Related papers: GRay2: A General Purpose Geodesic Integrator for K…
We consider the black hole solutions of five-dimensional gravity with a Gauss-Bonnet term in the bulk and an induced gravity term on a 2-brane of codimension-2. Applying the Kerr-Schild method we derive additional solutions which include…
In this paper we present a new public code, named $ynogkm$, for the fast calculation of time-like geodesics in the Kerr-Newmann (K-N) spacetime, which is a direct extension of $ynogk$ calculating null geodesics in a Kerr spacetime.…
A key obstacle for theory-specific tests of general relativity is the lack of accurate black-hole solutions in beyond-Einstein theories, especially for moderate to high spins. We address this by developing a general framework--based on…
In this paper, we recall some basic facts about the Kerr--Newman--(anti) de Sitter (KNdS) spacetime and review several formulations and integration methods for the geodesic equation of a test particle in such a spacetime. In particular, we…
This paper uses the Kerr geodesic equations for massless particles to derive an acceleration vector in both Boyer-Lindquist and Cartesian coordinates. As a special case, the Schwarzschild acceleration due to a non-rotating mass has a…
Following \cite{dexagol2009} we present a new public code for the fast calculation of null geodesics in the Kerr spacetime. Using Weierstrass' and Jacobi's elliptic functions, we express all coordinates and affine parameters as analytical…
Computing geodesics for Riemannian manifolds is a difficult task that often relies on numerical approximations. However, these approximations tend to be either numerically unstable, have slow convergence, or scale poorly with manifold…
Recent observations of the orbits of star clusters around Sgr $A^\star$, imaging of black holes and gravitational waveforms of merging compact objects require a detailed understanding of the general relativistic geodesic motion. We came up…
We revisit a little known theorem due to Beltrami, through which the integration of the geodesic equations of a curved manifold is accomplished by a method which, even if inspired by the Hamilton-Jacobi method, is purely geometric. The…
The present work deals with the search of useful physical applications of some generalized groups of metric transformations. We put forward different proposals and focus our attention on the implementation of one of them. Particularly, the…
In this article, we describe and numerically implement a method for relativistic location in slightly curved but otherwise generic spacetimes. For terrestrial positioning in the context of Global Navigation Satellite Systems, our algorithm…
Accretion of magnetized gas on compact astrophysical objects such as black holes has been successfully modeled using general relativistic magnetohydrodynamic (GRMHD) simulations. These simulations have largely been performed in the Kerr…
We describe a method to analyze causal geodesics in static and spherically symmetric spacetimes of Kerr-Schild form which, in particular, allows for a detailed study of the geodesics in the vicinity of the central singularity by means of a…
The integration of the equations of motion in gravitational dynamical systems -- either in our Solar System or for extra-solar planetary system -- being non integrable in the global case, is usually performed by means of numerical…
Regular black holes are often geodesically incomplete when their extensions to negative values of the radial coordinate are considered. Here, we propose to use the Simpson-Visser method of regularising a singular spacetime, and apply it to…
We develop a numerical code to compute gravitational waves induced by a particle moving on eccentric inclined orbits around a Kerr black hole. For such systems, the black hole perturbation method is applicable. The gravitational waves can…
GYOTO, a general relativistic ray-tracing code, is presented. It aims at computing images of astronomical bodies in the vicinity of compact objects, as well as trajectories of massive bodies in relativistic environments. This code is…
In a recent work of Wu, Wang, Sun and Liu, a second-order explicit symplectic integrator was proposed for the integrable Kerr spacetime geometry. It is still suited for simulating the nonintegrable dynamics of charged particles moving…
We describe recent numerical simulations of the merger of a class of equal mass, non-spinning, eccentric binary black hole systems in general relativity. We show that with appropriate fine-tuning of the initial conditions to a region of…
Graph similarity is critical in graph-related tasks such as graph retrieval, where metrics like maximum common subgraph (MCS) and graph edit distance (GED) are commonly used. However, exact computations of these metrics are known to be…