Asymptotically flat space‐times have no conformal Killing fields

1987 ◽  
Vol 28 (1) ◽  
pp. 28-32 ◽  
Author(s):  
David Garfinkle
Keyword(s):  
Flat Space ◽  
Conformal Killing ◽  
Asymptotically Flat ◽  
Killing Fields

scholarly journals Quantum BMS transformations in conformally flat space-times and holography

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Laura Donnay ◽  
Gaston Giribet ◽  
Felipe Rosso
Keyword(s):  
Hilbert Space ◽  
Black Holes ◽  
Flat Space ◽  
Conformal Killing ◽  
Conformally Flat ◽  
Asymptotically Flat ◽  
Conformal Killing Vectors ◽  
Classical Gravity ◽  
Holographic Description ◽  
Extremal Black Holes

Abstract We define and study asymptotic Killing and conformal Killing vectors in d-dimensional Minkowski, (A)dS, ℝ × Sd−1 and AdS2× Sd−2. We construct the associated quantum charges for an arbitrary CFT and show they satisfy a closed algebra that includes the BMS as a sub-algebra (i.e. supertranslations and superrotations) plus a novel transformation we call ‘superdilations’. We study representations of this algebra in the Hilbert space of the CFT, as well as the action of the finite transformations obtained by exponentiating the charges. In the context of the AdS/CFT correspondence, we propose a bulk holographic description in semi-classical gravity that reproduces the results obtained from CFT computations. We discuss the implications of our results regarding quantum hairs of asymptotically flat (near-)extremal black holes.

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.

Flat space holography

2008 ◽  
Vol 86 (4) ◽  
pp. 563-570
Author(s):  
R B Mann
Keyword(s):  
Field Theory ◽  
Flat Space ◽  
De Sitter ◽  
Spacetime Dimension ◽  
Asymptotically Flat ◽  
Conformal Field ◽  
Recent Developments ◽  
Concrete Realization ◽  
Flat Spacetimes ◽  
Spacelike Infinity

The implementation of holography in gravitational physics has its most concrete realization in the context of the anti-de Sitter/conformal field theory (AdS/CFT) correspondence conjecture, an implication of which is that counterterms from the boundary CFT can be understood as surface terms that render the variational principle finite and well-defined for the gravity theory in the bulk. I discuss recent developments that show how such gravitational counterterms can be deployed for asymptotically flat spacetimes in any spacetime dimension d ≥ 4. These actions yield conserved quantities at spacelike infinity that agree with the usual Arnowitt–Deser–Misner results but are more general. This approach removes the need for ill-defined background subtraction methods and suggests the possibility of obtaining a dual field theory to gravity theories in asymptotically flat spacetimes.PACS Nos.: 04.20.Ha, 04.60.–m, 11.25.Tq

ON THE PHYSICAL INTERPRETATION OF ASYMPTOTICALLY FLAT GRAVITATIONAL FIELDS

2008 ◽  
Vol 17 (13n14) ◽  
pp. 2599-2606
Author(s):  
CARLOS KOZAMEH ◽  
EZRA T. NEWMAN ◽  
GILBERTO SILVA-ORTIGOZA
Keyword(s):  
Vector Fields ◽  
Center Of Mass ◽  
Flat Space ◽  
Einstein Equations ◽  
Position Vector ◽  
Approximate Symmetry ◽  
Asymptotically Flat ◽  
Gravitational Fields ◽  
Maxwell Fields ◽  
Physical Information

A problem in general relativity is how to extract physical information from solutions to the Einstein equations. Most often information is found from special conditions, e.g., special vector fields, symmetries or approximate symmetries. Our concern is with asymptotically flat space–times with approximate symmetry: the BMS group. For these spaces the Bondi four-momentum vector and its evolution, found at infinity, describes the total energy–momentum and the energy–momentum radiated. By generalizing the simple idea of the transformation of (electromagnetic) dipoles under a translation, we define (analogous to center of charge) the center of mass for asymptotically flat Einstein–Maxwell fields. This gives kinematical meaning to the Bondi four-momentum, i.e., the four-momentum and its evolution is described in terms of a center of mass position vector, its velocity and spin-vector. From dynamical arguments, a unique (for our approximation) total angular momentum and evolution equation in the form of a conservation law is found.

Pseudo-Minkowskian coordinates in asymptotically flat space-times

1997 ◽  
Vol 55 (4) ◽  
pp. 1971-1976 ◽  
Author(s):  
Simonetta Frittelli ◽  
Ezra T. Newman
Keyword(s):  
Flat Space ◽  
Asymptotically Flat
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