Related papers: The Bach equations in Spin-Coefficient form
We study gauge and gravitational field theories in which the gauge fixing conditions are imposed as constraints on classical fields. Quantization of fluctuations can be performed in a BRST invariant manner, while the main novelty is that…
Assuming that the mechanism proposed by Gell-Mann and Hartle works as a mechanism for decoherence and classicalization of the metric field, we formally derive the form of an effective theory for the gravitational field in a semiclassical…
The Einstein equations for a plane-symmetric gravitational field coupled to an arbitrary nonlinear sigma model (NSM) are shown to be represented in the form of dynamical equations of a {\it generalized effective NSM}. The gravitational…
This is a survey paper of our current research on the theory of partial differential equations in conformal geometry. Our intention is to describe some of our current works in a rather brief and expository fashion. We are not giving a…
In this paper we continue a study of cosmological perturbations in the conformal gravity theory. In previous work we had obtained a restricted set of solutions to the cosmological fluctuation equations, solutions that were required to be…
Geometric structure of spherically-symmetric space-time in metric-affine gauge theory of gravity is studied. Restrictions on curvature tensor and Bianchi identities are obtained. By using certain simple gravitational Lagrangian the solution…
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…
The theory of macroscopic gravity provides a formalism to average the Einstein field equations from small scales to largest scales in space-time. It is well known that averaging is an operation that does not commute with calculating the…
The extended-BMS algebra of asymptotically flat spacetime contains an SO(3,1) subgroup that acts by conformal transformations on the celestial sphere. It is of interest to study the representations of this subgroup associated with…
The constructive gravity programme applied to electrodynamics with vacuum birefringence yields the---up to unknown gravitational constants---unique compatible gravity theory for the underlying non-metric geometry. Starting from a…
In the framework of metric-like approach, totally symmetric arbitrary spin bosonic conformal fields propagating in flat space-time are studied. Depending on the values of conformal dimension, spin, and dimension of space-time, we classify…
Recently, a unique class of local Higher Spin Gravities with propagating massless fields in $4d$ - Chiral Higher Spin Gravity - was given a covariant formulation both in flat and $(A)dS_4$ spacetimes at the level of equations of motion. We…
Global properties of vacuum static, spherically symmetric configurations are studied in a general class of scalar-tensor theories (STT) of gravity in various dimensions. The conformal mapping between the Jordan and Einstein frames is used…
We obtain exact solutions to the class of parabolic partial differential equations of arbitrary dimensionality and with arbitrary potentials. The solutions are presented in a compact-form: as explicit mathematical expressions consisting of…
We use the conformal method to obtain solutions of the Einstein-scalar field gravitational constraint equations. Handling scalar fields is a bit more challenging than handling matter fields such as fluids, Maxwell fields or Yang-Mills…
A new class of conformal field theories is presented, where the background gravitational field is conformally flat. Conformally flat (CF) spacetimes enjoy conformal properties quite similar to the ones of flat spacetime. The conformal…
It is shown that an arbitrary static, spherically symmetric metric can be presented as an exact solution of a scalar-tensor theory (STT) of gravity with certain nonminimal coupling function $f(\phi)$ and potential $U(\phi)$. The scalar…
In principle, global properties of solution of Einstein equations need to be addressed using the conformal Einstein equations, because this conformal compactification allows a clean definition of the `infinities' (spacelike, timelike and…
The phase space of gravitational theories in asymptotically Anti-de Sitter (AAdS) spacetimes consists of geometries, matter configurations, and their conjugate momenta on a Cauchy surface, subject to the Hamiltonian, momentum, and…
A discussion is given of the conformal Einstein field equations coupled with matter whose energy-momentum tensor is trace-free. These resulting equations are expressed in terms of a generic Weyl connection. The article shows how in the…