The many ways of the characteristic Cauchy problem

Chruściel, Piotr T.; Paetz, Tim-Torben

doi:10.48550/arxiv.1203.4534

Cited by 15 publications

(44 citation statements)

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“…This has to do with gravitational edge modes 1 on manifolds with boundaries [16][17][18][19][20][21][22][23][24][25][26]. The characteristic initial value problem [27][28][29][30][31][32] provides a simple framework to understand the emergence of such edge degrees of freedom in gravity. At null infinity, initial data is characterised by the two radiative modes, namely the leading O(r −2 ) term of the outgoing shear.…”

Section: Outline and Motivationmentioning

confidence: 99%

Twistor representation of Jackiw-Teitelboim gravity

Wieland

2020

Preprint

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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.

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Section: Outline and Motivationmentioning

confidence: 99%

Twistor representation of Jackiw-Teitelboim gravity

Wieland

2020

Preprint

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“…It is well known that by considering the characteristic Cauchy problem in general relativity, the treatment of the initial data constraints problem is considerably simplified as the constraints reduce to propagations equations along null geodesics generating the initial manifold carrying the data provided free data are well-chosen [2], [6], [9], [10], [12], [17], [18], [19], [20], [21], [22]. This is a particular interesting feature of the characteristic Cauchy problem in general relativity opposed to the ordinary spacelike Cauchy problem where the constraints equations are of elliptic type.…”

Section: Introduction and Various Issuesmentioning

confidence: 99%

“…This is a particular interesting feature of the characteristic Cauchy problem in general relativity opposed to the ordinary spacelike Cauchy problem where the constraints equations are of elliptic type. However, a full description of the constraints in the characteristic Cauchy problem setting requires a priori investigation of the geometry of the null initial hypersurfaces in consideration and derivation on it of explicit expressions of various null geometry quantities [6], [9], [10], [12], [17], [18], [19], [20], [21], [22]. Furthermore, while in the case of the ordinary spacelike Cauchy problem in general relativity the constraints are standard, depend only of the geometric nature of the Einstein's equations (i.e.…”

Section: Introduction and Various Issuesmentioning

confidence: 99%

“…Furthermore, while in the case of the ordinary spacelike Cauchy problem in general relativity the constraints are standard, depend only of the geometric nature of the Einstein's equations (i.e. the so called Hamiltonian and momentum constraints) [3], [5], in the case of the characteristic initial value problem, one faces the difficult task of highlighting additional gauge-dependent constraints essential to the construction of the full set of initial data [6], [9], [10], [12], [17], [18], [19], [20], [21], [22]. These latter are induced by: the evolution system deduced of the splitting of the Einstein equations by the choice of a gauge, the form of the stress-energy momentum tensor of the matter involved, and their hierarchy depends heavily on the prescribed free data.…”

Section: Introduction and Various Issuesmentioning

confidence: 99%

“…The interest for the characteristic Cauchy problem in general relativity is well known [21], and there is a growing interest for this since the work of D. Christodoulou on the formation of Black holes in general relativity [7]. The gauge mostly used in this context is the harmonic or wave gauge (its generalization is the "generalized wave map gauge") [4], [6], [9], [10], [15], [17], [21], [22], which fits well to some types of matter. Another gauge ie.…”

Section: Introduction and Various Issuesmentioning

confidence: 99%

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This article is concerned with the derivation of the Gauss-Codazzi's constraints equations on the initial light cone for geometric transport equations in general relativity. Temporal-gauge-dependent constraints are addressed too and gaugepreservation is established. The global resolution of the constraints is studied, a large class of initial data sets is deduced from appropriate free data and their behavior at the vertex of the cone is examined.

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Coarse graining holographic black holes

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Wall

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173

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We expand our recent work on the outer entropy, a holographic coarsegrained entropy defined by maximizing the boundary entropy while fixing the classical bulk data outside some surface. When the surface is marginally trapped and satisfies certain "minimar" conditions, we prove that the outer entropy is exactly equal to a quarter the area (while for other classes of surfaces, the area gives an upper or lower bound). We explicitly construct the entropy-maximizing interior of a minimar surface, and show that it satisfies the appropriate junction conditions. This provides a statistical explanation for the area-increase law for spacelike holographic screens foliated by minimar surfaces. Our construction also provides an interpretation of the area for a class of non-minimal extremal surfaces.On the boundary side, we define an increasing simple entropy by maximizing the entropy subject to a set of "simple experiments" performed after some time. We show (to all orders in perturbation theory around equilibrium) that the simple entropy is the boundary dual to our bulk construction.

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The many ways of the characteristic Cauchy problem

Cited by 15 publications

References 0 publications

Twistor representation of Jackiw-Teitelboim gravity

Twistor representation of Jackiw-Teitelboim gravity

On the Initial Data Constraints on the Light cone for the Einstein-Vlasov system

Coarse graining holographic black holes

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