Related papers: A class of gauges for the Einstein equations
We consider gauge theories from the free evolution point of view, in which initial data satisfying constraints of a theory are given. Because the constraints are compatible with the field equations they remain so. We study a model…
In this and a companion paper, we show that quantum field theories with gauge symmetries permit a broader class of classical dynamics than typically assumed. In this article, we show that the dynamics extracted from the path integral or…
A new gauge driver is introduced for the generalized harmonic (GH) representation of Einstein's equation. This new driver allows a rather general class of gauge conditions to be implemented in a way that maintains the hyperbolicity of the…
We perform a general computation of the off-shell one-loop divergences in Einstein gravity, in a two-parameter family of path integral measures, corresponding to different ways of parametrizing the graviton field, and a two-parameter family…
A gauge theory of quantum gravity is formulated, in which an internal, field dependent metric is introduced which non-linearly realizes the gauge fields on the non-compact group $SL(2,C)$, while linearly realizing them on $SU(2)$.…
We present a symmetric hyperbolic formulation of the Einstein equations in affine-null coordinates. Giannakopoulos et. al. (arXiv:2007.06419) recently showed that the most commonly numerically implemented formulations of the Einstein…
Solutions to Einstein's vacuum equations in three dimensions are locally maximally symmetric. They are distinguished by their global properties and their investigation often requires a choice of gauge. Although analyses of this sort have…
We revisit the problem of solving the Einstein constraint equations in vacuum by a new method, which allows us to prescribe four scalar quantities, representing the full dynamical degrees of freedom of the constraint system. We show that…
The {\it {gauge - fixing} } and {\it gaugeless } methods for reducing the phase space in the generalized Hamiltonian dynamics are compared with the aim to define the class of admissible gauges . In the gaugeless approach, the reduced phase…
The Cauchy problem of the vacuum Einstein's equations aims to find a semi-metric $g_{\alpha\beta}$ of a spacetime with vanishing Ricci curvature $R_{\alpha,\beta}$ and prescribed initial data. Under the harmonic gauge condition, the…
In hyperbolic reductions of the Einstein equations the evolution of gauge conditions or constraint quantities is controlled by subsidiary systems. We point out a class of non-linearities in these systems which may have the potential of…
We prove local existence of solutions to the Einstein--null dust system under polarized $\mathbb U(1)$ symmetry in an elliptic gauge. Using in particular the previous work of the first author on the constraint equations, we show that one…
We formulate the most general gravitational models with constant negative curvature ("hyperbolic gravity") on an arbitrary orientable two-dimensional surface of genus $g$ with $b$ circle boundaries in terms of a $\text{PSL}(2,\mathbb…
The Einstein theory of general relativity provides a peculiar example of classical field theory ruled by non-linear partial differential equations. A number of supplementary conditions (more frequently called gauge conditions) have also…
This is the second paper in a series of papers adressing the characteristic gluing problem for the Einstein vacuum equations. We solve the codimension-$10$ characteristic gluing problem for characteristic data which are close to the…
We derive a new symmetric hyperbolic formulation of the Einstein-Euler equations in Lagrange coordinates that are adapted to the Frauendiener-Walton formulation of the Euler equations. As an application, we use this system to show that the…
A generalization of General Relativity is studied. The standard Einstein-Hilbert action is considered in the Palatini formalism, where the connection and the metric are independent variables, and the connection is not symmetric. As a result…
We prove that the Einstein equations can be solved in a very general form for arbitrary spacetime dimensions and various types of vacuum and non-vacuum cases following a geometric method of anholonomic frame deformations for constructing…
Rigorous results on solutions of the Einstein-Vlasov system are surveyed. After an introduction to this system of equations and the reasons for studying it, a general discussion of various classes of solutions is given. The emphasis is on…
The Einstein equations are non-linear and the particles of which the gravitational effect is described by these equations are lastly unknown. If renormalizable fields are assumed, then results are obtained only in the case of a at space.…