Gravitation on a Homogeneous Domain

TL;DR

This paper explores the geometric structure of conformal deformations of the gravitational Lorentz vacuum using homogeneous spaces and coherent states, revealing Einstein-like conformal deformations on the compactified Minkowski space.

Contribution

It introduces a geometric framework for conformal deformations of gravity via homogeneous Kähler domains and coherent states, connecting them to Einstein-like deformations.

Findings

Coherent states on homogeneous Kähler domains induce Einstein-like conformal deformations.

The structure of the conformal group SU(2,2) is used to describe gravitational deformations.

The approach links geometric representation theory with gravitational physics.

Abstract

Among all plastic deformations of the gravitational Lorentz vacuum \cite{wr1} a particular role is being played by conformal deformations. These are conveniently described by using the homogeneous space for the conformal group SU(2,2)/S(U(2)x U(2)) and its Shilov boundary - the compactified Minkowski space \tilde{M} [1]. In this paper we review the geometrical structure involved in such a description. In particular we demonstrate that coherent states on the homogeneous Kae}hler domain give rise to Einstein-like plastic conformal deformations when extended to \tilde{M} [2].