On the multipole expansion for stationary space-times

1981 ◽  
Vol 376 (1765) ◽  
pp. 333-341 ◽  
Keyword(s):  
Flat Space ◽  
Multipole Expansion ◽  
Space Time ◽  
Multipole Moments ◽  
Spatial Infinity ◽  
Asymptotically Flat ◽  
Precise Sense

It is proved that a stationary, asymptotically flat space-time is (in a precise sense) analytic in a neighbourhood of spatial infinity. This implies that there exists a multipole expansion. Its terms are shown to be uniquely determined by the Geroch-Hansen multipole moments.

scholarly journals The Thermodynamic Relationship between the RN-AdS Black Holes and the RN Black Hole in Canonical Ensemble

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Yu-Bo Ma ◽  
Li-Chun Zhang ◽  
Jian Liu ◽  
Ren Zhao ◽  
Shuo Cao
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Flat Space ◽  
Space Time ◽  
Asymptotically Flat ◽  
Time Space ◽  
Ads Black Holes ◽  
Different Types ◽  
Thermodynamic Relationship ◽  
The Relationship

In this paper, by analyzing the thermodynamic properties of charged AdS black hole and asymptotically flat space-time charged black hole in the vicinity of the critical point, we establish the correspondence between the thermodynamic parameters of asymptotically flat space-time and nonasymptotically flat space-time, based on the equality of black hole horizon area in the two different types of space-time. The relationship between the cavity radius (which is introduced in the study of asymptotically flat space-time charged black holes) and the cosmological constant (which is introduced in the study of nonasymptotically flat space-time) is determined. The establishment of the correspondence between the thermodynamics parameters in two different types of space-time is beneficial to the mutual promotion of different time-space black hole research, which is helpful to understand the thermodynamics and quantum properties of black hole in space-time.

New conservation laws for zero rest-mass fields in asymptotically flat space-time

1968 ◽  
Vol 305 (1481) ◽  
pp. 175-204 ◽  
Keyword(s):  
Conservation Laws ◽  
Rest Mass ◽  
Power Series Expansion ◽  
Flat Space ◽  
Arbitrary Spin ◽  
Space Time ◽  
Maxwell Theory ◽  
Asymptotically Flat ◽  
Gravitational Fields ◽  
Higher Spin

Some recently discovered exact conservation laws for asymptotically flat gravitational fields are discussed in detail. The analogous conservation laws for zero rest-mass fields of arbitrary spin s = 0,½,1,...) in flat or asymptotically flat space-time are also considered and their connexion with a generalization of Kirchoff’s integral is pointed out. In flat space-time, an infinite hierarchy of such conservation laws exists for each spin value, but these have a somewhat trivial interpretation, describing the asymptotic incoming field (in fact giving the coefficients of a power series expansion of the incoming field). The Maxwell and linearized Einstein theories are analysed here particularly. In asymptotically flat space-time, only the first set of quantities of the hierarchy remain absolutely conserved. These are 4 s + 2 real quantities, for spin s , giving a D ( s , 0) representation of the Bondi-Metzner-Sachs group. But even for these quantities the simple interpretation in terms of incoming waves no longer holds good: it emerges from a study of the stationary gravitational fields that a contribution to the quantities involving the gravitational multipole structure of the field must also be present. Only the vacuum Einstein theory is analysed in this connexion here, the corresponding discussions of the Einstein-Maxwell theory (by Exton and the authors) and the Einstein-Maxwell-neutrino theory (by Exton) being given elsewhere. (A discussion of fields of higher spin in curved space-time along these lines would encounter the familiar difficulties first pointed out by Buchdahl.) One consequence of the discussion given here is that a stationary asymptotically flat gravitational field cannot become radiative and then stationary again after a finite time, except possibly if a certain (origin independent) quadratic combination of multipole moments returns to its original value. This indicates the existence of ‘tails’ to the outgoing waves (or back-scattered field),which destroys the stationary nature of the final field.

scholarly journals Asymptotic symmetries at null-infinity for the Rarita-Schwinger field with magnetic term

2021 ◽  
Author(s):  
Bilyana Lyudmilova Tomova
Keyword(s):  
Magnetic Charge ◽  
Flat Space ◽  
Space Time ◽  
Boundary Term ◽  
Null Infinity ◽  
Dimensional Algebra ◽  
Asymptotically Flat ◽  
Yang Mills ◽  
Infinite Dimensional ◽  
Asymptotic Symmetries

Abstract In this paper we study the magnetic charges of the free massless Rarita-Schwinger field in four dimensional asymptotically flat space-time. This is the first step towards extending the study of the dual BMS charges to supergravity. The magnetic charges appear due to the addition of a boundary term in the action. This term is similar to the theta term in Yang-Mills theory. At null-infinity an infinite dimensional algebra is discovered, both for the electric and magnetic charge.

