Related papers: Multipole moments do not uniquely characterize spa…
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…
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,…
In higher dimensions than four, conventional uniqueness theorem in asymptotically flat space-times does not hold, i.e., black objects can not be classified only by the mass, angular momentum and charge. In this paper, we define multipole…
We derive the multipole moments of the Kerr-NUT black hole spacetime using the Geroch-Hansen formalism, even though the spacetime is not asymptotically flat. Intriguingly, in the presence of the NUT charge, the absence of reflection…
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…
We analyze the applications of general relativity in relativistic astrophysics in order to solve the problem of describing the geometric and physical properties of the interior and exterior gravitational and electromagnetic fields of…
Multipole moments carry a lot of information about the gravitational field. Nonetheless, knowing all the multipole moments of an object does not determine conclusively the nature of the object itself. In particular, the multipole moments of…
In this work, we explicitly construct the vacuum solution of Einstein's equations with prescribed multipole moments. By observing the behavior of the multipole spacetime metric at small distances, we conjecture that for a sufficiently large…
Multipole moments are related to the physical properties of compact gravitating objects; therefore, understanding their structure is useful in accessing the nature of compact objects. We look into gravitational wave observables for black…
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…
We review uniqueness theorems as well as other general results about higher dimensional black hole spacetimes. This includes in particular theorems about the topology of higher dimensional spacetimes, theorems about their symmetries…
The formalism for describing a metric and the corresponding scalar in terms of multipole moments has recently been developed for scalar-tensor theories. We take advantage of this formalism in order to obtain expressions for the observables…
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…
A class of exact solutions of the Einstein-Maxwell equations is presented which contains infinite sets of gravitoelectric, gravitomagnetic and electromagnetic multipole moments. The multipolar structure of the solutions indicates that they…
The most general vacuum solution to Einstein's field equations with no incoming radiation can be constructed perturbatively from two infinite sets of canonical multipole moments, which are found to be mapped into each other under…
General relativity predicts the existence of black holes, compact objects whose spacetimes depend on only their mass, spin, and charge in vacuum (the "no hair" theorem). As various observations probe deeper into the strong fields of black…
The Geroch-Hansen and Thorne (ACMC) formalisms give rigorous and equivalent definitions for gravitational multipoles in stationary vacuum spacetimes. However, despite their ubiquitous use in gravitational physics, it has not been shown that…
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…
We define the mass and current multipole moments for an arbitrary theory of gravity in terms of canonical Noether charges associated with specific residual transformations in canonical harmonic gauge, which we call multipole symmetries. We…
Singularity theorems of general relativity utilize the notion of causal geodesic incompleteness as a criterion of the presence of a spacetime singularity. The incompleteness of a causal curve implies the end and/or beginning of the…