Related papers: Sector models - A toolkit for teaching general rel…
The grand challenges of contemporary fundamental physics---dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem---all involve gravity as a key component. And of all…
Contents: 1. Introduction 2. Causal Structure and Penrose Diagrams: Minkowski Space; 1+1 Dimensional Minkowski Space; Schwarzchild Black Holes; Gravitational Collapse and the Vaidya Spacetimes; Event Horizons, Apparent Horizons, and Trapped…
Working in a semi-classical setting, we consider solutions of the Einstein equations that exhibit light trapping in finite time according to distant observers. In spherical symmetry, we construct near-horizon quantities from the assumption…
Effective field theory methods suggest that some rather-general extensions of General Relativity include, or are mimicked by, certain higher-order curvature corrections, with coupling constants expected to be small but otherwise arbitrary.…
The classical spacetime is usually described by a differentiable manifold with infinitely many degrees of freedom. Occasionally though, it is useful to consider an approximation whose number of degrees of freedom is finite. There are…
Equations arising in General Relativity are usually too complicated to be solved analytically and one has to rely on numerical methods to solve sets of coupled partial differential equations. Among the possible choices, this paper focuses…
Interpreting horizon-scale observations of astrophysical black holes demands a general understanding of null geodesics in the Kerr spacetime. These may be divided into two classes: "direct" rays that primarily determine the observational…
Photons emitted by light sources in the neighbourhood of a black hole can wind several times around it before fleeing towards the observer. For spherically symmetric black holes, two infinite sequences of images are created for any given…
An overview is given on those theoretical gravitational lensing results that can be formulated in a spacetime setting, without assuming that the gravitational fields are weak and that the bending angles are small. The first part is devoted…
In this work the model is constructed to describe the black hole enclosed in the dust cosmological background in case of zero spatial curvature. This model is based on our exact solution of the class of LTB inhomogeneous solutions. We…
Rendering images of black holes by utilizing ray tracing techniques is a common methodology employed in many aspects of scientific and astrophysical visualizations. Similarly, general ray tracing techniques are widely used in areas related…
A promising way to introduce general relativity in the classroom is to study the physical implications of certain given metrics, such as the Schwarzschild one. This involves lower mathematical expenditure than an approach focusing on…
Lecture notes from the mini-course "Topics in Lorentz Geometry" taught at the University of S\~{a}o Paulo, in March/2019. The text has three parts: (i) an overall view of linear algebra in the pseudo-Euclidean space $\mathbb{R}^n_\nu$, with…
In the vicinity of black holes, the influence of strong gravity, plasma physics, and emission processes govern the behavior of the system. Since observations such as those carried out by the EHT are not yet able to unambiguously constrain…
A general physical mechanism of the formation of line-driven winds at the vicinity of strong gravitational field sources is investigated in the frame of General Relativity. We argue that gravitational redshifting should be taken into…
This is the second lecture of `RAGtime' series on electrodynamical effects near black holes. We will summarize the basic equations of relativistic electrodynamics in terms of spin-coefficient (Newman-Penrose) formalism. The aim of the…
We are entering an era where the numerical construction of generic spacetimes is becoming a reality. The use of computer simulations, in principle, allows us to solve Einstein equations in their full generality and unravel important…
Machine learning techniques offer a precious tool box for use within astronomy to solve problems involving so-called big data. They provide a means to make accurate predictions about a particular system without prior knowledge of the…
Improved semiclassical techniques are developed and applied to a treatment of a real scalar field in a $D$-dimensional gravitational background. This analysis, leading to a derivation of the thermodynamics of black holes, is based on the…
This paper presents a pedagogical introduction to the issue of how to implement Lorentz transformations in relativistic visualization. The most efficient approach is to use the even geometric algebra in 3+1 spacetime dimensions, or…