Related papers: Geometry, EFE's and Foundations for Brane Cosmolog…
There are many complementary approaches to the construction of solutions to the field equations of general relativity. Among these, numerical approximation offers the only possibility to compute a variety of dynamical spacetimes, and so has…
The observable universe could be a 1+3-surface (the "brane") embedded in a 1+3+\textit{d}-dimensional spacetime (the "bulk"), with Standard Model particles and fields trapped on the brane while gravity is free to access the bulk. At least…
The intention of this article is to give a flavour of some global problems in General Relativity. We cover a variety of topics, some of them related to the fundamental concept of 'Cauchy hypersurfaces': (1) structure of globally hyperbolic…
This article, written to appear as a chapter in "The Springer Handbook of Spacetime", is a review of the initial value problem for Einstein's gravitational field theory in general relativity. Designed to be accessible to graduate students…
This paper gives a detailed pedagogic presentation of the central concepts underlying a new algorithm for the numerical solution of Einstein's equations for gravitation. This approach incorporates the best features of the two leading…
We study the brane world cosmology in the RS2 model where the electric charge varies with time in the manner described by the varying fine-structure constant theory of Bekenstein. We map such varying electric charge cosmology to the dual…
We investigate the existence of brane solutions in braneworld scenarios described by real scalar field in the presence of modified $f(R)$ gravity with a single extra dimension. In the case of constant curvature, we obtain first-order…
This is a review on cosmological perturbation theory. After an introduction, it presents the problem of gauge transformation. Gauge invariant variables are introduced and the Einstein and conservation equations are written in terms of these…
This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local in time Cauchy problem, which is relatively well understood, is…
In the present paper the gauge-invariant formalism is developed for perturbations of the brane-world model in which our universe is realized as a boundary of a higher-dimensional spacetime. For the background model in which the bulk…
The most general geometrical scenario in which the brane-world program can be implemented is investigated. The basic requirement is that it should be consistent with the confinement of gauge interaction, the existence of quantum states and…
Extra-dimensional theories contain additional degrees of freedom related to the geometry of the extra space which can be interpreted as new particles. Such theories allow to reformulate most of the fundamental problems of physics from a…
I construct solutions to Einstein's equations in 6 dimensions with bulk cosmological constant and intersecting 4-branes. Solutions exist for a continuous range of 4-brane tension, with long distance gravity localized to a 3+1 dimensional…
We show how the gravity, gauge, and matter fields are induced on dynamically localized brane world.
A new cosmological solution of the gravitational field equations in the generalized Randall-Sundrum model for an anisotropic brane with Bianchi I geometry and with perfect fluid as matter sources is presented. The matter is described by a…
Unified theories suggest that space is intrinsically 10 dimensional, even though everyday phenomena seem to take place in only 3 large dimensions. In ``Brane World'' models, matter and radiation are localized to a ``brane'' which has a…
This article gives a comprehensive review on thick brane solutions and related topics. Such models have attracted much attention from many aspects since the birth of the brane world scenario. In many works, it has been usually assumed that…
We consider the cosmology of a 3-brane universe, in a five dimensional space time (Bulk). We present some solutions to the five-dimensional Einstein equation, where a perfect fluid is confined to the 3-brane. We investigate the evolution of…
A brane universe moving in a curved higher dimensional bulk space is considered. The motion induces a cosmological evolution on the universe brane that is indistiguishable from a similar one induced by matter density on the brane. The…
Brief account of results on the Cauchy problem for the Einstein equations starting with early the works of Darmois and Lichnerowicz and going up to the proofs of the existence and uniqueness of solutions global in space and local in time,…