Related papers: Codimension Two Branes and Distributional Curvatur…
In physical theories where the energy (action) is localized near a submanifold of a constant curvature space, there is a universal expression for the energy (or the action). We derive a multipole expansion for the energy that has a finite…
Brane-world cosmology is motivated by recent developments in string/M-theory and offers a new perspective on the hierarchy problem. In the brane-world scenario, our Universe is a four-dimensional subspace or {\em brane} embedded in a…
We critically assess a recent assertion (arXiv:1508.01124) concerning using delta-functions to analyze how higher-codimension branes back-react on their environment. We also briefly summarize the state of the art: describing how…
The cosmology of the Randall-Sundrum scenario for a positive tension brane in a 5-D Universe with localized gravity has been studied extensively recently. Here we extend it to more general situations. We consider the time-dependent…
A method for obtaining solutions to the classical equations for scalars plus gravity in five dimensions is applied to some recent suggestions for brane-world phenomenology. The method involves only first order differential equations. It is…
Extra-dimensional scenarios have become widespread among particle and gravitational theories of physics to address several outstanding problems, including cosmic acceleration, the weak hierarchy problem, and the quantization of gravity. In…
The observable universe could be a 1+3-surface (the "brane") embedded in a 1+3+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 one of the…
The general exact solution describing the dynamics of anisotropic elastic spheres supported only by tangential stresses is reduced to a quadrature using Ori's mass-area coordinates. This leads to the explicit construction of the root…
A family of quasilocal mass definitions that includes as special cases the Hawking mass and the Brown-York ``rest mass'' energy is derived for spacelike 2-surfaces in spacetime. The definitions involve an integral of powers of the norm of…
Simplicial distributions provide a framework for studying quantum contextuality, a generalization of Bell's non-locality. Understanding extremal simplicial distributions is of fundamental importance with applications to quantum computing.…
We consider cosmological models where the universe, governed by Einstein's equations, is a piece of a five dimensional double-sided anti-de Sitter spacetime (that is, a "$Z_2$-symmetric bulk") with matter confined to its four dimensional…
We show that the two-dimensional structure of a rigidly rotating self-gravitating body is accessible with relatively good precision by assuming a purely spheroidal stratification. With this hypothesis, the two-dimensional problem becomes…
Space-filling S-branes can mediate a transition between a contracting and an expanding universe in the Einstein frame. Following up on previous work that uncovered such bouncing solutions in the context of weakly coupled thermal…
Biconformal deformations take place in the presence of a conformal foliation, deforming by different factors tangent to and orthogonal to the foliation. Four-manifolds endowed with a conformal foliation by surfaces present a natural context…
A model describing cell membranes as optimal shapes with regard to the $L^2$-deficit of their mean curvature to a given constant called spontaneous curvature is considered. It is shown that the corresponding energy functional is lower…
We prove that codimension two surfaces satisfying a nonlinear curvature condition depending on normal curvature are smoothly deformed by mean curvature flow to round points.
We describe how to approximate the Riemann curvature tensor as well as sectional curvatures on possibly infinite-dimensional shape spaces that can be thought of as Riemannian manifolds. To this end, we extend the variational time…
String theory contains various extended objects. Among those, objects of codimension two (such as the D7-brane) are particularly interesting. Codimension two objects carry non-Abelian charges which are elements of a discrete U-duality group…
Vacuum energy density and stresses are investigated for a scalar field in de Sitter spacetime with an arbitrary number of toroidally compactified spatial dimensions and in anti-de Sitter spacetime with two parallel branes. On the branes the…
The so-called spectral dimension is a scale-dependent number associated with both geometries and field theories that has recently attracted much attention, driven largely though not exclusively by investigations of causal dynamical…