Related papers: Source Integrals for Multipole Moments in Static S…
We derive source integrals for multipole moments that describe the behaviour of static and axially symmetric spacetimes close to spatial infinity. We assume isolated non-singular sources but will not restrict the matter content otherwise.…
The multipole moments are defined as the multipole expansion coefficients of the gravitational field at infinity. In Newtonian gravity, the multipole moments are determined by the source distribution -- the multipole integrals of the…
The definition of Komar for the mass of a relativistic source is used as a starting point to introduce volume integrals for Relativistic Multipole Moments (RMM). A certain generalization of the classical Gauss theorem is used to rewrite…
In this paper, the problem of finding an axisymmetric stationary spacetime from a specified set of multipole moments, is studied. The condition on the multipole moments, for existence of a solution, is formulated as a convergence condition…
In this article we develop a method of finding the static axisymmetric space-time corresponding to any given set of multipole moments. In addition to an implicit algebraic form for the general solution, we also give a power series…
This paper reviews work, largely due to W. Simon and the author, on multipole theory of static spacetimes. The main purpose is to make this work, which lies at the interface of potential theory, conformal geometry and general relativity,…
The multipole expansion is a key tool in the study of light-matter interactions. All the information about the radiation of and coupling to electromagnetic fields of a given charge-density distribution is condensed into few numbers: The…
In this article we present some recent results on identifying correctly the relativistic multipole moments of numerically constructed spacetimes, and the consequences that this correction has on searching for appropriate analytic spacetimes…
A general formulation of the relativistic multipole moments in axistationary electrovac spacetimes is introduced in a closed analytical form. We give a complete description of how the Ernst potentials on the symmetry axis can be completely…
While it is known that any spherical fluid distribution may only source the spherically symmetric Schwarzschild space-time, the inverse is not true. Thus, in this manuscript, we find exact axially symmetric and static fluid (interior)…
This paper constructs the multipole expansion (in general relativity) of the gravitational field generated by a slowly-moving isolated source. We introduce some definitions for the source multipole moments, valid to all orders in a…
Within the scope of a spherically symmetric space-time we study the role of different types of matter in the formation of different configurations with spherical symmetries. Here we have considered matter with barotropic equation of state,…
Stationary, asymptotically flat spacetimes in general relativity can be characterized by their multipole moments. The moments have proved to be very useful tools for extracting information about the spacetime from various observables and,…
This work outlines a time-domain numerical integration technique for linear hyperbolic partial differential equations sourced by distributions (Dirac $\delta$-functions and their derivatives). Such problems arise when studying binary black…
In this paper we consider the electric multipole moments of fractal distribution of charges. To describe fractal distribution, we use the fractional integrals. The fractional integrals are considered as approximations of integrals on…
We present a physically reasonable source for an static, axially--symmetric solution to the Einstein equations. Arguments are provided, supporting our belief that the exterior space--time produced by such source, describing a quadrupole…
By adding a particle source term in the Boltzmann equation of kinetic theory, it is possible to represent particles appearing and disappearing throughout the fluid with a specified distribution of particle velocities. By deriving the wave…
This paper derives the expressions of the multipole moments of an isolated gravitating source with an accuracy corresponding to the second post-Newtonian (2-PN) approximation of general relativity. The moments are obtained by a procedure of…
The multipole expansions for massive vector and symmetric tensor fields in the region outside spatially compact stationary sources are obtained by using the symmetric and trace-free formalism in terms of the irreducible Cartesian tensors,…
The multipole moments of stationary axially symmetric vacuum or electrovacuum spacetimes can be expressed in terms of the power series expansion coefficients of the Ernst potential on the axis. In this paper we present a simpler, more…