Related papers: Comparison of metrics obtained with analytic pertu…
From the beginning of KAM theory, it was realized that its applicability to realistic problems depended on developing quantitative estimates on the sizes of the perturbations allowed. In this paper we present results on the existence of…
Motivated from the theory of quantum error correcting codes, we investigate a combinatorial problem that involves a symmetric $n$-vertices colourable graph and a group of operations (colouring rules) on the graph: find the minimum sequence…
Numerical methods: mimetic finite differences and finite elements, are analyzed from a numerical point of view. It seeks to conclude on the efficiency, order of convergence and computational cost of these methods. The analysis is done in…
The full set of cosmological observables coming from linear scalar and tensor perturbations of loop quantum cosmology is computed in the presence of inverse-volume corrections. Background inflationary solutions are found at linear order in…
Perturbation theory of vacuum spherically-symmetric spacetimes is a crucial tool to understand the dynamics of black hole perturbations. Spherical symmetry allows for an expansion of the perturbations in scalar, vector, and tensor…
Analysing two-dimensional shallow water equations with idealised bottom topographies have many applications in the atmospheric and oceanic sciences; however, restrictive flow pattern assumptions have been made to achieve explicit solutions.…
We study spectral parametric correlations in quantum chaotic systems and introduce the number covariance as a measure of such correlations. We derive analytic results for the classical random matrix ensembles using the binary correlation…
We formulate cosmological perturbation theory around the spatially curved FLRW background in the context of metric-affine gauge theory of gravity which includes torsion and nonmetricity. Performing scalar-vector-tensor decomposition of the…
We solve the wave equation for gravitational waves emitted by compact objects systems using the Multipolar Post-Minkowskian (MPM) method, and in the presence of Lorentz invariance violating terms. We select a Lorentz-violating extension of…
Increasing attention has been recently devoted to the study of Kantowski-Sachs spacetime as a way to explore the interior of a Schwarzschild black hole. In this work, we construct a Hamiltonian formulation for polar perturbations of this…
We use analytic perturbation theory to present a new approximate metric for a rigidly rotating perfect fluid source with equation of state (EOS) $\epsilon+(1-n)p=\epsilon_0$. This EOS includes the interesting cases of strange matter,…
This article begins with a brief introduction to numerical relativity aimed at readers who have a background in applied mathematics but not necessarily in general relativity. I then introduce and summarise my work on the problem of treating…
We review the most recent progress in our understanding of quantum mechanical observables in cosmology in the perturbative regime. It relies on an approach that considers them directly as functions of the data at the space-like boundary at…
In this paper, we perform a parallel analysis to the model proposed in [25]. By considering the central co-tetrad (instead of the central metric), we investigate the modifications in the gravitational metrics coming from the noncommutative…
Utilizing the ADM equations, we derive a metric and reduced field equations describing a general, spherically symmetric perfect fluid. The metric describes both the interior perfect fluid region and exterior vacuum Schwarzschild spacetime…
We suggest two metrics for assessing the quality of atomistic configurations of disordered materials, both of which are based on quantifying the orientational distribution of neighbours around each atom in the configuration. The first…
The non-linear collision-induced breakage equation has significant applications in particulate processes. Two semi-analytical techniques, namely homotopy analysis method (HAM) and accelerated homotopy perturbation method (AHPM) are…
We derive a formalism for solving the Lorenz gauge equations for metric perturbations of Kerr spacetime sourced by an arbitrary stress-energy tensor. The metric perturbation is obtained as a sum of differential operators acting on a set of…
Approximate all-terrain spacetimes for astrophysical applications are presented. The metrics possess five relativistic multipole moments, namely mass, rotation, mass quadrupole, charge, and magnetic dipole moment. All these spacetimes…
The decomposition of the linear-order metric perturbation is discussed in the context of the higher-order gauge-invariant perturbation theory. We show that the linear order metric perturbation is decomposed into gauge-invariant and…