scholarly journals Brown-York charges at null boundaries

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Venkatesa Chandrasekaran ◽  
Éanna É. Flanagan ◽  
Ibrahim Shehzad ◽  
Antony J. Speranza
Keyword(s):  
General Relativity ◽  
Variational Principle ◽  
Stress Tensor ◽  
Simple Form ◽  
Conservation Equation ◽  
Asymptotically Flat ◽  
Constraint Equations ◽  
Null Surface ◽  
Timelike Hypersurface ◽  
Flat Spacetimes

Abstract The Brown-York stress tensor provides a means for defining quasilocal gravitational charges in subregions bounded by a timelike hypersurface. We consider the generalization of this stress tensor to null hypersurfaces. Such a stress tensor can be derived from the on-shell subregion action of general relativity associated with a Dirichlet variational principle, which fixes an induced Carroll structure on the null boundary. The formula for the mixed-index tensor Tij takes a remarkably simple form that is manifestly independent of the choice of auxiliary null vector at the null surface, and we compare this expression to previous proposals for null Brown-York stress tensors. The stress tensor we obtain satisfies a covariant conservation equation with respect to any connection induced from a rigging vector at the hypersurface, as a result of the null constraint equations. For transformations that act covariantly on the boundary structures, the Brown-York charges coincide with canonical charges constructed from a version of the Wald-Zoupas procedure. For anomalous transformations, the charges differ by an intrinsic functional of the boundary geometry, which we explicity verify for a set of symmetries associated with finite null hyper-surfaces. Applications of the null Brown-York stress tensor to symmetries of asymptotically flat spacetimes and celestial holography are discussed.

scholarly journals Bulk supertranslation memories: A concept reshaping the vacua and black holes of general relativity

2016 ◽  
Vol 25 (12) ◽  
pp. 1644006 ◽  
Author(s):  
Geoffrey Compère
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Black Hole ◽  
Memory Effect ◽  
Null Infinity ◽  
Asymptotically Flat ◽  
Fundamental Symmetry ◽  
Geometrical Features ◽  
Flat Spacetimes ◽  
Future Null Infinity

The memory effect is a prediction of general relativity on the same footing as the existence of gravitational waves. The memory effect is understood at future null infinity as a transition induced by null radiation from a Poincaré vacuum to another vacuum. Those are related by a supertranslation, which is a fundamental symmetry of asymptotically flat spacetimes. In this paper, I argue that finite supertranslation diffeomorphisms should be extended into the bulk spacetime consistently with canonical charge conservation. It then leads to fascinating geometrical features of gravitational Poincaré vacua. I then argue that in the process of black hole merger or gravitational collapse, dramatic but computable memory effects occur. They lead to a final stationary metric which qualitatively deviates from the Schwarzschild metric.

scholarly journals BMS field theories and Weyl anomaly

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Arjun Bagchi ◽  
Sudipta Dutta ◽  
Kedar S. Kolekar ◽  
Punit Sharma
Keyword(s):  
Three Dimensions ◽  
Field Theories ◽  
Partition Functions ◽  
Two Dimensional ◽  
Speed Of Light ◽  
Asymptotically Flat ◽  
Weyl Invariance ◽  
Flat Spacetimes ◽  
Liouville Action ◽  
Null Surfaces

Abstract Two dimensional field theories with Bondi-Metzner-Sachs symmetry have been proposed as duals to asymptotically flat spacetimes in three dimensions. These field theories are naturally defined on null surfaces and hence are conformal cousins of Carrollian theories, where the speed of light goes to zero. In this paper, we initiate an investigation of anomalies in these field theories. Specifically, we focus on the BMS equivalent of Weyl invariance and its breakdown in these field theories and derive an expression for Weyl anomaly. Considering the transformation of partition functions under this symmetry, we derive a Carrollian Liouville action different from ones obtained in the literature earlier.

scholarly journals Soft photon theorem in the small negative cosmological constant limit

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Nabamita Banerjee ◽  
Karan Fernandes ◽  
Arpita Mitra
Keyword(s):  
Cosmological Constant ◽  
Tree Level ◽  
Leading Order ◽  
Asymptotically Flat ◽  
Soft Factor ◽  
Flat Spacetime ◽  
Electromagnetic Interactions ◽  
Flat Spacetimes ◽  
Perturbative Corrections ◽  
Soft Factors

