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In this work, we investigate geodesics and black hole shadows in the Kerr-Bertotti-Robinson spacetime. We show that the equations of motion for null geodesics are separable and admit analytical treatment, whereas timelike geodesics are…
In section 2, we introduce fundamental concepts of GR concerning the measurement of time, relativistic reference systems and we review the recent literature of chronometric geodesy. In section 3 we introduce the theory of frequency standard…
We give an accessible introduction and elaboration on the methods used in obtaining a geodesic, which is the curve of shortest length connecting two points lying on the surface of a function. This is found through computing what's known as…
Starting with an exact and simple geodesic, we generate approximate geodesics by summing up higher-order geodesic deviations within a General Relativistic setting, without using Newtonian and post-Newtonian approximations. We apply this…
The introduction of automated deduction systems in secondary schools face several bottlenecks, the absence of the subject of rigorous mathematical demonstrations in the curricula, the lack of knowledge by the teachers about the subject and…
Interpreting horizon-scale observations of astrophysical black holes demands a general understanding of null geodesics in the Kerr spacetime. These may be divided into two classes: "direct" rays that primarily determine the observational…
One of geodesy's main tasks is to determine the gravity field of the Earth. High precision clocks have the potential to provide a new tool in a global determination of the Earth's gravitational potential based on the gravitational redshift.…
Given the extreme accuracy reached by future global space astrometry, one needs a global relativistic modeling of observations. A relativistic definition of astrometric observables is then essential to find uniquely coordinates, parallax…
Geodesic orbit equations in the Schwarzschild geometry of general relativity reduce to ordinary conic sections of Newtonian mechanics and gravity for material particles in the non-relativistic limit. On the contrary, geodesic orbit…
A universal method to solve the differential equations of light-like geodesics is developed. The validity of this method depends on a new theorem, which is introduced for light-like geodesics in analogy to Beltrami's "geometrical" method…
We present a class of general prolate and oblate spheroidal spacetimes for the description of cosmic structures in the Universe. They are exact geometries which represent, in an appropriated way, the imbedding of spheroidal matter-energy…
The Earth's geoid is one of the most essential and fundamental concepts to provide a gravity field-related height reference in geodesy and associated sciences. To keep up with the ever-increasing experimental capabilities and to…
These lecture notes are intended as a guide to Graduate level readers that are already familiar with basic General Relativity. They present in a concise way some advanced concepts and problems encountered in the study of gravitation. In…
In considering the mathematical problem of describing the geodesics on a torus or any other surface of revolution, there is a tremendous advantage in conceptual understanding that derives from taking the point of view of a physicist by…
Teaching modern physics in high school is of increasingly importance as it can offer students a more realistic and updated vision of the world, and can provide an opportunity to understand the most recent scientific discoveries. In this…
These are the lecture notes for an introductory course on black holes and some aspects of their interaction with the classical and quantum world. The focus is on phenomena of "fundamental physics" in the immediate surroundings of the black…
Geodesy in a Newtonian framework is based on the Newtonian gravitational potential. The general-relativistic gravitational field, however, is not fully determined by a single potential. The vacuum field around a stationary source can be…
The search for solutions of Einstein's equations representing relativistic cosmological models with a discrete matter content has been remarkably fruitful in the last decade. In this review we discuss the progress made in the study of a…
The observation of the motion of particles and light near a gravitating object is until now the only way to explore and to measure the gravitational field. In the case of exact black hole solutions of the Einstein equations the…
We present GravLensX, an innovative method for rendering black holes with gravitational lensing effects using neural networks. The methodology involves training neural networks to fit the spacetime around black holes and then employing…