Related papers: Junction conditions and sharp gradients in general…
Motivated by the power of subregion/subregion duality for constraining the bulk geometry in gauge/gravity duality, we pursue a comprehensive and systematic approach to the behavior of extremal surfaces under perturbations. Specifically, we…
This paper extends the geometric mechanics theory of constraint systems on principal bundles from the flat connection case to the general situation with non-zero curvature. Based on the theoretical foundation of compatible pairs under…
The junction conditions for the infinite derivative gravity theory ${R{+}RF(\Box)R}$ are derived under the assumption that the conditions can be imposed by avoiding the `ill-defined expressions' in the theory of distributions term by term…
We present a general method to derive the appropriate Darmois-Israel junction conditions for gravitational theories with higher-order derivative terms by integrating the bulk equations of motion across the singular hypersurface. In higher…
Using the constrained superfields formalism to describe the interactions of a light goldstino to matter fields in supersymmetric models, we identify generalised, higher-order holomorphic superfield constraints that project out the…
In conventional gauge theory, a charged point particle is described by a representation of the gauge group. If we propagate the particle along some path, the parallel transport of the gauge connection acts on this representation. The…
The junction condition across a singular surface in general relativity, formulated by Israel, has double covariance. In this paper, a general perturbation scheme of the junction condition around an arbitrary background is given in a doubly…
Motions of continuous media presenting singularities are associated with phenomena involving shocks, interfaces or material surfaces. The equations representing evolutions of these media are irregular through geometrical manifolds. A unique…
We develop a strong coupling approach for a general lattice problem. We argue that this strong coupling perspective represents the natural framework for a generalization of the dynamical mean field theory (DMFT). The main result of this…
The two dark sectors of the universe - dark matter and dark energy - may interact with each other. Background and linear density perturbation evolution equations are developed for a generic coupling. We then establish the general conditions…
We examine an extension of General Relativity with an explicit non-minimal coupling between matter and curvature. The purpose of this work is to present an overview of the implications of the latter to various contexts, ranging from…
This short communication investigates impurity coupling in generalized field theories where scalar coupling is introduced directly at the level of the kinetic and gradient contributions of the energy. We show that the fundamental aspects of…
GR can be interpreted as a theory of evolving 3-geometries. A recent such formulation, the 3-space approach of Barbour, Foster and \'{O} Murchadha, also permits the construction of a limited number of other theories of evolving…
An important, if relatively less well known aspect of the singularity theorems in Lorentzian Geometry is to understand how their conclusions fare upon weakening or suppression of one or more of their hypotheses. Then, theorems with modified…
This paper studies the singularities of jet schemes of homogeneous hypersurfaces of general type. We obtain the condition of the degree and the dimension for the singularities of the jet schemes to be of dense $F$-regular type. This…
While M- and F-theory compactifications describe a much larger class of vacua than perturbative string compactifications, they typically need singularities to generate non-abelian gauge fields and charged matter. The physical explanation…
I present the junction conditions for F(R) theories of gravity and their implications: the generalized Israel conditions and equations. These junction conditions are necessary to construct global models of stars, galaxies, etc., where a…
We discuss the junction conditions in the context of the Randall-Sundrum model with the Gauss-Bonnet interaction. We consider the $Z_2$ symmetric model where the brane is embedded in an $AdS_5$ bulk, as well as a model without $Z_2$…
A formal correspondence is established between the curvature theory of generalized implicit hypersurfaces, electromagnetism as expressed in terms of exterior differential systems, and thermodynamics. Starting with a generalized implicit…
It has been proposed that quantum complexity is dual to the volume of the extremal surface, the action of the Wheeler-DeWitt patch, and the spacetime volume of the patch. Recently, a generalized volume-complexity observable was formulated…