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Whether the space-time is curved or not? The experimental criterions to judge this point are: (1) The results of three classical relativistic experiments in essence are favorable to the special relativistic gravitational theory (base in the…
For the last 100 years, General Relativity (GR) has taken over the gravitational theory mantle held by Newtonian Gravity for the previous 200 years. This article reviews the status of GR in terms of its self-consistency, completeness, and…
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…
The geometrical nature of gravity emerges from the universality dictated by the equivalence principle. In the usual formulation of General Relativity, the geometrisation of the gravitational interaction is performed in terms of the…
Quantum gravity (or quantum spacetime) is to unify general relativity and quantum mechanics into a single theoretical framework and presented as the most important open puzzle in fundamental physics. The development of a microscopic theory…
Einstein-aether theory is general relativity coupled to a dynamical unit timelike vector field. A brief review of current theoretical understanding and observational constraints on the four coupling parameters of the theory is given.
There is evidence that Newton and Einstein's theories of gravity cannot explain the dynamics of a universe made up solely of baryons and radiation. To be able to understand the properties of galaxies, clusters of galaxies and the universe…
The four-dimensional gauge group of general relativity corresponds to arbitrary coordinate transformations on a four-manifold. Theories of gravity with a dynamical structure remarkably like Einstein's theory can be obtained on the basis of…
In these lectures general relativity is outlined as the classical field theory of gravity, emphasizing physical phenomena rather than mathematical formalism. Dynamical solutions representing traveling waves as well as stationary fields like…
Black holes are one of the most fascinating predictions of general relativity. They are the natural product of the complete gravitational collapse of matter and today we have a body of observational evidence supporting the existence of…
Modified gravity theories have received increased attention lately to understand the late time acceleration of the universe. This viewpoint essentially modifies the geometric components of the universe. Among numerous extension to…
We present a resum\'e on the modified theory of gravity, called pseudo-complex General Relativity (pc-GR). It is the second in a series of papers, where the first one (Boller et al. 2019, referred to as paper I) discussed the observational…
A challenging issue in General Relativity concerns the determination of the manifestly-covariant continuum Hamiltonian structure underlying the Einstein field equations and the related formulation of the corresponding covariant…
The construction of an averaged theory of gravity based on Einstein's General Relativity is very difficult due to the non-linear nature of the gravitational field equations. This problem is further exacerbated by the difficulty in defining…
General Relativity (GR) remains the cornerstone of gravitational physics, providing remarkable success in describing a wide range of astrophysical and cosmological phenomena. However, several challenges underscore the urgent need to explore…
Modified General Relativity (MGR) is the natural extension of General Relativity (GR). MGR explicitly uses the smooth regular line element vector field $(\bm{X},-\bm{X}) $, which exists in all Lorentzian spacetimes, to construct a…
The field equations of a generalized $f(R)$ type gravity model, in which there is an arbitrary coupling between matter and geometry, are obtained. The equations of motion for test particles are derived from a variational principle in the…
The quantum description of time evolution in non-linear gravitational systems such as cosmological space-times is not well understood. We show, in the simplified setting of mini-superspace, that time evolution of this system can be obtained…
A scalar, preferred-frame theory of gravitation is summarized. Space-time is endowed with both a flat metric and a curved, "physical" metric. Motion is governed by a natural extension of Newton's second law, which implies geodesic motion…
Relativity is an integral part of positioning systems, and this is taken into account in today's practice by applying many "relativistic corrections" to computations performed using concepts borrowed from Galilean physics. A different,…