Related papers: The Hole Argument and Beyond, Part II: Treating No…
We explore the spacetime structure near non-extremal horizons in any spacetime dimension greater than two and discover a wealth of novel results: 1. Different boundary conditions are specified by a functional of the dynamical variables,…
Studying the dynamical, nonlinear regime of modified theories of gravity remains a theoretical challenge that limits our ability to test general relativity. Here we consider two generally applicable, but approximate methods for treating…
The concept of time-space defined in an earlier paper of the author is a certain generalization of the so-called space-time. In this paper we introduce the concept of time-space manifolds. In the homogeneous case, a time-space manifold is a…
Motivated by prominent problems like the Hilali conjecture Yamaguchi--Yokura recently proposed certain estimates on the relations of the dimensions of rational homotopy and rational cohomology groups of fibre, base and total spaces in a…
In this thesis three separate problems relevant to general relativity are considered. Methods for algorithmically producing all the solutions of isotropic fluid spheres have been developed over the last five years. A different and somewhat…
Arguing from his "hole" thought experiment, Einstein became convinced that, in cases in which the energy-momentum-tensor source vanishes in a spacetime hole, a solution to his general relativistic field equation cannot be uniquely…
We extend the T-duality for gauge theory to that on curved space described as a nontrivial fiber bundle. We also present a new viewpoint concerning the consistent truncation and the T-duality for gauge theory and discuss the relation…
Several hairy black hole solutions are known to violate the original version of the celebrated no-hair conjecture. This prompted the development of a new theorem that establishes a universal lower bound on the extension of hairs outside any…
I discuss black hole evaporation in two different coordinate systems and argue that the results of the two are compatible once one takes the holographic principle into account. de Sitter space is then discussed along similar lines. Finally…
We consider the quantization of the complete extension of the Schwarzschild space-time using spherically symmetric loop quantum gravity. We find an exact solution corresponding to the semi-classical theory. The singularity is eliminated but…
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…
How to include spacetime translations in fibre bundle gauge theories has been a subject of controversy, because spacetime symmetries are not internal symmetries of the bundle structure group. The standard method for including affine…
The equivalence of a conformal metric on 4-dimensional space-time and a local field of 3-dimensional subspaces of the space of 2-forms over space-time is discussed and the basic notion of transection is introduced. Corresponding relation is…
It is proposed that the mathematical formalism that is most appropriate for the study of spatially non-integrable cosmological models is the transverse geometry of a one-dimensional foliation (congruence) defined by a physical observer. By…
Black holes play a crucial role in the understanding of the gravitational interaction. Through the direct observation of the shadow of a black hole by the event horizon telescope and the detection of gravitational waves of merging black…
In this paper we will extend the notion of tangent bundle to a $\z$ graded tangent bundle. This graded bundle has a Lie algebroid structure and we can develop notions semi-riemannian metrics, Levi-civita connection, and curvature, on it. In…
It is well-known that blackhole and cosmological horizons in equilibrium situations are well-modeled by non-expanding horizons (NEHs). In the first part of the paper we introduce multipole moments to characterize their geometry, removing…
This work has the purpose of applying the concept of Geometric Calculus (Clifford Algebras) to the Fibre Bundle description of Quantum Mechanics. Thus, it is intended to generalize that formulation to curved spacetimes [the base space of…
In this MSc. thesis, we have attempted to give an overview of the firewall paradox and various approaches towards its resolution. After an introductory chapter on some basic concepts in quantum field theory in curved spacetimes such as…
We construct the spacetime in the vicinity of a general isolated, rotating, charged black hole. The black hole is modeled as a weakly isolated horizon, and we use the characteristic initial value formulation of the Einstein equations with…