scholarly journals Symmetries and conformal bridge in Schwarschild-(A)dS black hole mechanics

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Jibril Ben Achour ◽  
Etera R. Livine
Keyword(s):  
Black Hole ◽  
Three Dimensional ◽  
Spacelike Hypersurface ◽  
Diffeomorphism Invariance ◽  
Hidden Symmetry ◽  
Constant Radius ◽  
Physical Symmetry ◽  
Exterior Regions ◽  
Black Hole Interior ◽  
Ads Geometry

Abstract We show that the Schwarzschild-(A)dS black hole mechanics possesses a hidden symmetry under the three-dimensional Poincaré group. This symmetry shows up after having gauge-fixed the diffeomorphism invariance in the symmetry-reduced homogeneous Einstein-Λ model and stands as a physical symmetry of the system. It dictates the geometry both in the black hole interior and exterior regions, as well as beyond the cosmological horizon in the Schwarzschild-dS case. It follows that one can associate a set of non-trivial conserved charges to the Schwarzschild-(A)dS black hole which act in each causally disconnected regions. In T-region, they act on fields living on spacelike hypersurface of constant time, while in R-regions, they act on time-like hypersurface of constant radius. We find that while the expression of the charges depend explicitly on the location of the hypersurface, the charge algebra remains the same at any radius in R-regions (or time in T-regions). Finally, the analysis of the Casimirs of the charge algebra reveals a new solution-generating map. The $$ \mathfrak{sl}\left(2,\mathrm{\mathbb{R}}\right) $$ sl 2 ℝ Casimir is shown to generate a one-parameter family of deformation of the black hole geometry labelled by the cosmological constant. This gives rise to a new conformal bridge allowing one to continuously deform the Schwarzschild-AdS geometry to the Schwarzschild and the Schwarzschild-dS solutions.

scholarly journals Geometric secret sharing in a model of Hawking radiation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Vijay Balasubramanian ◽  
Arjun Kar ◽  
Onkar Parrikar ◽  
Gábor Sárosi ◽  
Tomonori Ugajin
Keyword(s):  
Field Theory ◽  
Black Hole ◽  
Secret Sharing ◽  
Hawking Radiation ◽  
Entanglement Entropy ◽  
Three Dimensional ◽  
External Radiation ◽  
Sharing Scheme ◽  
Black Hole Interior ◽  
Pass Through

Abstract We consider a black hole in three dimensional AdS space entangled with an auxiliary radiation system. We model the microstates of the black hole in terms of a field theory living on an end of the world brane behind the horizon, and allow this field theory to itself have a holographic dual geometry. This geometry is also a black hole since entanglement of the microstates with the radiation leaves them in a mixed state. This “inception black hole” can be purified by entanglement through a wormhole with an auxiliary system which is naturally identified with the external radiation, giving a realization of the ER=EPR scenario. In this context, we propose an extension of the Ryu-Takayanagi (RT) formula, in which extremal surfaces computing entanglement entropy are allowed to pass through the brane into its dual geometry. This new rule reproduces the Page curve for evaporating black holes, consistently with the recently proposed “island formula”. We then separate the radiation system into pieces. Our extended RT rule shows that the entanglement wedge of the union of radiation subsystems covers the black hole interior at late times, but the union of entanglement wedges of the subsystems may not. This result points to a secret sharing scheme in Hawking radiation wherein reconstruction of certain regions in the interior is impossible with any subsystem of the radiation, but possible with all of it.

scholarly journals Six-point functions and collisions in the black hole interior

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Felix M. Haehl ◽  
Alexandre Streicher ◽  
Ying Zhao
Keyword(s):  
Black Hole ◽  
Three Dimensional ◽  
Quantum Circuits ◽  
Late Time ◽  
Factorization Property ◽  
Boundary Operators ◽  
Dimensional Gravity ◽  
Black Hole Interior ◽  
Left And Right ◽  
Extract Information

Abstract In the eternal AdS black hole geometry, we consider two signals sent from the boundaries into the black hole interior shared between the two asymptotic regions. We compute three different out-of-time-order six-point functions to quantify various properties of the collision of these signals behind the horizons: (i) We diagnose the strength of the collision by probing the two-signal state on a late time slice with boundary operators. (ii) We quantify two-sided operator growth, which provides a dual description of the signals meeting in the black hole interior, in terms of the quantum butterfly effect and quantum circuits. (iii) We consider an explicit coupling between the left and right CFTs to make the wormhole traversable and extract information about the collision product from behind the horizon. At a technical level, our results rely on the method of eikonal resummation to obtain the relevant gravitational contributions to Lorentzian six-point functions at all orders in the GN-expansion. We observe that such correlation functions display an intriguing factorization property. We corroborate these results with geodesic computations of six-point functions in two- and three-dimensional gravity.

