Related papers: Null Conservation Laws for Gravity
We undertake a general study of the boundary (or edge) modes that arise in gauge and gravitational theories defined on a space with boundary, either asymptotic or at finite distance, focusing on efficient techniques for computing the…
Using the maximal Lie algebra of point symmetries of a system of nonlinear equations used in geophysical fluid dynamics, two conservation laws are found in addition to the conservation of energy.
In this work, the dynamic of isolated systems in general relativity is described when gravitational radiation and electromagnetic fields are present. In this construction, the asymptotic fields received at null infinity together with the…
We consider systems of conservation laws endowed with a convex entropy. We show the contraction, up to a translation, to extremal entropic shocks, for a pseudo-distance based on the notion of relative entropy. The contraction holds for…
Using the concept of variational tricomplex endowed with a presymplectic structure, we formulate the general notion of symmetry. We show that each generalized symmetry of a gauge system gives rise to a sequence of conservation laws that are…
This paper presents an overview of the derivation and significance of recently derived conservation laws for the matrix moments of Hermitean random matrices with dominant exponential weights that may be either even or odd. This is based on…
A quasilocal framework of stationary and dynamical untrapped hypersurfaces is introduced to generalize the notions of energy and angular momentum of isolated and dynamical trapping horizons to general strong gravitating systems.
In all 2d theories of gravity a conservation law connects the (space-time dependent) mass aspect function at all times and all radii with an integral of the matter fields. It depends on an arbitrary constant which may be interpreted as…
We investigate the behavior of null geodesics near future null infinity in asymptotically flat spacetimes. In particular, we focus on the asymptotic behavior of null geodesics that correspond to worldlines of photons initially emitted in…
We propose a novel but natural definition of conserved quantities for gravity models quadratic and higher in curvature. Based on the spatial asymptotics of curvature rather than of metric, it avoids the GR energy machinery's more egregious…
The asymptotic structure of the gravitational field of isolated systems has been analyzed in great detail in the case when the cosmological constant $\Lambda$ is zero. The resulting framework lies at the foundation of research in diverse…
Through the discussion of the fundamental properties of Lagrangian density for a gravitational system, the theoretical foundations of the modified Einstein field equations and the Lorentz and Levi-Civita conservation laws are systematically…
On any asymptotically-flat spacetime, we show that the asymptotic symmetries and charges of Maxwell fields on past null infinity can be related to those on future null infinity as recently proposed by Strominger. We extend the covariant…
We review issues related to conservation laws for gravity with a negative cosmological constant subject to asymptotically (locally) anti-de Sitter boundary conditions. Beginning with the empty AdS spacetime, we introduce asymptotically…
Backgrounds are pervasive in almost every application of general relativity. Here we consider the Lagrangian formulation of general relativity for large perturbations with respect to a curved background spacetime. We show that Noether's…
Apart from the flat space with an angular deficit, Einstein general relativity possesses another cylindrically symmetric solution. Because this configuration displays circles whose "circumferences" tend to zero when their "radius" go to…
We consider conservation of momentum in AQUAL, a field-theoretic extension to Modified Newtonian Dynamics (MOND). We show that while there is a sense in which momentum is conserved, it is only if momentum is attributed to the gravitational…
We provide global and semi-global controllability results for hyperbolic conservation laws on a bounded domain, with a general (not necessarily convex)flux and a time-dependent source term acting as a control. The results are achieved for,…
The spatial discretization of convective terms in compressible flow equations is studied from an abstract viewpoint, for finite-difference methods and finite-volume type formulations with cell-centered numerical fluxes. General conditions…
There are two strong clues about the quantum structure of spacetime and the gravitational dynamics, which are almost universally ignored in the conventional approaches to quantize gravity. The first clue is that null surfaces exhibit…