Related papers: Null Geodesics and Wave Front Singularities in the…
We prove the first bifurcation result of time quasi-periodic traveling waves solutions for space periodic water waves with vorticity. In particular we prove existence of small amplitude time quasi-periodic solutions of the gravity-capillary…
Non-metricity provides a natural extension of Riemannian geometry, yet its experimental signatures remain largely unexplored. In this work we investigate how spacetime non-metricity can be probed through high-precision observations,…
We reconsider the unique continuation property for a general class of tensorial Klein-Gordon equations of the form \begin{align*} \Box_{g} \phi + \sigma \phi = \mathcal{G}(\phi,\nabla \phi) \text{,} \qquad \sigma \in \mathbb{R} \end{align*}…
Within the closed universe, we obtain the amplitude and frequency of gravitational waves in the terms of discrete wave numbers, wave propagation time, and cosmological constant using the deviation equation in the first-order perturbed…
In this work we find analytical solutions to the null geodesics around a black hole in the conformal Weyl gravity. Exact expressions for the horizons are found, and they depend on the cosmological constant and the coupling constants of the…
We derive the effects of a non-zero cosmological constant $\Lambda$ on gravitational wave propagation in the linearized approximation of general relativity. In this approximation we consider the situation where the metric can be written as…
The null distance for Lorentzian manifolds was recently introduced by Sormani and Vega. Under mild assumptions on the time function of the spacetime, the null distance gives rise to an intrinsic, conformally invariant metric that induces…
We study null geodesics that connect the two asymptotically flat regions of the maximally extended Kerr spacetime. These vortical geodesics traverse both horizons and pass through the ring singularity, linking the positive-$r$ exterior to…
We experimentally implement a virtual geometric periodicity in an elastic metamaterial. First, unwanted boundary reflections at the domain ends are cancelled through the iterative injection of the polarity reversed, reflected wavefield. The…
We investigate the polarization modes of gravitational waves in $f(Q)$ non-metric gravity without gauge fixing. The main result of this study is that no further scalar mode appears more than the two standard plus and cross transverse…
The problem of deriving a shock-wave geometry with cosmological constant by boosting a Schwarzschild-de Sitter (or anti-de Sitter) black hole is re-examined. Unlike previous work in the literature, we deal with the exact Schwarzschild-de…
We describe an approach to the issue of the singularities of null hypersurfaces, due to the focusing of null geodesics, in the context of the recently introduced formulation of GR via null foliations.
The geometry of impulsive pp-waves is explored via the analysis of the geodesic and geodesic deviation equation using the distributional form of the metric. The geodesic equation involves formally ill-defined products of distributions due…
The theory of noncommutative geometry provides an interesting mathematical background for developing new physical models. In particular, it allows one to describe the classical Standard Model coupled to Euclidean gravity. However,…
We use the conformal approach to numerical relativity to evolve hyperboloidal gravitational wave data without any symmetry assumptions. Although our grid is finite in space and time, we cover the whole future of the initial data in our…
In this paper, we study the polarization of a gravitational wave (GW) emitted by an astrophysical source at a cosmic distance propagating through the Friedmann-Lema\^itre-Robertson-Walk universe. By considering the null geodesic deviations,…
In this paper we demonstrate that using a mathematical physics approach (focusing the attention to the physics and using mathematics as a tool) it is possible to visualize the formation of the transverse modes inside a cylindrical…
Each and every observational information we obtain from the sky regarding the brightnesses, distances or image distortions resides on the deviation of a null geodesic bundle. In this talk, we present the symplectic evolution of this bundle…
Glasses have a large excess of low-frequency vibrational modes in comparison with crystalline solids. We show that such a feature is a necessary consequence of the geometry generic to weakly connected solids. In particular, we analyze the…
The geometric concept of geodesic completeness depends on the choice of the metric field or "metric frame". We develop a frame-invariant concept of "generalised geodesic completeness" or "time completeness". It is based on the notion of…