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Teleparallel gravity has significantly increased in popularity in recent decades, bringing attention to Einstein's other theory of gravity. In this Review, we relate this form of geometry to the broader metric-affine approach to forming…
In this article we use the idea of algorithmic complexity (AC) to study various cosmological scenarios, and as a means of quantizing the gravitational interaction. We look at 5D and 7D cosmological models where the Universe begins as a…
We survey a variety of cosmological problems where the issue of generality has arisen. This is aimed at providing a wider context for many claims and deductions made when philosophers of science choose cosmological problems for…
Einstein's general relativity is the best available theory of gravity. In recent years, spectacular proofs of Einstein's theory have been conducted, which have aroused interest that goes far beyond the narrow circle of specialists. The aim…
We develop a new approach to building cosmological models, in which small pieces of perturbed Minkowski space are joined together at reflection-symmetric boundaries in order to form a global, dynamical space-time. Each piece of this…
The geometric trinity of gravity comprises three distinct formulations of general relativity: (i) the standard formulation describing gravity in terms of spacetime curvature, (ii) the teleparallel equivalent of general relativity describing…
Minisuperpace Quantum Cosmology is an approach by which it is possible to infer initial conditions for dynamical systems which can suitably represent observable and non-observable universes. Here we discuss theories of gravity which, from…
We discuss the application of computer algebra to problems commonly arising in numerical relativity, such as the derivation of 3+1-splits, manipulation of evolution equations and automatic code generation. Particular emphasis is put on…
It is commonly remarked that contemporary physics faces a challenge in reconciling quantum theory with Relativity, specifically General Relativity as a theory of gravity. But "challenge" is too mild a descriptor. Once one understands both…
The reduction of 4D Einstein gravity with $N$ minimal scalars leads to specific 2D dilaton gravity with dilaton coupled scalars. Applying s-wave and large $N$ approximation (where large $N$ quantum contribution due to dilaton itself is…
There has never been a more exciting time in the overlapping areas of nuclear physics, particle physics and relativistic astrophysics than today. Orbiting observatories such as the Hubble Space Telescope, Rossi X-ray Timing Explorer (RXTE),…
The Einstein-Cartan theory of gravitation and the classical theory of defects in an elastic medium are presented and compared. The former is an extension of general relativity and refers to four-dimensional space-time, while we introduce…
Extended Theories of Gravity can be considered a new paradigm to cure shortcomings of General Relativity at infrared and ultraviolet scales. They are an approach that, by preserving the undoubtedly positive results of Einstein's Theory, is…
Kaiser redshift-space distortion formula describes well the clustering of galaxies in redshift surveys on small scales, but there are numerous additional terms that arise on large scales. Some of these terms can be described using Newtonian…
The equations governing null and timelike geodesics are derived within the 3+1 formalism of general relativity. In addition to the particle's position, they encompass an evolution equation for the particle's energy leading to a 3+1…
The dynamics of general relativity is encoded in a set of ten differential equations, the so-called Einstein field equations. It is usually believed that Einstein's equations represent a physical law describing the coupling of spacetime…
The strong proper time dilation and radial contraction in the gravitational field of compact sources leads to a frozen state of matter. It is shown that the falling particles and photons can not cross the gravitational radius due to the…
This paper explores the theoretical implications of quantum gravity by analyzing compact stellar objects, presenting three distinct models that serve as alternatives to traditional black holes. These models are characterized by their…
In this review, I have tried to focus on the development of the field, from the first speculations to the current lines of research. According to Einstein's theory of general relativity, black holes are relatively simple objects and…
Electromagnetic observations have been used over the past decades to understand the nature of black holes and the material around them. Our ability to learn about the fundamental physics relies on our understanding of two key ingredients in…