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General relativity has passed all solar system experiments and neutron star based tests, such as binary pulsar observations, with flying colors. A more exotic arena for testing general relativity is in systems that contain one or more black…
Sector models are tools that make it possible to teach the basic principles of the general theory of relativity without going beyond elementary mathematics. This contribution shows how sector models can be used to determine geodesics. We…
The problem of deforming geometries is particularly important in the context of constructing new exact solutions of Einstein's equation. This issue often appears when extensions of the general relativity are treated, for instance in brane…
For the quadratic theory of gravity with a scalar field, exact solutions are found for gravitational-wave models in Shapovalov~I~type spacetimes, which do not arise in models of the general theory of relativity. The theory of gravity under…
We consider the domain of applicability of general relativity (GR), as a classical theory of gravity, by considering its applications to a variety of settings of physical interest as well as its relationship with real observations. We argue…
We consider the dilaton gravity models derived by reductions of generalized theories of gravity and study one-dimensional dynamical systems simultaneously describing cosmological and static states in any gauge. Our approach is fully…
General relativity is a mathematical model that uses sophisticated geometry to describe simple physics. It agrees with experiment in the few tests that can be made, but the whole edifice is not physics. Instead of using observations to test…
An introductory overview of vector spaces, algebras, and linear geometries over an arbitrary commutative field is given. Quotient spaces are emphasized and used in constructing the exterior and the symmetric algebras of a vector space.…
The objective of this work is to revisit fundamental aspects of relativistic hydrodynamics, aiming at the construction of a first course in relativistic hydrodynamics and its applications to astrophysics at the level of end of undergraduate…
Many of the technical complications associated with the general theory of relativity ultimately stem from the nonlinearity of Einstein's equation. It is shown here that an appropriate choice of dynamical variables may be used to eliminate…
A number of recent proposals for a quantum theory of gravity are based on the idea that spacetime geometry and gravity are derivative concepts and only apply at an approximate level. There are two fundamental challenges to any such…
A covariant reformulation of General Relativity is briefly considered from three points of view: geometrodynamics, Lagrange-Euler field theory, and gauge field theory. From a geometrodynamics perspective, a definition of the reference frame…
The relativistic hydrodynamic model is applied to describe the expansion of the dense matter formed in relativistic heavy-ion collisions. The hydrodynamic expansion of the fluid, supplemented with the statistical emission of hadrons at…
Recently there has been developed a reformulation of General Relativity - referred to as {\it the null surface version of GR} - where instead of the metric field as the basic variable of the theory, families of three-surfaces in a…
Gravitational wave astronomy has tremendous potential for studying extreme astrophysical phenomena and exploring fundamental physics. The waves produced by binary black hole mergers will provide a pristine environment in which to study…
This paper gives a summary of the author's works concerning the emergent general relativity in a particular class of tensor models, which possess Gaussian classical solutions. In general, a classical solution in a tensor model may be…
We propose a generic, phenomenological approach to modifying the dispersion of gravitational waves, independent of corrections to the generation mechanism. This model-independent approach encapsulates all previously proposed…
Gravitational waves provide a unique window into gravity, cosmology, and high-energy physics, enabling the exploration of fundamental phenomena across a wide range of scales. This review presents a coherent and pedagogical framework that…
Since physical theories employ mathematical models to describe and predict physical phenomena, our knowledge depends on the models available to that end. To increase their scope we present a particular type of simplified models, serial…
A simple general relativity theory for objects moving in gravitational fields is developed based on studying the behavior of an atom in a gravitational field. The theory is applied to calculate the satellite time dilation, light deflection…