Hawking temperature in the eternal BTZ black hole: an example of holography in AdS spacetime

Ortíz, L.

doi:10.1007/s10714-012-1480-y

Cited by 5 publications

(22 citation statements)

References 23 publications

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“…Turning next from Maldacena holography back to fixed-background holography, if we assume our bulk theory (i.e. the covariant Klein Gordon equation on the maximally extended BTZ spacetime with vanishing boundary conditions on the conformal boundary) to be in the HHI state, then, one of us (LO) [29,30] has obtained, by taking a direct boundary limit as in (3), a similar result involving two mutually entangled thermal states (i.e. for the conformal generalized free field with anomalous scaling dimension ∆ (2)) on the same pair of boundary cylinders -again at the relevant Hawking temperature <xi>.…”

Section: The Contrasting Accounts Of the Origin Of Thermality And Entmentioning

confidence: 99%

“…This result had previously been obtained, with reference to the duality schema (6), for the same covariant Klein Gordon model, by Keski-Vakkuri [31] (and quoted in the paper by Maldacena [24] to which we referred above). However, the method by which they are obtained in [29,30], summarized here in Sections 3 and 4, may be of interest as an alternative derivation, closer in spirit to the boundary-limit holography work of [9].…”

Section: The Contrasting Accounts Of the Origin Of Thermality And Entmentioning

confidence: 99%

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Brick walls and AdS/CFT

Kay

Ortíz

2014

Gen Relativ Gravit

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Abstract. We discuss the relationship between the bulk-boundary correspondence in Rehren's algebraic holography (and in other 'fixed-background', QFT-based, approaches to holography) and in mainstream string-theoretic 'Maldacena AdS/CFT'. Especially, we contrast the understanding of black-hole entropy from the point of view of QFT in curved spacetime -in the framework of 't Hooft's 'brick wall' model -with the understanding based on Maldacena AdS/CFT. We show that the brickwall modification of a Klein Gordon field in the Hartle-Hawking-Israel state on 1+2 dimensional Schwarzschild AdS (BTZ) has a well-defined boundary limit with the same temperature and entropy as the brick-wall-modified bulk theory. One of our main purposes is to point out a close connection, for general AdS/CFT situations, between the puzzle raised by Arnsdorf and Smolin regarding the relationship between Rehren's algebraic holography and mainstream AdS/CFT and the puzzle embodied in the 'complementarity principle' proposed by Mukohyama and Israel in their work on the brick-wall approach to black hole entropy. Working on the assumption that similar results will hold for bulk QFT other than the Klein Gordon field and for Schwarzschild AdS in other dimensions, and recalling the first author's proposed resolution to the Mukohyama-Israel puzzle based on his 'matter-gravity entanglement hypothesis', we argue that, in Maldacena AdS/CFT, the algebra of the boundary CFT is isomorphic only to a proper subalgebra of the bulk algebra, albeit (at non-zero temperature) the (GNS) Hilbert spaces of bulk and boundary theories are still the 'same' -the total bulk state being pure, while the boundary state is mixed (thermal). We also argue from the finiteness of its boundary (and hence, on our assumptions, also bulk) entropy at finite temperature, that the Rehren dual of the Maldacena boundary CFT cannot itself be a QFT and must, instead, presumably be something like a string theory.

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Section: The Contrasting Accounts Of the Origin Of Thermality And Entmentioning

confidence: 99%

Section: The Contrasting Accounts Of the Origin Of Thermality And Entmentioning

confidence: 99%

Brick walls and AdS/CFT

Kay

Ortíz

2014

Gen Relativ Gravit

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“…As far as we know no one else before has pointed out this relation. The fact that the normalizable modes contribute on equal footing to the state on the boundary as the non-normalizable modes has been implicitly done in [19]. However in [17] we did QFT in AdS then went to the boundary by using the Boundary-limit Holography [9] then took the restriction to the exterior of the BTZ black hole.…”

