Extreme Black Hole Anabasis

Abstract

We study the $\mathsf{SL}(2)$ transformation properties of spherically symmetric perturbations of the Bertotti-Robinson universe and identify an invariant $\mu$ that characterizes the backreaction of these linear solutions. The only backreaction allowed by Birkhoff's theorem is one that destroys the $Ad{S}_2\times S^2$ boundary and builds the exterior of an asymptotically flat Reissner-Nordström black hole with $Q=M\sqrt{1-\mu /4}$. We call such backreaction with boundary condition change an anabasis. We show that the addition of linear anabasis perturbations to Bertotti-Robinson may be thought of as a boundary condition that defines a connected $Ad{S}_2\times S^2$. The connected $Ad{S}_2$ is a nearly-$Ad{S}_2$ with its $\mathsf{SL}(2)$ broken appropriately for it to maintain connection to the asymptotically flat region of Reissner-Nordström. We perform a backreaction calculation with matter in the connected $Ad{S}_2\times S^2$ and show that it correctly captures the dynamics of the asymptotically flat black hole.

arXiv comment20 pages, 4 figures; v2: typo corrected, refs added; v3: minor edits, more refs added, matches published version

References in corpus (27)

• Chaos in AdS${}_2$ holography
• An Investigation of AdS${}_2$ Backreaction and Holography
• Anti-de Sitter Fragmentation
• The Extreme Kerr Throat Geometry: A Vacuum Analog of AdS_2 x S^2
• Near-horizon symmetries of extremal black holes
• Cutoff AdS${}_3$ versus the $T\bar{T}$ deformation
• On the Dynamics of Near-Extremal Black Holes
• Vacuum States for AdS_2 Black Holes
• $T\bar{T}$ and the mirage of a bulk cutoff
• Holography Beyond AdS
• No Dynamics in the Extremal Kerr Throat
• Conservation Laws and 2D Black Holes in Dilaton Gravity
• Kerr-CFT and gravitational perturbations
• A Solvable Irrelevant Deformation of $Ad{S}_3/CF{T}_2$
• 5D Rotating Black Holes and the nAdS${}_2$/nCFT${}_1$ Correspondence
• Conformal Symmetry Breaking and Thermodynamics of Near-Extremal Black Holes
• Universal low temperature theory of charged black holes with AdS${}_2$ horizons
• The Case of the Missing Gates: Complexity of Jackiw-Teitelboim Gravity
• $T\bar{T}$-deformations, AdS/CFT and correlation functions
• Extremal and Near-Extremal Black Holes and Near-$CF{T}_1$
• What happens at the horizon(s) of an extreme black hole?
• Constructing AdS_2 flow geometries
• Breaking away from the near horizon of extreme Kerr
• Near-extremal black holes at late times, backreacted
• On the black hole limit of electrically counterpoised dust configurations
• Scattering of gravitational and electromagnetic waves off $Ad{S}_2\times S^2$ in extreme Reissner-Nordstrom
• Near-$Ad{S}_2$ perturbations and the connection with near-extreme Reissner-Nordstrom

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• Sudden breakdown of effective field theory near cool Kerr-Newman black holes
• Gravitational perturbations from NHEK to Kerr
• Rotating 5D Black Holes: Interactions and deformations near extremality
• Gravitational Waves on Kerr Black Holes I: Reconstruction of Linearized Metric Perturbations
• Charged Dilatonic Spacetimes in String Theory
• Horizon Acoustics of the GHS Black Hole and the Spectrum of ${\mathrm{AdS}}_2$
• Near-extremal dynamics away from the horizon
• Large Diffeomorphisms and Accidental Symmetry of the Extremal Horizon
• Accidental Symmetry Near Extreme Spinning Black Holes
• Approaching a dynamical extreme black hole horizon