scholarly journals SPECTROSCOPY OF AN AdS REISSNER–NORDSTRØM BLACK HOLE

2006 ◽  
Vol 15 (03) ◽  
pp. 439-457 ◽  
Author(s):  
CLAUDIO DAPPIAGGI ◽  
SIMONA RASCHI
Keyword(s):  
Black Hole ◽  
Cosmological Constant ◽  
Flat Space ◽  
Space Time ◽  
Charged Black Hole ◽  
Area Spectrum ◽  
Asymptotically Flat ◽  
Negative Cosmological Constant

In the framework of black hole spectroscopy, we extend the results obtained for a charged black hole in an asymptotically flat space–time to the scenario with non-vanishing negative cosmological constant. In particular, exploiting Hamiltonian techniques, we construct the area spectrum for an AdS Reissner–Nordstrøm black hole.

scholarly journals On the structure and applications of the Bondi–Metzner–Sachs group

2018 ◽  
Vol 15 (02) ◽  
pp. 1830002 ◽  
Author(s):  
Francesco Alessio ◽  
Giampiero Esposito
Keyword(s):  
Minkowski Space ◽  
Isometry Group ◽  
Black Hole Physics ◽  
Flat Space ◽  
Space Time ◽  
Poincaré Group ◽  
Poincare Group ◽  
Curved Space ◽  
Asymptotically Flat ◽  
Minkowski Space Time

This work is a pedagogical review dedicated to a modern description of the Bondi–Metzner–Sachs (BMS) group. Minkowski space-time has an interesting and useful group of isometries, but, for a generic space-time, the isometry group is simply the identity and hence provides no significant informations. Yet symmetry groups have important role to play in physics; in particular, the Poincaré group describing the isometries of Minkowski space-time plays a role in the standard definitions of energy-momentum and angular-momentum. For this reason alone it would seem to be important to look for a generalization of the concept of isometry group that can apply in a useful way to suitable curved space-times. The curved space-times that will be taken into account are the ones that suitably approach, at infinity, Minkowski space-time. In particular we will focus on asymptotically flat space-times. In this work, the concept of asymptotic symmetry group of those space-times will be studied. In the first two sections we derive the asymptotic group following the classical approach which was basically developed by Bondi, van den Burg, Metzner and Sachs. This is essentially the group of transformations between coordinate systems of a certain type in asymptotically flat space-times. In the third section the conformal method and the notion of “asymptotic simplicity” are introduced, following mainly the works of Penrose. This section prepares us for another derivation of the BMS group which will involve the conformal structure, and is thus more geometrical and fundamental. In the subsequent sections we discuss the properties of the BMS group, e.g. its algebra and the possibility to obtain as its subgroup the Poincaré group, as we may expect. The paper ends with a review of the BMS invariance properties of classical gravitational scattering discovered by Strominger, that are finding application to black hole physics and quantum gravity in the literature.

scholarly journals Non-expanding horizons: multipoles and the symmetry group

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Abhay Ashtekar ◽  
Neev Khera ◽  
Maciej Kolanowski ◽  
Jerzy Lewandowski
Keyword(s):  
Symmetry Group ◽  
Strong Field ◽  
Flat Space ◽  
Companion Paper ◽  
Multipole Moments ◽  
Asymptotically Flat ◽  
Compact Binary ◽  
Wave Tomography ◽  
Physically Attractive ◽  
Made In

Abstract It is well-known that blackhole and cosmological horizons in equilibrium situations are well-modeled by non expanding horizons (NEHs) [1–3]. In the first part of the paper we introduce multipole moments to characterize their geometry, removing the restriction to axisymmetric situations made in the existing literature [4]. We then show that the symmetry group $$ \mathfrak{G} $$ G of NEHs is a 1-dimensional extension of the BMS group $$ \mathfrak{B} $$ B . These symmetries are used in a companion paper [5] to define charges and fluxes on NEHs, as well as perturbed NEHs. They have physically attractive properties. Finally, it is generally not appreciated that $$ \mathcal{I} $$ I ±of asymptotically flat space-times are NEHs in the conformally completed space-time. Forthcoming papers will (i) show that $$ \mathcal{I} $$ I ± have a small additional structure that reduces $$ \mathfrak{G} $$ G to the BMS group $$ \mathfrak{B} $$ B , and the BMS charges and fluxes can be recovered from the NEH framework; and, (ii) develop gravitational wave tomography for the late stage of compact binary coalescences: reading-off the dynamics of perturbed NEHs in the strong field regime (via evolution of their multipoles), from the waveform at $$ \mathcal{I} $$ I +.

scholarly journals BRANE WORLD IN A TOPOLOGICAL BLACK HOLES IN ASYMPTOTICALLY FLAT SPACE–TIME

2001 ◽  
Vol 16 (26) ◽  
pp. 1703-1710 ◽  
Author(s):  
DONAM YOUM
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Scalar Field ◽  
Flat Space ◽  
Space Time ◽  
Brane World ◽  
Black Hole Horizon ◽  
World Model ◽  
Asymptotically Flat ◽  
Bulk Scalar Field

We study static brane configurations in the bulk background of the topological black holes in asymptotically flat space–time and find that such configurations are possible even for flat black hole horizon, unlike the AdS black hole case. We construct the brane world model with an orbifold structure S1/Z2 in such bulk background and study massless bulk scalar field.

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