Related papers: The Higher Dimensional Positive Mass Theorem II
Beyond normal surfaces there are several open questions concerning 2- dimensional spaces. We present some results and conjectures along this line.
Any connection between dark matter and extra dimensions can be cognizably evinced from the associated effective energy-momentum tensor. In order to investigate and test such relationship, a higher dimensional spacetime endowed with a…
In this paper, we have studied a 5-dimensional warped product space-time with a time-dependent warp factor. This warp factor plays an important role in localizing matter to the 4-dimensional hypersurface constituting the observed universe…
Homogeneous cosmological solutions are obtained in five dimensional space time assuming equations of state $ p = k\rho $ and $ p_{5}= \gamma\rho$ where p is the isotropic 3 - pressure and $p_{5}$, that for the fifth dimension. Using…
This is the first in a series of papers where we develop new structural elements on singular area minimizing hypersurfaces, the skin structures. They disclose previously unapproachable and largely unexpected geometric and analytic…
Starting from a topological gauge theory in two dimensions with symmetry groups $ISO(2,1)$, $SO(2,1)$ and $SO(1,2)$ we construct a model for gravity with non-trivial coupling to matter. We discuss the equations of motion which are connected…
In this paper, we introduce a new family of mass-type invariants for time-symmetric initial data in space-times satisfying the Dominant Energy Condition. For positive cosmological constant, these invariants, unlike the total Hawking mass,…
In three dimensions, there are two distinct mass-generating mechanisms for gauge fields: adding the usual Proca/Pauli-Fierz, or the more esoteric Chern-Simons (CS), terms. Here we analyze the three-term models where both types are present,…
This article discusses various methods of representing and manipulating arbitrary coverage information in two dimensions, with a focus on space- and time-efficiency when processing such coverages, storing them on disk, and transmitting them…
Generic cosmological models derived from higher dimensional theories with warped extra dimensions have a nonzero cosmological constant-like term induced on the 3+1 space-time, or a physical 3-brane. In the scenario where this 3+1 space-time…
We show that a pure gauge theory in higher dimensions may lead to an effective lower-dimensional theory with massive vector field, broken gauge symmetry and no fundamental Higgs boson. The mechanism we propose employs the localization of a…
Optics of metamaterials is shown to provide interesting table top models of many non-trivial space-time metrics. The range of possibilities is broader than the one allowed in classical general relativity. For example, extraordinary waves in…
This is the third in a series of papers on the geometry and analysis of singular area minimizing hypersurfaces. We show how to derive obstruction and structure theories for scalar curvature constraints without imposing dimensional or…
We summarize main properties of vacuum Kerr-Schild spacetimes in higher dimensions.
Ten-dimensional models, arising from a gravitational action which includes terms up to the fourth order in curvature tensor, are discussed. The spacetime consists of one timelike dimension and two maximally symmetric subspaces, filled with…
We consider versions of the Penrose singularity theorem and the Hawking horizon topology theorem in weighted spacetimes that contain weighted versions of trapped surfaces, for arbitrary spacetime dimension and synthetic dimension. We find…
For asymptotically hyperbolic manifolds of dimension $n$ with scalar curvature at least equal to $-n(n-1)$ the conjectured positive mass theorem states that the mass is non-negative, and vanishes only if the manifold is isometric to…
Hubble expansion in warped braneworld model is addressed in presence of more than one warped extra dimensions. It is shown that while the expansion depends on all the moduli, an exponential nature of the expansion of the scale factor…
We provide a partial characterization of the conformal infinity of asymptotically de Sitter spacetimes by deriving constraints that relate the asymptotics of the stress-energy tensor with conformal geometric data. The latter is captured…
The higher dimensional cosmology provides a natural setting to treat, at a classical level, the cosmological effects of vacuum energy. Here we discuss two situations where starting with an ordinary matter field without any equation of state…