Related papers: Gravitational multipole moments from Noether charg…
In classical electromagnetic theory, one formally defines the complex dipole moment (the electric plus 'i' magnetic dipole) and then computes (and defines) the complex center of charge by transforming to a complex frame where the complex…
We discuss the motion of extended objects in a spacetime by considering a gravitational field created by these objects. We define multipole moments of the objects as a classification by Lie group SO(3). Then, we construct an energy-momentum…
A definition of gravitational energy is proposed for any theory described by a diffeomorphism-invariant Lagrangian. The mathematical structure is a Noether- current construction of Wald involving the boundary term in the action, but here it…
Using an integral definition to calculate the relativistic multipole moments (RMM), and the ensuing generalized relativistic Gauss theorem, we prove that the evaluation of that volume integral in Erez-Rosen coordinates, leads to a specific…
The Noether currents are derived in a generic metric-affine theory of gravity, and the holographic nature of the gravitational entropy and energy-momentum is clarified. The main result is the verification of the canonical resolution to the…
There exist instances of dynamical systems possessing symmetry transformations of which the conserved Noether charges generating these symmetries feature an explicit time dependence in their functional representation over phase space. The…
We propose a consistent approach to the definition of electric, magnetic, and toroidal multipole moments. Electric and magnetic fields are split into potential, vortex, and radiative terms, with the latter ones dropped off in the…
This thesis deals with the construction of conserved charges for asymptotically flat spacetimes at spatial infinity in four spacetime dimensions in a hopefully pedagogical way. As a first motivation of this work, it highlights the…
A family of vector fields that are the infinitesimal generators of determined one-parameter groups of transformations are constructed. It is shown that these vector fields represent symmetries of the system of differential equations…
Up to the third post-Newtonian (3PN) order, we compute (i) the current-type quadrupole moment of (non-spinning) compact binary systems, as well as (ii) the corresponding gravitational-wave mode $(2,1)$ (constituting a 3.5PN correction in…
Using a proper gauge condition the static spherically symmetric solutions of Einstein-Maxwell equations with charged point source at the center are derived. It is shown that the solutions of the field equations are a three-parameter family…
Multipole moments in general relativity serve as a powerful tool for characterising the gravitational field. In this paper, we review the construction of the Geroch--Hansen multipole moments for stationary asymptotically flat vacuum…
Utilizing various gauges of the radial coordinate we give a description of static spherically symmetric space-times with point singularity at the center and vacuum outside the singularity. We show that in general relativity (GR) there exist…
We transform the metric of an isolated matter source in the multipolar post-Minkowskian approximation from harmonic (de Donder) coordinates to radiative Newman-Unti (NU) coordinates. To linearized order, we obtain the NU metric as a…
In this short review we compare the rigid Noether charges to topological gauge charges. One important extension is that one should consider each boundary component of spacetime independently. The argument that relates bulk charges to…
The geometry around a rotating massive body, which carries charge and electrical currents, could be described by its multipole moments (mass moments, mass-current moments, electric moments, and magnetic moments). When a small body is…
We study integral expressions of electromagnetic multipole moments of arbitrary order in Cartesian coordinates. The volume and surface integrals of charge-induced and current-induced multipole moment tensors are formulated and the…
A binary system, composed of a compact object orbiting around a massive central body, will emit gravitational waves which will depend on the central body's spacetime geometry. We expect that the gravitational wave observables will somehow…
The gravitational radiation originating from a compact binary system in circular orbit is usually expressed as an infinite sum over radiative multipole moments. In a slow-motion approximation, each multipole moment is then expressed as a…
A method is presented which allows the exact construction of conserved (i.e. divergence-free) current vectors from appropriate sets of multipole moments. Physically, such objects may be taken to represent the flux of particles or electric…