Related papers: The Conformal Method and the Conformal Thin-Sandwi…
The role of the Taub time gauge in cosmology is linked to the use of the densitized lapse function instead of the lapse function in the variational principle approach to the Einstein equations. The spatial metric variational equations then…
In this paper we investigate the existence of singular solutions to the conformal Dirac-Einstein system. Because of its conformal invariance, there are many similarities with the classical construction of singular solutions for the Yamabe…
For conformal geometries of Riemannian signature, we provide a comprehensive and explicit treatment of the core local theory for embedded submanifolds of arbitrary dimension. This is based in the conformal tractor calculus and includes a…
The Einstein-Bianchi system uses symmetric and traceless tensors to reformulate Einstein's original field equations. However, preserving these algebraic constraints simultaneously remains a challenge for numerical methods. This paper…
Controlled Lagrangian and matching techniques are developed for the stabilization of relative equilibria and equilibria of discrete mechanical systems with symmetry as well as broken symmetry. Interesting new phenomena arise in the…
A framework is introduced which explains the existence and similarities of most exact solutions of the Einstein equations with a wide range of sources for the class of hypersurface-homogeneous spacetimes which admit a Hamiltonian…
In this manuscript, a conformally invariant theory of gravitation in the context of metric measure space is studied. The proposed action is invariant under both diffeomorphism and conformal transformations. Using the variational method, a…
The convergence of Levenberg-Marquard method is discussed for the inverse problem to reconstruct the storage modulus and loss modulus for the so called scalar model by single interior measurement. The scalar model is the most simplest model…
The recently introduced backward Monte-Carlo method [Johan Carlsson, arXiv:math.NA/0010118] is validated, benchmarked, and compared to the conventional, forward Monte-Carlo method by analyzing the error in the Monte-Carlo solutions to a…
The special conformal transformation (composed by inversion - translation - inversion) is used to generate a time dependent conformally flat spacetime. In order to be an exact solution of Einstein's equations, we need as a source a stress…
In this paper, we establish a compactness result for a class of conformally compact Einstein metrics defined on manifolds of dimension $d\ge 4$. As an application, we derive the global uniqueness of a class of conformally compact Einstein…
We consider dynamical spherically symmetric spacetimes, which are conformal to the static spherically symmetric metrics, and find new solutions of Einstein equations by symmetry considerations. Our study help us classify various conformal…
We study conformally-invariant theories of gravity in six dimensions. In four dimensions, there is a unique such theory that is polynomial in the curvature and its derivatives, namely Weyl-squared, and furthermore all solutions of Einstein…
This paper belongs to the realm of conformal geometry and deals with Euclidean submanifolds that admit smooth variations that are infinitesimally conformal. Conformal variations of Euclidean submanifolds is a classical subject in…
The question of whether classically conformal modifications of the standard model are consistent with experimental obervations has recently been subject to renewed interest. The method of Gildener and Weinberg provides a natural framework…
Several recent works have explored stochastic gradient methods for variational inference that exploit the geometry of the variational-parameter space. However, the theoretical properties of these methods are not well-understood and these…
A Lagrangian depending on geometric variables (metric, affine connection, gauge group generators) is given which maintains compatibility with General Relativity. It generates the dynamics for Electromagnetism and other Gauge Fields along…
It is known that some cosmological perturbations are conformal invariant. This facilitates the studies of perturbations within some gravitational theories alternative to general relativity, for example the scalar-tensor theory, because it…
In this work we develop and analyze an adaptive finite element method for efficiently solving electrical impedance tomography -- a severely ill-posed nonlinear inverse problem for recovering the conductivity from boundary voltage…
This paper initiates the study of the Einstein equation on homogeneous supermanifolds. First, we produce explicit curvature formulas for graded Riemannian metrics on these spaces. Next, we present a construction of homogeneous…