Goursat's problem and the holographic principle

Álvarez, Enrique; Conde, Jorge; Hernández, Lorenzo

doi:10.1016/j.nuclphysb.2004.04.015

Cited by 9 publications

(12 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…40) i.e., κ ab is precisely the stress-tensor of L (σ) . See Appendices B and C, and in particular around (C.142), for more properties of this tensor.…”

mentioning

confidence: 99%

On asymptotic flatness and Lorentz charges

Compère¹,

Dehouck²,

Virmani³

2011

Class. Quantum Grav.

View full text Add to dashboard Cite

A la mémoire de notre ami et professeur Laurent Houart. AbstractIn this paper we establish two results concerning four-dimensional asymptotically flat spacetimes at spatial infinity. First, we show that the six conserved Lorentz charges are encoded in two unique, distinct, but mutually dual symmetric divergence free tensors that we construct from the equations of motion. Second, we show that integrability of Einstein's equations in the asymptotic expansion is sufficient to establish the equivalence between counter-term charges defined from the variational principle and charges defined by Ashtekar and Hansen. These results clarify earlier constructions of conserved charges in the hyperboloid representation of spatial infinity. In showing this, parity condition on the mass aspect is not needed. Along the way in establishing these results, we prove two lemmae on tensor fields on three dimensional de Sitter spacetime stated by Ashtekar-Hansen and Beig-Schmidt and state and prove three additional lemmae.

show abstract

“…40) i.e., κ ab is precisely the stress-tensor of L (σ) . See Appendices B and C, and in particular around (C.142), for more properties of this tensor.…”

mentioning

confidence: 99%

On asymptotic flatness and Lorentz charges

Compère¹,

Dehouck²,

Virmani³

2011

Class. Quantum Grav.

View full text Add to dashboard Cite

show abstract

“…We also highlighted certain similarities and differences with the asymptotically AdS setting. Further exploration in this direction should provide additional insights into the still elusive nature of holography for flat space [32,35,45,46,47,48,49,50].…”

Section: Discussionmentioning

confidence: 99%

Supertranslations and holographic stress tensor

Virmani

2012

J. High Energ. Phys.

View full text Add to dashboard Cite

It is well known in the context of four dimensional asymptotically flat spacetimes that the leading order boundary metric must be conformal to unit de Sitter metric when hyperbolic cutoffs are used. This situation is very different from asymptotically AdS settings where one is allowed to choose an arbitrary boundary metric. The closest one can come to changing the boundary metric in the asymptotically flat context, while maintaining the group of asymptotic symmetries to be Poincaré, is to change the so-called 'supertranslation frame' ω. The most studied choice corresponds to taking ω = 0. In this paper we study consequences of making alternative choices. We perform this analysis in the covariant phase space approach as well as in the holographic renormalization approach. We show that all choices for ω are allowed in the sense that the covariant phase space is well defined irrespective of how we choose to fix supertranslations. The on-shell action and the leading order boundary stress tensor are insensitive to the supertranslation frame. The next to leading order boundary stress tensor depends on the supertranslation frame but only in a way that the transformation of angular momentum under translations continues to hold as in special relativity. Supertranslations and Holographic Stress Tensor

show abstract

“…[β − SL(2, C)β]ψ(β) = 0, whereβ is a distribution over S 2 such that Lβ =β, • a mass equation selecting a specific value of the mass for (6) […”

Section: Whered(λ) Is a Unitary But Non Necessary Irreducible Represementioning

confidence: 99%

“…Though the Maldacena conjecture is widely accepted and, to a certain degree, it can be extended to asymptotically AdS spacetimes, it addresses only the specific scenario of negative cosmological constant Λ. It it thus natural to wonder if the holographic principle could be implemented if we consider different kind of backgrounds and, in particular, we will deal with solutions of Einstein's equations with Λ = 0 or more precisely with asymptotically flat spacetimes (see [5,6] for different approaches to the same problem).…”

Section: Introductionmentioning

confidence: 99%

BMS field theory and the open roads

Dappiaggi

2006

J. Phys.: Conf. Ser.

View full text Add to dashboard Cite

Abstract.We develop the basic ingredients of a field theory intrinsically defined on the null infinity boundary of an asymptotically flat spacetime. We also discuss some recent related results and open questions. IntroductionThe last decade witnessed several proposals to solve the long standing quest to formulate a satisfactory quantum version of Einstein theory. Compared to previous attempts, the most recent ones are characterized by the ubiquitous presence of a new paradigm: "the holographic principle". Its origin can be traced back to the seminal paper by G. 't Hooft [1] who remarked that one of the main obstruction in the quantization of general relativity lies in the existence of sources of extreme gravitational fields i.e. black holes. The peculiarity of such objects can be appreciated already studying their behaviour at a classical level and in particular the three laws of black hole thermodynamic. Within this context, the most striking property originates from the Bekenstein formula which relates the entropy S of a black hole to a quarter 1 of the area of its event horizon. From a mere classical perspective this relation is rather counterintuitive since the entropy of a common physical system is proportional to the volume of the region of spacetime where it evolves. Furthermore, if we add to this reasoning, the remark that S can be read as a measure of the degrees of freedom accessible to the system itself, we have the key ingredients leading 't Hooft to claim the following: S =

show abstract

Goursat's problem and the holographic principle

Cited by 9 publications

References 28 publications

On asymptotic flatness and Lorentz charges

On asymptotic flatness and Lorentz charges

Supertranslations and holographic stress tensor

BMS field theory and the open roads

Contact Info

Product

Resources

About