Related papers: Geodesic deviation on symmetry axis in Taub-NUT me…
The measurement of frequency shifts for light beams exchanged between two test masses nearly in free fall is at the heart of gravitational wave detection. It is envisaged that the derivative of the frequency shift is in fact limited by…
When in a tight binary, the mutual tidal deformations of neutron stars imprint onto observables, encoding information about their internal structure at supranuclear densities and gravity in the extreme-gravity regime. Gravitational wave…
Gowdy's model of cosmological spacetimes is a much investigated subject in classical and quantum gravity. Depending on spatial topology recollapsing as well as expanding models are known. Several analytic tools were used in order to clarify…
We start by constructing a Hilbert manifold T of orientation preserving diffeomorphisms of the circle (modulo the group of bi-holomorphic self-mappings of the disc). This space, which could be thought of as a completion of the universal…
Geodesics escape is widely used to study the scattering of hyperbolic equations. However, there are few progresses except in a simply connected complete Riemannian manifold with nonpositive curvature. We propose a kind of complete…
With the first detections of binary neutron star mergers by gravitational-wave detectors, it proves timely to consider how the internal structure of neutron stars affects the way in which they can be asymmetrically deformed. Such…
A relativistic self-gravitating equilibrium system with steady flow as well as spherical symmetry is discovered. The energy-momentum tensor contains the contribution of a current related to the flow and the metric tensor does an…
Atomic wave interferometers are tied to a telescope pointing towards a faraway star in a nearly free falling satellite. Such a device is sensitive to the acceleration and the rotation relatively to the local inertial frame and to the tidal…
In this paper, we investigate gravitational waves beyond the linear approximation, focusing on second-order contributions sourced by linearized waves in the transverse-traceless (TT) gauge. A general spacetime metric is constructed, and…
The geodesic deviation of a pair of test particles is an natural observable for the gravitational memory effect. Nevertheless in curved spacetime, this observable is plagued with various issues that need to be clarified before one can…
A model in statistical mechanics, characterised by the corresponding Gibbs measure, is a subset of the totality of probability distributions on the phase space. The shape of this subset, i.e., the geometry, then plays an important role in…
We present a proof of Thue-Siegel-Roth's Theorem (and its more recent variants, such as those of Lang for number fields and that "with moving targets" of Vojta) as an application of Geometric Invariant Theory (GIT). Roth's Theorem is…
In this manuscript, we show how conformal invariance can be incorporated in a classical theory of gravitation, in the context of metric measure space. Metric measure space involves a geometrical scalar $f$, dubbed as density function, which…
The response of astrophysical compact objects to external tidal fields carries valuable information on the nature of these objects, on the equation of state of matter, and on the underlying gravitational theory. In this work, we highlight…
We investigate the impact of spacetime non-commutativity on the tidal deformability of compact objects and explore the feasibility of detecting non-commutative (NC) effects through gravitational wave (GW) observations. We considered NC…
Unimodular gravity is a modified theory with respect to general relativity by an extra condition that the determinant of the metric is fixed. Especially, if the energy-momentum tensor is not imposed to be conserved separately, a new…
We study geodesics along a noncompact Kerr-Newman instanton, where the asymptotic geometry is either de Sitter or anti-de Sitter. We use first integrals for the Hamilton-Jacobi equation to characterize trajectories both near and away from…
In this article we introduce a diffeomorphism-invariant Riemannian metric on the space of vector valued one-forms. The particular choice of metric is motivated by potential future applications in the field of functional data and shape…
General relativistic effects in the spacetime around the massive astrophysical objects can be captured using a spinning test gyro orbiting around the object in a circular geodesic. This article discusses how the tidal disruption due to a…
We study relative motion of nearby test particles in Topologically Massive Gravity (TMG) in three spacetime dimensions, using the equation of geodesic deviation. We show that, in a suitable reference frame, the influence of any…