Related papers: The Birkhoff Theorem in Multidimensional Gravity
Gravity and matter are universally coupled, and this unique universality provides us with an intriguing way to quantifying quantum aspects of space-time in terms of the number of gravitons within a given box. In particular, we will provide…
Quantum manifestations of the dynamics around resonant tori in perturbed Hamiltonian systems, dictated by the Poincar\'e--Birkhoff theorem, are shown to exist. They are embedded in the interactions involving states which differ in a number…
A unified version of Machado-Bishop theorem in weighted spaces is given. A number of applications illustrate its importance.
Motivated by the Pierce-Birkhoff conjecture, we launch an extension program for single variable expansivity theory. We study this notion under tuples of polynomials in the ring $\mathbb{R}[x_1,x_2,\ldots,x_n]$. As an application, we develop…
In this article we study invariance properties of shift-invariant spaces in higher dimensions. We state and prove several necessary and sufficient conditions for a shift-invariant space to be invariant under a given closed subgroup of…
It is argued that the existence of a minimum size of spacetime may imply the fundamental existence of gravity as a geometric property of spacetime described by general relativity.
The two dimensional substructure of general relativity and gravity, and the two dimensional geometry of quantum effect by black hole are disclosed. Then the canonical quantization of the two dimensional theory of gravity is performed. It is…
The gravitation equations of the general relativity, written for Riemannian space-time geometry, are extended to the case of arbitrary (non-Riemannian) space-time geometry. The obtained equations are written in terms of the world function…
We extend one of the Hawking-Penrose singularity theorems in general relativity to the case of some scalar-tensor gravity theories in which the scalar field has a geometrical character and space-time has the mathematical structure of a Weyl…
We study the local causality issue via the Shapiro time-delay computations in the on-shell consistent exotic massive gravity in three dimensions. The theory shows time-delay as opposed to time-advance despite having a ghost at the…
These lectures are intended as a broad introduction to Chern Simons gravity and supergravity. The motivation for these theories lies in the desire to have a gauge invariant action -in the sense of fiber bundles- in more than three…
We consider the motion of charged point particles on Minkowski spacetime. The questions of whether the self-force is finite and whether mass renormalisation is necessary are discussed within three theories: In the standard Maxwell vacuum…
Dynamics of a self-gravitating shell of matter is derived from the Hilbert variational principle and then described as an (infinite dimensional, constrained) Hamiltonian system. A method used here enables us to define singular Riemann…
The Einstein equation in D dimensions, if restricted to the class of space-times possessing n = D - 2 commuting hypersurface-orthogonal Killing vectors, can be equivalently written as metric-dilaton gravity in 2 dimensions with n scalar…
We study a deSitter/Anti-deSitter/Poincare Yang-Mills theory of gravity in d-space-time dimensions in an attempt to retain the best features of both general relativity and Yang-Mills theory: quadratic curvature, dimensionless coupling and…
We show the obstacle version of the Strauss conjecture holds when the spatial dimension is equal to 4. We also show that an almost global existence theorem of H\"ormander for (4+1)-dimensional Minkowski space holds in the obstacle setting.…
We demonstrate that generic two-dimensional Horndeski theories can arise from the reduction of pure gravities in $d \geq 4$ dimensions, and therefore generic onshell configurations for the two-dimensional metric and scalar field correspond…
Spherically symmetric shock waves are shown to exist in Lovelock gravity. They amount to a change of branch of the spherically symmetric solutions across a null hypersurface. The implications of their existence for the status of Birkhoff's…
We discuss entropy bounds for a class of two-dimensional gravity models. While the Bekenstein bound can be proved to hold in general for weakly gravitating matter, the analogous of the holographic bound is not universal, but depends on the…
In three dimensions, there exist modifications of Einstein's gravity akin to the topologically massive gravity that describe massive gravitons about maximally symmetric backgrounds. These theories are built on the three-dimensional version…