Section: After All Similar Languagesmentioning

confidence: 99%

“…Now we show that we get (4) by two distinct procedures for the massless conformal real scalar field. This is done by taking into account our previous work [19] and the work of Lifschytz-Ortiz [17].…”

Section: After All Similar Languagesmentioning

confidence: 99%

AdS/CFT and its proof

Ortíz

2019

Mod. Phys. Lett. A

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“…Various authors have considered the definition of states for quantum fields on asymptotically adS black hole backgrounds, largely focussing on the analogues of the Boulware [13] and states. Some work on these states for eternal Schwarzschild-anti-de Sitter (SadS) black holes in two or more dimensions can be found in [15,16,17,18,19,20,21].In this paper we address the question of the existence, for asymptotically adS black holes, of a quantum state analogous to the Unruh vacuum [2] on asymptotically flat black hole space-times. Working in two space-time dimensions for simplicity, we consider an SadS black hole formed by the gravitational…”

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confidence: 99%

Vacuum for a massless quantum scalar field outside a collapsing shell in anti-de Sitter space–time

Abel

Winstanley

2016

Gen Relativ Gravit

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We consider a massless quantum scalar field on a two-dimensional space-time describing a thin shell of matter collapsing to form a Schwarzschildanti-de Sitter black hole. At early times, before the shell starts to collapse, the quantum field is in the vacuum state, corresponding to the Boulware vacuum on an eternal black hole space-time. The scalar field satisfies reflecting boundary conditions on the anti-de Sitter boundary. Using the Davies-Fulling-Unruh prescription for computing the renormalized expectation value of the stress-energy tensor, we find that at late times the black hole is in thermal equilibrium with a heat bath at the Hawking temperature, so the quantum field is in a state analogous to the Hartle-Hawking vacuum on an eternal black hole space-time. the fully dynamical space-time consisting of matter collapsing to form a black hole. However, quantum field theory on static space-times is technically much easier than on dynamical space-times. For an eternal Schwarzschild black hole, the Unruh state [2] contains an outgoing thermal flux of radiation at future null infinity, and therefore is the state analogous to that at late times for a black hole formed by gravitational collapse.Since all two-dimensional space-times are locally conformally flat, quantum field theory on two-dimensional space-times is rather simpler than in four space-time dimensions, particularly if one is considering dynamical spacetimes. In particular, two-dimensional black hole space-times have proven to be useful toy models for understanding various aspects of quantum field theory on four-dimensional black holes, in particular Hawking radiation and black hole evaporation [3]. One advantage of working in two space-time dimensions is that there is an exact prescription [4] for computing the renormalized expectation value of the stress-energy tensor T µν for a massless scalar field. Applying this prescription to a two-dimensional asymptotically flat space-time describing a black hole formed by gravitational collapse, it is found that at late times after the gravitational collapse, far from the black hole T µν contains an outgoing flux of energy compared to that at early times before the collapse starts [4]. This outgoing flux is the Hawking radiation and is also found in the expectation value T µν for the Unruh vacuum state on an eternal two-dimensional Schwarzschild black hole [5].A natural question is how the above picture is modified in space-times with different asymptotic structure. The case of a Schwarzschild-de Sitter black hole was studied many years ago. Working in two space-time dimensions, any static quantum state defined in the region between the event and cosmological horizons must have a stress-energy tensor T µν which diverges at either the event or the cosmological horizon [6,7], in agreement with the four-dimensional Kay-Wald theorem that there is no stationary, nonsingular state on Schwarzschild-de Sitter space-time [8]. However, a nonstatic quantum state can be defined which is regular on both the event and cosmo...

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Hawking temperature in the eternal BTZ black hole: an example of holography in AdS spacetime

Cited by 5 publications

References 23 publications

Brick walls and AdS/CFT

Brick walls and AdS/CFT

AdS/CFT and its proof

Vacuum for a massless quantum scalar field outside a collapsing shell in anti-de Sitter space–time

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