Related papers: What is a reduced boundary in general relativity?
In an attempt to simulate black hole echoes (generated by potential quantum-gravitational structure) in numerical relativity, we recently described how to implement a reflecting boundary outside of the horizon of a black hole in spherical…
Consider a compact, orientable, three dimensional Riemannian manifold with boundary with nonnegative scalar curvature. Suppose its boundary is the disjoint union of two pieces: the horizon boundary and the outer boundary, where the horizon…
We derive a geometrical version of the Regge-Wheeler and Zerilli equations, which allows us to study gravitational perturbations on an arbitrary spherically symmetric slicing of a Schwarzschild black hole. We explain how to obtain the…
Invariance principles determine many key properties in quantum field theory, including, in particular, the appropriate form of the boundary conditions. A crucial consistency check is the proof that the resulting boundary-value problem is…
Modified gravity theories have been suggested to address the limitations of general relativity, each exhibiting differences, particularly in their strong-field limits. Nonetheless, there lacks effective means to distinguish or test these…
This thesis embarks on a comprehensive investigation of modified gravity theories and their implications on the properties of compact objects. Our primary objective is to shed light on the fundamental nature of gravity by exploring…
In black hole physics, inflationary cosmology, and quantum field theories, it is conjectured that the physical laws are subject to radical changes below the Planck length. Such changes are due to effects of quantum gravity believed to…
The concept of minimum length, widely accepted as a low-energy effect of quantum gravity, manifests itself in quantum mechanics through generalized uncertainty principles. Curved momentum space, on the other hand, is at the heart of similar…
An equidistant spectrum of the horizon area of a quantized black hole does not follow from the correspondence principle or from general statistical arguments. On the other hand, such a spectrum obtained in loop quantum gravity (LQG) either…
A modification of General Relativity that is based on the gravitational Standard-Model Extension and incorporates nondynamical background fields has recently been studied via the ADM formalism. Our objective in this paper is to develop a…
The fundamental role played by black holes in our study of microquasars, gamma ray bursts, and the outflows from active galactic nuclei requires an appreciation for, and at times some in-depth analysis of, curved spacetime. We highlight…
The quasi-local notion of an isolated horizon is employed to study the entropy of black holes without any particular symmetry in loop quantum gravity. The idea of characterizing the shape of a horizon by a sequence of local areas is…
The principle part of Einstein equations in the harmonic gauge consists of a constrained system of 10 curved space wave equations for the components of the space-time metric. A well-posed initial boundary value problem based upon a new…
In this essay, we argue that certain aspects of the measurement require revision in Quantum Gravity. Using entropic arguments, we propose that the number of measurement outcomes and the accuracy (or the range) of the measurement are limited…
A review of the treatment of boundaries in general relativity is presented with the emphasis on application to the formulations of Einstein's equations used in numerical relativity. At present, it is known how to treat boundaries in the…
Any spacetime containing a degenerate Killing horizon, such as an extremal black hole, possesses a well-defined notion of a near-horizon geometry. We review such near-horizon geometry solutions in a variety of dimensions and theories in a…
A proper understanding of boundary-value problems is essential in the attempt of developing a quantum theory of gravity and of the birth of the universe. The present paper reviews these topics in light of recent developments in spectral…
A reformulation of a physical theory in which measurements at the initial and final moments of time are treated independently is discussed, both on the classical and quantum levels. Methods of the standard quantum mechanics are used to…
We develop the General Theory of Relativity in a formalism with extended causality that describes physical interaction through discrete, transversal and localized pointlike fields. The homogeneous field equations are then solved for a…
After reviewing the shortcomings of existing definitions used to characterize the boundary of a black hole, we present a new method for its characterization. This definition could potentially be applied to locate the boundary of general…