and technology is a very delicate task
and to it corresponds a big part of a mission's fund and time budget. Unlike for other �elds, in
space science, the level of assurance over the functionality of implemented technologies needs
to be very high, as risks often come with a very high cost. In this work an optical test-bench
is presented for inter-satellite interferometry (ISI) photoreceivers, in particular for the grav-
itational wave observatory Laser Interferometer Space Antenna (LISA) , together with the
tools, concepts and techniques used for its development. The presented test-bench is able to
characterise photoreceivers in terms of input-noise, frequency response and phase-temperature
dependence. In order to certify the functionality and accuracy of the tests, a custom LISA-
like photoreceiver has been developed that is presented alongside the test-bench. This work
provides as well with a discussion and overview of gravitational waves, inter-satellite interfer-
ometry , the LISA mission and state of the art photodetection technology.
... General Relativity predicts that space can be dilated and contracted by gravitational waves (Tiec, Novak, 2017), which were discovered in (Abott et al., 2016). However, the idea that a gravity wave could shrink and dilate space and therefore affect the beams of the LIGO interferometer, has no bijective correspondence with the physical world. ...
A bijective function f: X → Y is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and where each element of the other set is paired with exactly one element of the first set. We can define every physical equation as the set X and the corresponding physical reality that the equation describes as the set Y. Every element in a given equation is an element in the set X, and each element in set X should have exactly one paired element in the set Y. The bijective analysis confirms that Newtonian physics satisfies the bijective function. On the other hand, not all of the equations in the Theory of Relativity satisfy the bijective function. Additionally, the Higgs mechanism does not satisfy the bijective function.
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We solve the Laplace equation $\Box h_{ij}=0$ describing the propagation of gravitational waves in an expanding background metric with a power law scale factor in the presence of a point mass in the weak field approximation (Newtonian McVittie background). We use boundary conditions at large distances from the mass corresponding to a plane gravitational wave in an expanding background. We compare the solution with the corresponding solution in the absence of the point mass and show that the point mass increases the amplitude of the wave and also decreases its frequency (as observed by an observer at infinity) in accordance with gravitational time delay.
We present the formal solution for a quantum mechanical particle responding to gravitational wave (GW) in the framework of modified theories of gravity (MTG) where, apart from the two standard tensorial modes of polarization of GW, we have considered an additional scalar mode. The presence of this longitudinal scalar mode makes it necessary to extend the usual two-dimensional description of matter-GW interaction to a three-dimensional one. Naturally this requires non-trivial changes in the quantum mechanical treatment which we elaborate in this paper.
