Related papers: On the embedding of spacetime in five-dimensional …
In this paper we deal with the cosmological dynamics of Randall-Sundrum brane-world type scenarios in which the five-dimensional Weyl tensor has a non-vanishing projection onto the three-brane where matter fields are confined. Using…
One can argue that on flat space $\mathbb{R}^d$ the Weyl quantization is the most natural choice and that it has the best properties (e.g. symplectic covariance, real symbols correspond to Hermitian operators). On a generic manifold, there…
We show how braneworld cosmology with bulk matter can explain structure formation. In this scenario, the nonlocal corrections to the Friedmann equations supply a Weyl fluid that can dominate over matter at late times due to the energy…
For any closed smooth Riemannian manifold H. Weyl has defined a sequence of numbers called today intrinsic volumes. They include volume, Euler characteristic, and integral of the scalar curvature. We conjecture that absolute values of all…
In reference gr-qc/0104036 a four-dimensional effective theory of gravity embeddable in a five-dimensional "distorted" Randall-Sundrum brane scenario was derived. The present paper is aimed at the application of such a theory to describe…
We study the evolution of the Weyl curvature invariant in all spatially homogeneous universe models containing a non-tilted gamma-law perfect fluid. We investigate all the Bianchi and Thurston type universe models and calculate the…
Geodesics become an essential element of the geometry of a semi-Riemannian manifold. In fact, their differences and similarities with the (positive definite) Riemannian case, constitute the first step to understand semi-Riemannian Geometry.…
In a recent paper Shiromizu, Maeda and Sasaki derived the gravitational equations of motion which would hold on a brane which is embedded in a higher dimensional bulk spacetime, showing that even when the Einstein equations are imposed in…
We study Sobolev spaces of radial functions on spherically symmetric Riemannian manifolds. Using geodesic polar coordinates, we give a sharp one-dimensional reduction: a radial function belongs to the Sobolev space on the manifold if and…
Just after Weyl's paper (Weyl in Gravitation und Elektrizit\"at, Sitzungsber. Preuss. Akad., Berlin, 1918) Einstein claimed that a gravity model written in a spacetime geometry with non-metricity suffers from a phenomenon, the so-called…
The first part of this thesis focuses on the Weyl-covariant nature of holography. We generalize the Fefferman-Graham ambient construction for conformal geometry to a corresponding construction for Weyl geometry. Through the Weyl-ambient…
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 higher dimensional Weyl curvature induces on the brane a new source of gravity. This Weyl fluid of geometrical origin (reducing in the spherically symmetric, static configuration to a dark radiation and dark pressure) modifies…
A model is constructed for the confinement of test particles moving on a brane. Within the classical framework of this theory, confining a test particle to the brane eliminates the effects of extra dimensions, rendering them undetectable.…
We investigate (2+1)-dimensional gravity in a Weyl integrable spacetime (WIST). We show that, unlike general relativity, this scalar-tensor theory has a Newtonian limit for any dimension and that in three dimensions the congruence of world…
Nonlocality is an interesting topic in quantum physics and is usually mediated by some unique quantum states. Here we investigate a Weyl semimetal slab and find an exotic nonlocal correlation effect when placing two potential wells merely…
It is hard to imagine curved spacetimes of General Relativity. A simple but powerful way how to achieve this is visualizing them via embedding diagrams of both ordinary geometry and optical reference geometry. They facilitate to gain an…
The problem of obtaining an explicit representation for the fourth invariant of geodesic motion (generalized Carter constant) of an arbitrary stationary axisymmetric vacuum spacetime generated from an Ernst Potential is considered. The…
The Cosmological Problem is considered in a five-dimensional (bulk) manifold with two time coordinates, obeying vacuum Einstein field equations. The evolution formalism is used there, in order to get a simple form of the resulting…
We discuss the cosmology of a 3-brane embedded in a 5D bulk space-time with a cosmological constant when an intrinsic curvature Ricci scalar is included in the brane action. After deriving the `brane-Friedmann' equations for a Z_2…