Abstract We study the effect of electromagnetic interactions on the classical soft theorems on an asymptotically AdS background in 4 spacetime dimensions, in the limit of a small cosmological constant or equivalently a large AdS radius l. This identifies 1/l2 perturbative corrections to the known asymptotically flat spacetime leading and subleading soft factors. Our analysis is only valid to leading order in 1/l2. The leading soft factor can be expected to be universal and holds beyond tree level. This allows us to derive a 1/l2 corrected Ward identity, following the known equivalence between large gauge Ward identities and soft theorems in asymptotically flat spacetimes.

scholarly journals Observations of Hawking radiation: the Page curve and baby universes

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Donald Marolf ◽  
Henry Maxfield
Keyword(s):  
Black Holes ◽  
Quantum Systems ◽  
Late Time ◽  
Asymptotically Flat ◽  
Black Hole Information ◽  
Flat Spacetimes ◽  
The Cost ◽  
Baby Universes ◽  
Time Extrapolation ◽  
Asymptotic Observers

AbstractWe reformulate recent insights into black hole information in a manner emphasizing operationally-defined notions of entropy, Lorentz-signature descriptions, and asymptotically flat spacetimes. With the help of replica wormholes, we find that experiments of asymptotic observers are consistent with black holes as unitary quantum systems, with density of states given by the Bekenstein-Hawking formula. However, this comes at the cost of superselection sectors associated with the state of baby universes. Spacetimes studied by Polchinski and Strominger in 1994 provide a simple illustration of the associated concepts and techniques, and we argue them to be a natural late-time extrapolation of replica wormholes. The work aims to be self-contained and, in particular, to be accessible to readers who have not yet mastered earlier formulations of the ideas above.

scholarly journals Plebański–Demiański solution of general relativity and its expressions quadratic and cubic in curvature: Analogies to electromagnetism

2015 ◽  
Vol 24 (10) ◽  
pp. 1550079 ◽  
Author(s):  
Jens Boos
Keyword(s):  
General Relativity ◽  
Electromagnetic Field ◽  
General Type ◽  
Coordinate Systems ◽  
Irreducible Decomposition ◽  
Asymptotically Flat ◽  
Type D ◽  
Curvature Invariants ◽  
Free Parameters ◽  
First Time

Analogies between gravitation and electromagnetism have been known since the 1950s. Here, we examine a fairly general type D solution — the exact seven parameter solution of Plebański–Demiański (PD) — to demonstrate these analogies for a physically meaningful spacetime. The two quadratic curvature invariants B2 - E2 and E⋅B are evaluated analytically. In the asymptotically flat case, the leading terms of E and B can be interpreted as gravitoelectric mass and gravitoelectric current of the PD solution, respectively, if there are no gravitomagnetic monopoles present. Furthermore, the square of the Bel–Robinson tensor reads (B2 + E2)2 for the PD solution, reminiscent of the square of the energy density in electrodynamics. By analogy to the energy–momentum 3-form of the electromagnetic field, we provide an alternative way to derive the recently introduced Bel–Robinson 3-form, from which the Bel–Robinson tensor can be calculated. We also determine the Kummer tensor, a tensor cubic in curvature, for a general type D solution for the first time, and calculate the pieces of its irreducible decomposition. The calculations are carried out in two coordinate systems: In the original polynomial PD coordinates and in a modified Boyer–Lindquist-like version introduced by Griffiths and Podolský (GP) allowing for a more straightforward physical interpretation of the free parameters.

scholarly journals On mean curvature flow of spacelike hypersurfaces in asymptotically flat spacetimes

1993 ◽  
Vol 55 (1) ◽  
pp. 41-59 ◽  
Author(s):  
Klaus Ecker
Keyword(s):  
Mean Curvature ◽  
Mean Curvature Flow ◽  
A Priori Estimates ◽  
A Priori ◽  
Curvature Flow ◽  
Lorentzian Manifold ◽  
Asymptotically Flat ◽  
Spacelike Hypersurfaces ◽  
Flat Spacetimes ◽  
Weaker Conditions

AbstractWe prove a priori estimates for the gradient and curvature of spacelike hypersurfaces moving by mean curvature in a Lorentzian manifold. These estimates are obtained under much weaker conditions than have been previously assumed. We also use mean curvature flow in the construction of maximal slices in asymptotically flat spacetimes. An essential tool is a maximum principle for sub-solutions of a parabolic operator on complete Riemannian manifolds with time-dependent metric.

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