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Among theoretical issues in General Relativity the problem of constructing its Hamiltonian formulation is still of interest. The most of attempts to quantize Gravity are based upon Dirac generalization of Hamiltonian dynamics for system…
We use the Fundamental Plane of Elliptical Galaxies to constrain the so-called Hybrid Gravity, a modified theory of gravity where General Relativity is improved by further degrees of freedom of metric-affine Palatini formalism of $f(\cal…
The infinite dimensional generalization of the quantum mechanics of extended objects, namely, the quantum field theory of extended objects is employed to address the hitherto nonrenormalizable gravitational interaction following which the…
We study the cosmological dynamics of a class of symmetric teleparallel gravity theories known as ``newer general relativity'' using the methods of dynamical systems, restricted to the case of vacuum solutions with a spatially flat…
This thesis focuses on late-time cosmic acceleration within modified theories of gravity, using various observational data sets and statistical analysis. The Universe is assumed to be spatially homogeneous and isotropic and is described by…
There are many complementary approaches to the construction of solutions to the field equations of general relativity. Among these, numerical approximation offers the only possibility to compute a variety of dynamical spacetimes, and so has…
Starting from the weak field limit, we discuss astrophysical applications of Extended Theories of Gravity where higher order curvature invariants and scalar fields are considered by generalizing the Hilbert-Einstein action linear in the…
Numerical relativity is an essential tool for solving Einstein's equations of general relativity for dynamical systems characterized by high velocities and strong gravitational fields. The implementation of new algorithms that can solve…
The interpretations of solutions of Einstein field's equations led to the prediction and the observation of physical phenomena which confirm the important role of general relativity, as well as other relativistic theories in physics. In…
We develop a formalism for General Relativistic N-body simulations in the weak field regime, suitable for cosmological applications. The problem is kept tractable by retaining the metric perturbations to first order, the first derivatives…
Within the theory of General Relativity, we study the solution and range of applicability of the standard geodesic deviation equation in highly symmetric spacetimes. In the Schwarzschild spacetime, the solution is used to model satellite…
It has long been known that Newtonian dynamics applied to the visible matter in galaxies and clusters does not correctly describe the dynamics of those systems. While this is generally taken as evidence for dark matter it is in principle…
It is shown that in the weak field approximation solutions of Brans-Dicke equations are simply related to the solutions of General Relativity equations for the same matter distribution. A simple method is developed which permits to obtain…
The Hamiltonian approach to the General Relativity is formulated as a joint nonlinear realization of conformal and affine symmetries by means of the Dirac scalar dilaton and the Maurer-Cartan forms. The dominance of the Casimir vacuum…
We study Einstein-Yang-Mills equations in the presence of a gravitating non-topological soliton field configuration consisted of a Higgs doublet, in Brans-Dicke and general scalar-tensor gravitational theories. The results of General…
Dynamical system methods are used in the study of the stability of spatially flat homogeneous cosmologies within a large class of generalized modified gravity models in the presence of a relativistic matter-radiation fluid. The present…
Schwarzschild's solution to the Einstein Field Equations was one of the first and most important solutions that lead to the understanding and important experimental tests of Einstein's theory of General Relativity. However, Schwarzschild's…
From a previous paper where we proposed a description of general relativity within the gravito-electromagnetic limit, we propose an alternative modified gravitational theory. As in the former version, we analyze the vector and tensor…
We show that a general solution of the Einstein equations that describes approach to an inhomogeneous and anisotropic sudden spacetime singularity does not experience geodesic incompleteness. This generalises the result established for…
We propose a new generalisation of general relativity which incorporates a variation in both the speed of light in vacuum (c) and the gravitational constant (G) and which is both covariant and Lorentz invariant. We solve the generalised…