On the Architecture of Spacetime Geometry

Bianchi, Eugenio; Myers, Robert Cobb

doi:10.48550/arxiv.1212.5183

Cited by 90 publications

(185 citation statements)

References 0 publications

Supporting

Mentioning

170

Contrasting

Order By: Relevance

“…In fact, it turns out that all the ingredients necessary to perform the computations according to [96] are available for general boundaries [55] and one computes the entanglement entropy of the gravitational field in a maximally mixed state [53][54][55]. This in particular agrees with recent results from other approaches to quantum gravity [248]. The two main open questions are thus the following:…”

Section: Black Hole Entropysupporting

confidence: 74%

“…However, these computations have been in the realm of (fundamental) large spins and do not apply to the continuum, at least naively. It is noteworthy that these computations do not require the boundary to be a horizon slice, supporting [248]. If one furthermore assumes an energy-area relation appropriate for black holes [251], additional results specific to horizons can be derived [252,253].…”

Section: Black Hole Entropymentioning

confidence: 71%

See 1 more Smart Citation

An elementary introduction to loop quantum gravity

Bodendorfer

2016

Preprint

View full text Add to dashboard Cite

An introduction to loop quantum gravity is given, focussing on the fundamental aspects of the theory, different approaches to the dynamics, as well as possible future directions. It is structured in five lectures, including exercises, and requires only little prior knowledge of quantum mechanics, gauge theory, and general relativity. The main aim of these lectures is to provide non-experts with an elementary understanding of loop quantum gravity and to evaluate the state of the art of the field. Technical details are avoided wherever possible.

show abstract

Section: Black Hole Entropysupporting

confidence: 74%

Section: Black Hole Entropymentioning

confidence: 71%

An elementary introduction to loop quantum gravity

Bodendorfer

2016

Preprint

View full text Add to dashboard Cite

show abstract

“…For given energy and angular momentum, there is an exponentially large number of boundary excitations at the horizon. The entropy is the logarithm of this number, which is proportional to the area of the horizon [36][37][38][39][40][41][42].…”

Section: Outline and Motivationmentioning

confidence: 99%

“…which is the sum of the gravitational bulk plus boundary action for JT gravity (41) and the action for the AdS 2 particles (38), which are charged under SL(2, R). The manifold M contains the worldine of the particle, which splits the manifold M into two adjacent regions M + ∪ M − = M, whose boundaries are ∂M − = γ −1 − ∪ γ and ∂M + = γ −1 ∪ γ + respectively.…”

Section: Physical Phase Spacementioning

confidence: 99%

Twistor representation of Jackiw-Teitelboim gravity

Wieland

2020

Preprint

View full text Add to dashboard Cite

Jackiw -Teitelboim (JT) gravity is a 1+1-dimensional toy model for quantum gravity in four spacetime dimensions. In the absence of matter, JT gravity is a topological field theory and there are no local observables. The introduction of a boundary changes the situation. What was an unphysical gauge direction before turns into a physical boundary degree of freedom (a gravitational edge mode). Starting from the BF formulation of JT gravity, we develop a twistor representation for the boundary charges of JT gravity. We introduce point sources in the bulk and study the coupled gravity plus matter system at the quantum level. Eigenstates of quasi-local energy are built from the tensor product of unitary irreducible representations of SL(2, R). Empty patches of AdS 2 are characterised by the continuous series representations, point sources are related to the discrete series. Physical states are constructed by fusing the SL(2, R) representations into an SL(2, R) invariant singlet. The singlet lies in the kernel of the constraints, which are the analogue of the Wheeler -DeWitt equations in the presence of distributional matter sources.

show abstract

“…but suggests that this Bianchi-Myers conjecture ought to be modified by replacing the phrase "the degrees of freedom" by "the matter degrees of freedom". As far as we aware, all the evidence adduced in [25] for the correctness of the conjecture may equally be taken to be evidence for its correctness when thus modified. Furthermore, if we assume the validity of our suggestion at the end of Point (4), then, in view of our remark in the previous sentence, the evidence adduced in [25] provides us with an independent explanation for Property P. (See the remark immediately following the statement of Property P above.)…”

mentioning

confidence: 91%

Entanglement entropy and algebraic holography

Kay¹

2016

Preprint

View full text Add to dashboard Cite

In 2006, Ryu and Takayanagi (RT ) pointed out that (with a suitable cutoff) the entanglement entropy between two complementary regions of an equal-time surface of a d+1dimensional conformal field theory on the conformal boundary of AdS d+2 is, when the AdS radius is appropriately related to the parameters of the CFT, equal to 1/4G times the area of the d-dimensional minimal surface in the AdS bulk which has the junction of those complementary regions as its boundary, where G is the bulk Newton constant. (More precisely, RT showed this for d = 1 and adduced evidence that it also holds in many examples in d > 1.) We point out here that the RT-equality implies that, in the quantum theory on the bulk AdS background which is related to the boundary CFT according to Rehren's 1999 algebraic holography theorem, the entanglement entropy between two complementary bulk Rehren wedges is equal to one 1/4G times the (suitably cut off) area of their shared ridge. (This follows because of the geometrical fact that, for complementary ball-shaped regions, the RT minimal surface is precisely the shared ridge of the complementary bulk Rehren wedges which correspond, under Rehren's bulk-wedge to boundary double-cone bijection, to the complementary boundary double-cones whose bases are the RT complementary balls.) This is consistent with the Bianchi-Meyers conjecture -that, in a theory of quantum gravity, the entanglement entropy, S between the degrees of freedom of a given region with those of its complement takes the form S = A/4G (plus lower order terms) -but only if the phrase 'degrees of freedom' is replaced by 'matter degrees of freedom'. It also supports related previous arguments of the author -consistent with the author's 'matter-gravity entanglement hypothesis' -that the AdS/CFT correspondence is actually only a bijection between just the matter (i.e. non-gravity) sector operators of the bulk and the boundary CFT operators.

show abstract

On the Architecture of Spacetime Geometry

Cited by 90 publications

References 0 publications

An elementary introduction to loop quantum gravity

An elementary introduction to loop quantum gravity

Twistor representation of Jackiw-Teitelboim gravity

Entanglement entropy and algebraic holography

Contact Info

Product

Resources

About