Related papers: Numerical solutions to lattice-refined models in l…
Considerable attention has been paid to the study of the quantum geometry of nonrotating black holes within the framework of Loop Quantum Cosmology. This interest has been reinvigorated since the introduction of a novel effective model by…
We present a covariant model of a spherically symmetric black hole with corrections motivated by loop quantum gravity. The effective modifications, parametrized by a positive constant $\lambda$, are implemented through a canonical…
We propose a quantum algorithm for solving physical problems represented by the lattice Boltzmann formulation. Specifically, we deal with the case of a single phase, incompressible fluid obeying the Bhatnagar-Gross-Krook model. We use the…
Loop quantum cosmology homogeneous models with a massless scalar field show that the big-bang singularity can be replaced by a big quantum bounce. To gain further insight on the nature of this bounce, we study the semi-discrete loop quantum…
Relativistic numerical cosmology is most often based either on the exact solutions of the Einstein equations, or perturbation theory, or weak-field limit, or the BSSN formalism. The Silent Universe provides an alternative approach to…
Loop quantization of Schwarzschild black holes with a cosmological constant for polymerization parameters which are constant is studied in the effective spacetime description. We show that for the positive cosmological constant there can be…
We study the dynamics of the homogeneous and isotropic cosmological background in the recently proposed ``quantum phenomenological gravitational dynamics'', characterised by logarithmic corrections to the Bekenstein entropy. We show that…
This thesis is concerned with the development and application of conformal techniques to numerical calculations of asymptotically flat spacetimes. The conformal compactification technique enables us to calculate spatially unbounded domains,…
The Einstein-Maxwell (or Einstein) system of field equations plays a substantial role in the modeling of compact stars. Although due to its non-linearity getting an exact solution for the system of field equations is a difficult task, the…
We present the method of describing an evolution in quantum cosmology in the framework of the reduced phase space quantization of loop cosmology. We apply our method to the flat Friedman-Robertson-Walker model coupled to a massless scalar…
We present a new many-parameter family of hyperbolic representations of Einstein's equations, which we obtain by a straightforward generalization of previously known systems. We solve the resulting evolution equations numerically for a…
We study axisymmetric solution to the conformally invariant wave equation on a Kerr background by means of numerical and analytical methods. Our main focus is on the behaviour of the solutions near spacelike infinity, which is appropriately…
Emergent modified gravity provides a covariant, effective framework for obtaining spherically symmetric black hole solutions in models of loop quantum gravity with scale-dependent holonomy modifications. Exact solutions for vacuum black…
In Loop Quantum Gravity mathematically rigorous models of full quantum gravity were proposed. In this paper we study a cosmological sector of one of the models describing quantum gravity with positive cosmological constant coupled to…
This thesis is concerned with global properties of those cosmological solutions of Einstein's field equations which obey accelerated expansion into the future driven by a non-vanishing cosmological constant, as suggested by current…
We propose a quantum algorithm to solve systems of nonlinear algebraic equations. In the ideal case the complexity of the algorithm is linear in the number of variables $n$, which means our algorithm's complexity is less than $O(n^{3})$ of…
This thesis addresses whether it is possible to build a robust memory device for quantum information. A three-dimensional gapped lattice spin model is found which demonstrates for the first time that a reliable quantum memory at finite…
In this paper we construct a solvable toy model of the quantum dynamics of the interior of a spherical black hole with falling spherical scalar field excitations. We first argue about how some aspects of the quantum gravity dynamics of…
Computational techniques which establish the stability of an evolution-boundary algorithm for a model wave equation with shift are incorporated into a well-posed version of the initial-boundary value problem for gravitational theory in…
We present a new numerical code designed to solve the Einstein field equations for axisymmetric spacetimes. The long term goal of this project is to construct a code that will be capable of studying many problems of interest in axisymmetry,…