scholarly journals Symmetries of the black hole interior and singularity regularization

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Marc Geiller ◽  
Etera R. Livine ◽  
Francesco Sartini
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Black Hole Physics ◽  
Proper Time ◽  
White Hole ◽  
Formula Group ◽  
Physical Symmetry ◽  
Black Hole Interior ◽  
Group Quantization

We reveal an \mathfrak{iso}(2,1)𝔦𝔰𝔬(2,1) Poincar'e algebra of conserved charges associated with the dynamics of the interior of black holes. The action of these Noether charges integrates to a symmetry of the gravitational system under the Poincar'e group ISO(2,1)(2,1), which allows to describe the evolution of the geometry inside the black hole in terms of geodesics and horocycles of AdS{}_22. At the Lagrangian level, this symmetry corresponds to M"obius transformations of the proper time together with translations. Remarkably, this is a physical symmetry changing the state of the system, which also naturally forms a subgroup of the much larger \textrm{BMS}_{3}=\textrm{Diff}(S^1)\ltimes\textrm{Vect}(S^1)BMS3=Diff(S1)⋉Vect(S1) group, where S^1S1 is the compactified time axis. It is intriguing to discover this structure for the black hole interior, and this hints at a fundamental role of BMS symmetry for black hole physics. The existence of this symmetry provides a powerful criterion to discriminate between different regularization and quantization schemes. Following loop quantum cosmology, we identify a regularized set of variables and Hamiltonian for the black hole interior, which allows to resolve the singularity in a black-to-white hole transition while preserving the Poincar'e symmetry on phase space. This unravels new aspects of symmetry for black holes, and opens the way towards a rigorous group quantization of the interior.

scholarly journals Momentum/Complexity duality and the black hole interior

2020 ◽  
Vol 2020 (7) ◽  
Author(s):  
José L.F. Barbón ◽  
Javier Martín-García ◽  
Martin Sasieta
Keyword(s):  
Black Hole ◽  
Black Hole Interior

Three dimensional Lifshitz black hole and the Korteweg–de Vries equation

2012 ◽  
Vol 709 (3) ◽  
pp. 276-279 ◽  
Author(s):  
E. Abdalla ◽  
Jeferson de Oliveira ◽  
A. Lima-Santos ◽  
A.B. Pavan
Keyword(s):  
Black Hole ◽  
Vries Equation ◽  
Three Dimensional ◽  
De Vries ◽  
Lifshitz Black Hole

scholarly journals Black Hole Interior from Loop Quantum Gravity

2008 ◽  
Vol 2008 ◽  
pp. 1-12 ◽  
Author(s):  
Leonardo Modesto
Keyword(s):  
Black Hole ◽  
Quantum Gravity ◽  
Event Horizon ◽  
Loop Quantum Gravity ◽  
Planck Scale ◽  
Semiclassical Analysis ◽  
Schwarzschild Solution ◽  
Quantum Black Hole ◽  
Minimum Value ◽  
Black Hole Interior

We calculate modifications to the Schwarzschild solution by using a semiclassical analysis of loop quantum black hole. We obtain a metric inside the event horizon that coincides with the Schwarzschild solution near the horizon but that is substantially different at the Planck scale. In particular, we obtain a bounce of theS2sphere for a minimum value of the radius and that it is possible to have another event horizon close to ther=0point.

scholarly journals THE MILNE SPACETIME AND THE HADRONIC RINDLER HORIZON

2010 ◽  
Vol 19 (08n10) ◽  
pp. 1379-1384 ◽  
Author(s):  
H. CULETU
Keyword(s):  
Black Hole ◽  
Event Horizon ◽  
Time Dependent ◽  
Anisotropic Fluid ◽  
Direct Relation ◽  
Schwarzschild Black Hole ◽  
Black Hole Interior ◽  
Flat Metric ◽  
Shear Tensor ◽  
Hadronic Rindler Horizon

A direct relation between the time-dependent Milne geometry and the Rindler spacetime is shown. Milne's metric corresponds to the region beyond Rindler's event horizon (in the wedge t ≻ |x|). We point out that inside a Schwarzschild black hole and near its horizon, the metric may be Milne's flat metric. It was found that the shear tensor associated to a congruence of fluid particles of the RHIC expanding fireball has the same structure as that corresponding to the anisotropic fluid from the black hole interior, even though the latter geometry is curved.

Periodicity and area spectrum of the three dimensional BTZ black hole

2012 ◽  
Vol 44 (11) ◽  
pp. 2865-2872 ◽  
Author(s):  
Hui-Ling Li ◽  
Rong Lin ◽  
Li-Ying Cheng
Keyword(s):  
Black Hole ◽  
Three Dimensional ◽  
Area Spectrum ◽  
Btz Black Hole
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