Related papers: Lorentzian angles and trigonometry including light…
In this paper we investigate the strong gravitational lensing with Gauss-Bonnet gravity. By considering the logarithmic term for deflection angle, we obtain the deflection angle $\hat\alpha$ and corresponding parameters $\bar{a}$ and…
Beyond the Newtonian approximation, gravitational fields in general relativity can be described using a formalism known as gravitoelectromagnetism. In this formalism a vector potential, the gravitomagnetic potential, arises as a result of…
The Lorentz covariant theory of propagation of light in the (weak) gravitational fields of N-body systems consisting of arbitrarily moving point-like bodies with constant masses is constructed. The theory is based on the Lienard-Wiechert…
We present a concise new definition of Finsler spacetimes that generalize Lorentzian metric manifolds and provide consistent backgrounds for physics. Extending standard mathematical constructions known from Finsler spaces we show that…
In order to clarify effects of the finite distance from a lens object to a light source and a receiver, the gravitational deflection of light has been recently reexamined by using the Gauss-Bonnet (GB) theorem in differential geometry…
We present a general approach for the formulation of equations of motion for compact objects in general relativistic theories. The particle is assumed to be moving in a geometric background which in turn is asymptotically flat. Our approach…
We first define what we mean by gravitational lensing equations in a general space-time. A set of exact relations are then derived that can be used as the gravitational lens equations in all physical situations. The caveat is that into…
We establish three circles theorems for subharmonic functions on Riemannian manifolds with nonnegative Ricci curvature, as well as on gradient shrinking Ricci solitons with scalar curvature bounded from below by $\frac{n-2}{2}$. We also…
Vogt's theorem, concerning boundary angles of a convex arc with monotonic curvature (spiral arc), is taken as a starting point to establish basic properties of spirals. The theorem is expanded by removing requirements of convexity and…
In the authors' previous work, it was shown that if a zero mean curvature $C^4$-differentiable hypersurface in an arbitrarily given Lorentzian manifold admits a degenerate light-like point, then the hypersurface contains a light-like…
In this work, we study the gravitational lensing by a Lorentz-violating (LV) black hole inspired by the recent contribution [1]. Explicitly, we concentrate on a specific application: we perform the computation of gravitational lensing…
We apply the ``consistent discretization'' technique to the Regge action for (Euclidean and Lorentzian) general relativity in arbitrary number of dimensions. The result is a well defined canonical theory that is free of constraints and…
A key insight used in developing the theory of Causal Dynamical Triangulations (CDTs) is to use the causal (or light-cone) structure of Lorentzian manifolds to restrict the class of geometries appearing in the Quantum Gravity (QG) path…
New splitting theorems in a semi-Riemannian manifold which admits an irrotational vector field (not necessarily a gradient) with some suitable properties are obtained. According to the extras hypothesis assumed on the vector field, we can…
The standard General Relativity results for precession of particle orbits and for bending of null rays are derived as special cases of perturbation of a quantity that is conserved in Newtonian physics, the Runge-Lenz vector. First this…
We derive Carrollian field theories via null reduction from Lorentzian light-cone actions in Minkowski spacetime. By suitably deforming the light-cone action, we reduce the Poincar\'e invariance to a Bargmann subgroup, from which both…
A new derivation of the relativistic aberration formula for a plane-polarized light wave is presented that does not require any use of the Lorentz transformation. The method is based on a modification of the Huygens-Fresnel principle to…
On a time-oriented Lorentzian manifold $(M,g)$ with non-empty boundary satisfying a convexity assumption, we show that the topological, differentiable, and conformal structure of suitable subsets $S\subset M$ of sources is uniquely…
We present an abstract approach to Lorentzian Gromov-Hausdorff distance and convergence, and an alternative approach to Lorentzian length spaces that does not use auxiliary ``positive signature'' metrics or other unobserved fields. We begin…
We report on some recent results on a class of relativistic lagrangian field theories supporting non-topological soliton solutions and their applications in the contexts of Gravitation and Cosmology. We analyze one and many-components…