Related papers: A General Relativistic Rotating Evolutionary Unive…
We propose the metric for general rotating spacetimes. These spacetimes are stationary, axially symmetric and spatially asymptotically flat. They can be the spacetimes outside of rotating black holes or rotating celestial bodies such as the…
The standard numerical tools for studying non-linear collapse of matter are Newtonian $N$-body simulations. Previous work has shown that these simulations are in accordance with General Relativity (GR) up to first order in perturbation…
Modified gravity theories have been suggested to address the limitations of general relativity, each exhibiting differences, particularly in their strong-field limits. Nonetheless, there lacks effective means to distinguish or test these…
Using a novel, string theory-inspired formalism based on a Hamiltonian constraint, we obtain a conformal mechanical system for the spatially flat four-dimensional Robertson-Walker Universe. Depending on parameter choices, this system…
Modified gravity provides a possible explanation for the currently observed cosmic accelaration. In this paper, we study general classes of modified gravity models. The Einstein-Hilbert action is modified by using general functions of the…
Here, we derive the metric for the spacetime around rotating object for the gravity action having nonlocal correction of $R\Box^{-2} R $ to the Einstein-Hilbert action. Starting with the generic stationary, axisymmetric metric, we solve the…
In this thesis, we discuss some of the applications of cosmological perturbation theory in the late universe. We begin by reviewing the tools used to understand the standard model of cosmology theoretically and to compute its observational…
We discuss theoretical formalisms concerning with experimental verification of General Relativity (GR). Non-metric generalizations of GR are considered and a system of postulates is formulated for metric-affine and Finsler gravitational…
After a brief introduction to the sixteenth and seventeenth century views of the Universe and the nineteenth century paradox of Olbers, we start the history of the cosmic expansion with Hubble's epochal discovery of the recession velocities…
We construct a phenomenological theory of gravitation based on a second order gauge formulation for the Lorentz group. The model presents a long-range modification for the gravitational field leading to a cosmological model provided with an…
We discuss the question of gauge choice when analysing relativistic density perturbations at second order. We compare Newtonian and General Relativistic approaches. Some misconceptions in the recent literature are addressed. We show that…
A characterization of the foliation by spacelike slices of an $(n+1)$-dimensional spatially closed Generalized Robertson-Walker spacetime is given by means of studying a natural mean curvature type equation on spacelike graphs. Under some…
We study cosmologies in modified theories of gravity considering Lagrangian density $f(R)$ which is a polynomial function of scalar curvature ($R$) in the Einstein-Hilbert action in vacuum. The field equation obtained from the modified…
A very general class of axially-symmetric metrics in general relativity (GR) that includes rotations is used to discuss the dynamics of rotationally-supported galaxies. The exact vacuum solutions of the Einstein equations for this extended…
We add some comments to our old paper \cite{F-U} where the metric tensor was introduced as the gauge theory of general coordinate transformation. This formulation is more satisfactorily completed than the original one if it is required to…
Conformal geometry is considered within a general relativistic framework. An invariant distant for proper time is defined and a parallel displacement is applied in the distorted space-time, modifying Einstein's equation appropriately. A…
Alternative gravitational theories described by Lagrangians depending on general functions of the Ricci scalar have been proven to give coherent theoretical models to describe the experimental evidence of the acceleration of universe at…
An accelerating flat universe with a variable cosmological term is obtained in the Robertson-Walker metric. The variable cosmological term is defined by the correction terms of the metric tensor field. Simple solutions of the scale factor…
The gravitational field equations on cosmological scales are obtained by averaging the Einstein field equations of general relativity. By assuming spatial homogeneity and isotropy on the largest scales, the local inhomogeneities affect the…
The description of the universe evolving in time according to general relativity is given in comparison with the quantum description of the same universe in terms of semiclassical wave functions. The spacetime geometry is determined by the…