Related papers: Post-Newtonian Conservation Laws in Rigid Quasiloc…
Tidal interactions have a significant influence on the late dynamics of compact binary systems, which constitute the prime targets of the upcoming network of gravitational-wave detectors. We refine the theoretical description of tidal…
Quantum electrodynamics (QED) deals with the relativistic interaction of bosonic gauge fields and fermionic charged particles. In QED, global conservation laws of angular momentum for light-matter interactions are well-known. However, local…
Quasi-universal relations are known to exist among various neutron star observables that do not depend sensitively on the underlying nuclear matter equations of state. For example, some of these relations imply that the tidally induced…
For systems of partial differential equations in three spatial dimensions, dynamical conservation laws holding on volumes, surfaces, and curves, as well as topological conservation laws holding on surfaces and curves, are studied in a…
We describe energy--momentum conservation in relativistic perturbation theory in general FRW backgrounds with causal source terms, such as the presence of cosmic defect networks. We provide a prescription for a linear energy--momentum…
The existence of conservation laws is one of the most important requirement of physical theories. Some of them, like energy conservation, knows no experimental exception. However, the generalization of these conservation laws to curved…
Gravitational waves emitted in the late inspiral of binary neutron stars are affected by their tidal deformation. We study the tidal dynamics in full general relativity through matched-asymptotic expansions and prove that the dynamical…
Thorne elucidated that the relativistic tidal heating is the same as the Newtonian theory. Moreover, Thorne also claimed that the tidal heating is independent of how one localizes gravitational energy and is unambiguously given by a certain…
Quasilocal definitions of stress-energy-momentum -- that is, in the form of boundary densities (rather than local volume densities) -- have proven generally very useful in formulating and applying conservation laws in general relativity. In…
We present a practical framework for ideal hyperelasticity in numerical relativity. For this purpose, we recast the formalism of Carter and Quintana as a set of Eulerian conservation laws in an arbitrary 3+1 split of spacetime. The…
The quasi-local energy conservation law is derived from the vacuum Einstein's equations on the timelike boundary surface in the canonical (2,2)-formalism of general relativity. The quasi-local energy and energy flux integral agree with the…
We present a new approximation to include fully general relativistic pressure and velocity in Newtonian hydrodynamics. The energy conservation, momentum conservation and two Poisson's equations are consistently derived from Einstein's…
Using the Noether Charge formulation, we study a perturbation of the conserved gravitating system. By requiring the boundary term in the variation of the Hamiltonian to depend only on the symplectic structure, we propose a general…
With continuous advances in technology, future satellite gradiometry missions will be capable of performing precision relativistic experiments and imposing constraints on modern gravity theories. To this end, the full first-order…
Conservation laws are well-established in the context of Euclidean gradient flow dynamics, notably for linear or ReLU neural network training. Yet, their existence and principles for non-Euclidean geometries and momentum-based dynamics…
We explain the necessity of application of semi-metric in general relativity. A detailed discussion on the energy-momentum conservation in the general relativity is presented using the mathematical tool of semi-metric. By means of the…
The Fully Constrained Formulation (FCF) of General Relativity is a novel framework introduced as an alternative to the hyperbolic formulations traditionally used in numerical relativity. The FCF equations form a hybrid elliptic-hyperbolic…
Symmetries and conservation laws are studied for two classes of physically and analytically interesting radial wave equations with power nonlinearities in multi-dimensions. The results consist of two main classifications: all symmetries of…
We compute the gravitational-wave (GW) energy flux up to the next-to-next-to-leading (NNL) order of tidal effects in a spinless compact binary system on quasi-circular orbits. Starting from an effective matter action, we obtain the…
We present the general relativistic pressure correction terms in Newtonian hydrodynamic equations to the nonlinear order: these are equations (\ref{mass-conservation-Mink})-(\ref{Poisson-eq-Mink}). The derivation is made in the zero-shear…