Related papers: Characteristic Gluing with $\Lambda$ 1. Linearised…
Charges associated with gauge symmetries are defined on boundaries of spacetimes. But these constructions typically involve divergent quantities when considering asymptotic boundaries. Different prescriptions exist to address this problem,…
In this paper we study the spacelike-characteristic Cauchy problem for the Einstein vacuum equations. We prove that given initial data on a maximal compact spacelike hypersurface $\Sigma \simeq \overline{B(0,1)} \subset \mathbb{R}^3$ and…
We prove that given a solution of the Einstein equations $g_{ab}$ for the matter field $T_{ab}$, an autoparallel null vector field $l^{a}$ and a solution $(l_{a}l_{c}, \mathcal{T}_{ac})$ of the linearized Einstein equation on the given…
Standard cosmological models rely on an approximate treatment of gravity, utilizing solutions of the linearized Einstein equations as well as physical approximations. In an era of precision cosmology, we should ask: are these approximate…
On a spacetime $(M,g)$ endowed with a density function $h$, we consider the vacuum weighted Einstein field equations: \[h\rho-\operatorname{Hes}_h+\Delta h g=0.\] First, it is shown that the equation characterizes critical metrics for an…
We prove in this note that local geometric uniqueness holds true without loss of regularity for Einstein equations coupled with a large class of matter models. We thus extend the Planchon-Rodnianski uniqueness theorem for vacuum spacetimes.…
We develop a general setting for the quantization of linear bosonic and fermionic field theories subject to local gauge invariance and show how standard examples such as linearized Yang-Mills theory and linearized general relativity fit…
We consider a theory of modified gravity possessing d extra spatial dimensions with a maximally symmetric metric and a scale factor, whose (4+d)-dimensional gravitational action contains terms proportional to quadratic curvature scalars.…
It is shown that Einstein gravity in four dimensions with small cosmological constant and small extra dimensions can be obtained by spontaneous compactification of Lovelock gravity in vacuum. Assuming that the extra dimensions are compact…
The purpose of this paper is to extend the analysis of gravitational instability of the Linet - Tian solution to the case $\Lambda > 0$. A fundamental difference brought about by $\Lambda >0$, as compared to $\Lambda<0$ is in the structure…
We study static black holes in quadratic gravity with planar and hyperbolic symmetry and non-extremal horizons. We obtain a solution in terms of an infinite power-series expansion around the horizon, which is characterized by two…
We investigate Lie symmetries of Einstein's vacuum equations in N dimensions, with a cosmological term. For this purpose, we first write down the second prolongation of the symmetry generating vector fields, and compute its action on…
We introduce the method of topological quantization for gravitational fields in a systematic manner. First we show that any vacuum solution of Einstein's equations can be represented in a principal fiber bundle with a connection that takes…
In general relativity, perturbation theory about a background solution fails if the background spacetime has a Killing symmetry and a compact spacelike Cauchy surface. This failure, dubbed as {\it linearization instability}, shows itself as…
Consider compact objects --such as neutron star or black hole binaries-- in \emph{full, non-linear} general relativity. In the case with zero cosmological constant $\Lambda$, the gravitational radiation emitted by such systems is described…
A recently introduced approach for the dynamical analysis and quantization of field theoretical models with second class constraints is ilustrated applied to linearized gravity in 3-D. The canonical structure of two different models of…
In this paper, we prove the nonlinear stability in exponential time of Minkowki space-time with a translation space-like Killing field. In the presence of such a symmetry, the 3 + 1 vacuum Einstein equations reduce to the 2 + 1 Einstein…
This study of gauge field theories on kappa-deformed Minkowski spacetime extends previous work on field theories on this example of a noncommutative spacetime. We construct deformed gauge theories for arbitrary compact Lie groups using the…
The nonrelativistic bosonic string theory in a curved manifold is formulated here using gauging of symmetry approach ( Galilean Gauge theory ) . The corresponding model in flat space has some global symmetries . By localizing these…
Categories of models of algebraic theories have good categorical properties except for gluing. Building upon insights and examples from Synthetic Differential Geometry, we introduce a generalisation of models of algebraic theories to…