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In this thesis we consider several aspects of general relativity relating to exact solutions of the Einstein equations. In the first part gravitational plane waves in the Rosen form are investigated, and we develop a formalism for writing…
Many central problems in geometry, topology, and mathematical physics lead to questions concerning the long-time dynamics of solutions to ordinary and partial differential equations. Examples range from the Einstein field equations of…
Cosmologies with a time dependent Newton constant and cosmological constant are investigated. The scale dependence of $G$ and $\Lambda$ is governed by a set of renormalization group equations which is coupled to Einstein's equation in a…
This article discusses a dark energy cosmological model in the standard theory of gravity - general relativity with a broad scalar field as a source. Exact solutions of Einstein's field equations are derived by considering a particular form…
Assuming that the Universe is filled by one single fluid, we present in the context of General Relativity a possible explanation for the acceleration of the Universe. We use ordinary thermodynamics and the fact that small matter…
We study the cosmological evolution of scalar fields with arbitrary potentials in the presence of a barotropic fluid (matter or radiation) without making any assumption on which term dominates. We determine what kind of potentials V(phi)…
In this paper we investigate the quintessence model with a minimally coupled scalar field in the context of recent supernovae observations. By choosing a particular form of the deceleration parameter q, which gives an early deceleration and…
In this paper, we develop a new method to find the exact solutions of the Einstein's field equations by using which we construct time-periodic solutions. The singularities of the time-periodic solutions are investigated and some new…
We study the classical and quantum evolution of a universe in which the matter source is a massive Dirac spinor field and the universe is described by a Bianchi type I metric. We focus attention on those classical solutions that admit a…
By imposing natural geometrical and kinematical conditions on a conformal Killing vector in Bianchi I spacetime, we show that a class of axisymmetric metrics admits a conformal motion. This class contains new exact solutions of Einstein's…
We try to find the possibility of a Bianchi V universe in the modified gravitational field theory of $f(R,T)$. We have considered a Lagrangian model in the connection between the trace of the energy-momentum tensor $T$ and the Ricci scalar…
Global existence to the coupled Einstein-Maxwell-Massive Scalar Field system which rules the dynamics of a kind of charged pure matter in the presence of a massive scalar field is proved, in Bianchi I-VIII spacetimes; asymptotic behaviour,…
Motivated by the increasing evidence for the need of a geometry that resembles Bianchi morphology to explain the observed anisotropy in the WMAP data, we have discussed some features of the Bianchi type-$VI_{0}$ universes in the presence of…
In the context of modified tele-parallel theory of gravity, we undertake cosmological anisotropic models and search for their solutions. Within a suitable choice of non-diagonal tetrads, the decoupled equations of motion are obtained for…
Even if the luminosity distance as a function of redshift is obtained accurately using, for example, Type Ia supernovae, the equation of state of the Universe cannot be determined uniquely but depends on one free parameter $\Omega_{k0}…
We investigate late time acceleration of the universe in higher dimensional cosmology. The content in the universe is assumed to exert pressure which is different in the normal and extra dimensions. Cosmologically viable solutions are found…
Cosmological models arising from a generalized compactification of Einstein gravity are derived. It is shown that a redefinition of the moduli fields reduces the system to a set of massless fields and a single field with a single…
In this study we consider an exponential decaying form for dark energy as EoS parameter in order to discuss the dynamics of the universe. Firstly, assuming that universe is filled with an ideal fluid which consists of exponential decaying…
Recent observations suggest that the accelerated expansion of the Universe at late times is caused by a temporally changing dark energy component, rather than the constant one in the standard $\Lambda$CDM scenario. In this context…
A class of exact solutions for the Einstein-Maxwell field equations are obtained by assuming the erstwhile cosmological constant $ \Lambda $ to be a space-variable scalar, viz., $ \Lambda =\Lambda(r) $. The source considered here is static,…