An official website of the United States government
Entanglement, chaos, and complexity are as important for de Sitter space as for AdS, and for black holes. There are similarities and also great differences between AdS and dS in how these concepts are manifested in the space-time geometry.In the first part of this paper the Ryu–Takayanagi prescription, the theory of fast-scrambling, and the holographic complexity correspondence are reformulated for de Sitter space. Criteria are proposed for a holographic model to describe de Sitter space. The criteria can be summarized by the requirement that scrambling and complexity growth must be ``hyperfast."In the later part of the paper I show that a certain limit of the SYK model satisfies the hyperfast criterion. This leads tothe radical conjecture that a limit of SYK is indeed a concrete, computable, holographic model of de Sitter space. Calculations are described which support the conjecture.
more »
« less
Black Holes Hint Towards De Sitter-Matrix Theory
De Sitter black holes and other non-perturbative configurations can be used to probe the holographic degrees of freedom of de Sitter space. For small black holes evidence was first given in seminal work of Banks, Fiol, and Morrise; and followups by Banks and Fischler; showing that dS is described by a form of matrix theory. For large black holes the evidence given here is new: Gravitational calculations and matrix theory calculations of the rates of exponentially rare fluctuations match one another in surprising detail. The occurrence of the Nariai geometry and the "inside-out" transition are especially interesting examples which I explain.
more »
« less
- Award ID(s):
- 2014215
- PAR ID:
- 10352540
- Date Published:
- Journal Name:
- ArXivorg
- Volume:
- arXiv:2109.01322
- ISSN:
- 2331-8422
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
null (Ed.)A bstract Force-Free Electrodynamics for black holes in Anti de Sitter is considered. We present new, energy extracting solutions of Force-Free Electrodynamics in Anti de Sitter-Near Horizon Extremal Kerr and Super-Entropic Near Horizon Extremal Kerr geometries. The relevant equations of motion are derived from an action for force-free plasma surrounding spinning black holes with generic asymptotics. We consider the energy flux of electrodynamic fields in rotating frames to argue that the correct measure for energy extraction is the energy flux measured by a rotating observer in the near horizon region. We illustrate this procedure by application to near horizon solutions in Kerr, AdS-Kerr and BTZ.more » « less
-
Abstract In this note, we present a synopsis of geometric symmetries for (spin 0) perturbations around (4D) black holes and de Sitter space. For black holes, we focus on static perturbations, for which the (exact) geometric symmetries have the group structure of SO(1,3). The generators consist of three spatial rotations, and three conformal Killing vectors obeying a specialmelodiccondition. The static perturbation solutions form a unitary (principal series) representation of the group. The recently uncovered ladder symmetries follow from this representation structure; they explain the well-known vanishing of the black hole Love numbers. For dynamical perturbations around de Sitter space, the geometric symmetries are less surprising, following from the SO(1,4) isometry. As is known, the quasinormal solutions form a non-unitary representation of the isometry group. We provide explicit expressions for the ladder operators associated with this representation. In both cases, the ladder structures help connect the boundary condition at the horizon with that at infinity (black hole) or origin (de Sitter space), and they manifest as contiguous relations of the hypergeometric solutions.more » « less
-
A<sc>bstract</sc> We show that the general charged, rotating black hole in five-dimensional Einstein-Maxwell theory has a singular extremal limit. Only the known analytic solutions with exactly zero charge or zero angular momenta have smooth extremal horizons. We also consider general black holes in five-dimensional Einstein-Maxwell-Chern-Simons theory, and show that they also have singular extremal limits except for one special value of the coefficient of the Chern-Simons term (the one fixed by supergravity). Combining this with earlier results showing that extremal black holes have singular horizons in four-dimensional general relativity with small higher derivative corrections, and in anti-de Sitter space with perturbed boundary conditions, one sees that smooth extremal horizons are indeed the exception and not the rule.more » « less
-
A<sc>bstract</sc> We study black hole linear perturbation theory in a four-dimensional Schwarzschild (anti) de Sitter background. When dealing with apositivecosmological constant, the corresponding spectral problem is solved systematically via the Nekrasov-Shatashvili functions or, equivalently, classical Virasoro conformal blocks. However, this approach can be more complicated to implement for certain perturbations if the cosmological constant isnegative. For these cases, we propose an alternative method to set up perturbation theory for both small and large black holes in an analytical manner. Our analysis reveals a new underlying recursive structure that involves multiple polylogarithms. We focus on gravitational, electromagnetic, and conformally coupled scalar perturbations subject to Dirichlet and Robin boundary conditions. The low-lying modes of the scalar sector of gravitational perturbations and its hydrodynamic limit are studied in detail.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- The DOI is not currently available.
