Related papers: The Conformal Method and the Conformal Thin-Sandwi…
We develop a method to calculate generic time-dependent correlation functions for inhomogeneous quantum quenches in (1+1)-dimensional conformal field theory (CFT) induced by sudden Hamiltonian deformations that modulate the energy density…
The extended constraint equations arise as a special case of the conformal constraint equations that are satisfied by an initial data hypersurface $Z$ in an asymptotically simple spacetime satisfying the vacuum conformal Einstein equations…
It has long been considered that conformal superspace is the natural configuration space for canonical general relativity. However, this was never definitively demonstrated. We have found that the standard conformal method of solving the…
The analytic conformal bootstrap is an array of techniques to characterize, constrain, and solve strongly interacting quantum field theories using symmetries, causality, unitarity, and other general principles. In the last decade, bolstered…
The purpose of this paper is to demonstrate a new method of generating exact solutions to the Einstein's equations obtained by the Hamiltonian reduction. The key element to the successful Hamiltonian reduction is finding the privileged…
This paper considers the existence of conformally compact Einstein metrics on 4-manifolds. A reasonably complete understanding is obtained for the existence of such metrics with prescribed conformal infinity, when the conformal infinity is…
We study boundary regularity for conformally compact Einstein metrics in even dimensions by generalizing the ideas of Michael Anderson. Our method of approach is to view the vanishing of the Ambient Obstruction tensor as an nth order system…
The conformal method has been effective for parametrizing solutions to the Einstein constraint equations on closed 3-manifolds. However, it is still not well-understood; for example, existence of solutions to the conformal equations for…
Conformal field theories have been long known to describe the fascinating universal physics of scale invariant critical points. They describe continuous phase transitions in fluids, magnets, and numerous other materials, while at the same…
Multiple scalar fields appear in vast modern particle physics and gravity models. When they couple to gravity non-minimally, conformal transformation is utilized to bring the theory into Einstein frame. However, the kinetic terms of scalar…
Conformal predictors are machine learning algorithms developed in the 1990's by Gammerman, Vovk, and their research team, to provide set predictions with guaranteed confidence level. Over recent years, they have grown in popularity and have…
Hidden symmetries in a covariant Hamiltonian formulation are investigated involving gauge covariant equations of motion. The special role of the Stackel-Killing tensors is pointed out. A reduction procedure is used to reduce the original…
Numerical solutions to the Einstein constraint equations are constructed on a selection of compact orientable three-dimensional manifolds with non-trivial topologies. A simple constant mean curvature solution and a somewhat more complicated…
In this article we develop some new existence results for the Einstein constraint equations using the Lichnerowicz-York conformal rescaling method. The mean extrinsic curvature is taken to be an arbitrary smooth function without…
Conformal transformations are frequently used tools in order to study relations between various theories of gravity and the Einstein relativity. In this paper we discuss the rules of these transformations for geometric quantities as well as…
The equations of motion of four-dimensional conformal gravity, whose Lagrangian is the square of the Weyl tensor, require that the Bach tensor $E_{\mu\nu}= (\nabla^\rho\nabla^\sigma + \ft12 R^{\rho\sigma})C_{\mu\rho\nu\sigma}$ vanishes.…
The effectiveness of the hyperbolic relaxation method for solving the Einstein constraint equations numerically is studied here on a variety of compact orientable three-manifolds. Convergent numerical solutions are found using this method…
The inflation-free solution of problems of the modern cosmology (horizon, cosmic initial data, Planck era, arrow of time, singularity,homogeneity, and so on) is considered in the conformal-invariant unified theory given in the space with…
An important tool in the study of conformal geometry, and the AdS/CFT correspondence in physics, is the Fefferman-Graham expansion of conformally compact Einstein metrics. We show that conformally compact metrics satisfying a generalization…
Conformal gravity theories are defined by field equations that determine only the conformal structure of the spacetime manifold. The Bach equations represent an early example of such a theory, we present them here in component form in terms…