Related papers: On Global Conservation Laws at Null Infinity
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…
It is shown that a well-defined expression for the total electromagnetic force $f^{em}$ on a point charge source of the classical electromagnetic field can be extracted from the postulate of total momentum conservation whenever the…
We generalize a notion of 'conserved' charges given by Wald and Zoupas to the asymptotically de Sitter spacetimes. Surprisingly, our construction is less ambiguous than the one encountered in the asymptotically flat context. An expansion…
A set of exact quasi-local conservation equations is derived from the Einstein's equations using the first-order Kaluza-Klein formalism of general relativity in the (2,2)-splitting of 4-dimensional spacetime. These equations are interpreted…
We show that the BMS-supertranslations and their associated supermomenta on past null infinity can be related to those on future null infinity, proving the conjecture of Strominger for a class of spacetimes which are asymptotically-flat in…
The formalism of classical particle dynamics is reinvestigated according to the basic requirement of causal consistency, and a new equation of particle dynamics, which is more general and more in line with classical mechanics experiments…
An interesting question is to characterize the general class of allowed boundary conditions for gauge theories, including gravity, at spatial and null infinity. This has played a role in discussions of soft charges, where antipodal symmetry…
It is argued that when the dimension of space is a constant integer the full set of Einstein's field equations has more information than the spatial components of Einstein's equation plus the energy conservation law. Applying the former…
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…
When a system emits gravitational radiation, the Bondi mass decreases. If the Bondi energy is Hamiltonian, it can thus only be a time dependent Hamiltonian. In this paper, we show that the Bondi energy can be understood as a time-dependent…
Conservation laws of a class of time-dependent damped nonlinear multidimensional wave equations are derived by Noether's theorem. For arbitrary nonzero damping coefficient and nonlinear interaction term, its infinitesimal variational…
The theory of massive gravity proposed by Bergshoeff, Hohm and Townsend is considered in the special case of the pure irreducibly fourth order quadratic Lagrangian. It is shown that the asymptotically locally flat black holes of this theory…
The quasigroup approach to the conservation laws (Phys. Rev. D56, R7498 (1997)) is completed by imposing new gauge conditions for asymptotic symmetries. Noether charge associated with an arbitrary element of the Poincar\'e quasialgebra is…
For smooth solutions to Maxwell's equations sourced by a smooth charge-current distribution $j_a$ in stationary, asymptotically flat spacetimes, one can prove an energy conservation theorem which asserts the vanishing of the sum of (i) the…
Time-dependent models of fluid motion in thin layers, subject to signed source terms, represent important sub-problems within climate dynamics. Examples include ice sheets, sea ice, and even shallow oceans and lakes. We address these…
We show how a stress-energy pseudotensor can be constructed in two-dimensional dilatonic gravity theories (classical, CGHS and RST) and derive the expression for the ADM mass in these theories from it. We define the Bondi mass for these…
This article begins with a brief introduction to numerical relativity aimed at readers who have a background in applied mathematics but not necessarily in general relativity. I then introduce and summarise my work on the problem of treating…
The classical gravitational two-body problem is generalized in order to be applicable also to weak gravitational fields. The equation of motion holds both for terrestrial and large cosmic scales, the Newtonian gravitational law represents a…
I describe an approach which connects classical gravity with the quantum microstructure of spacetime. The field equations arise from maximizing the density of states of matter plus geometry. The former is identified using the thermodynamics…
For nonlinear Schr\"odinger equations in less than or equal to four dimension, with non-vanishing initial data at infinity, a new approach to derive the conservation law is obtained. Since this approach does not contain approximating…