Quantum Black Holes as Holograms in AdS Braneworlds

Three-dimensional quantum black holes arise via holographic braneworlds and are exact solutions to an induced higher-derivative theory of gravity consistently coupled to a large-c quantum field theory with an ultraviolet cutoff, accounting for all orders of semi-classical backreaction.

“We review constructions of three-dimensional 'quantum' black holes.Such spacetimes arise via holographic braneworlds and are exact solutions to an induced higher-derivative theory of gravity consistently coupled to a large-c quantum field theory with an ultraviolet cutoff, accounting for all orders of semi-classical backreaction.”

Conjecture: Classical black holes which localize on a brane in AdS_{d+1} exactly map to d-dimensional quantum-corrected black holes including all orders of backreaction.

“Conjecture: Classical black holes which localize on a brane in AdS d+1 exactly map to d-dimensional quantum-corrected black holes including all orders of backreaction.”

The conjecture that classical bulk black holes correspond to quantum-corrected black holes on the brane, in principle, holds in arbitrary spacetime dimensions.

“Indeed, while we focus on three-dimensional quantum black holes, the conjecture [22,34] that classical bulk black holes correspond to quantum-corrected black holes on the brane, in principle, holds in arbitrary spacetime dimensions.”

For d ≥ 4, it was qualitatively argued the obstruction to having static quantum black holes can be understood as a consequence of backreaction due to Hawking effects, such that any black hole that localizes on the brane must evaporate.

“In [22,34], for d ≥ 4, it was qualitatively argued the obstruction to having static quantum black holes can be understood as a consequence of backreaction due to Hawking effects, such that any black hole that localizes on the brane must evaporate.”

Classical AdS d+1 black holes which localize on the ETW brane are conjectured to precisely map to black holes in d-dimensions, including all orders of quantum backreaction.

“In particular, classical AdS d+1 black holes which localize on the ETW brane are conjectured to precisely map to black holes in d-dimensions, including all orders of quantum backreaction [22], i.e., 'quantum' black holes.”

Quantum black holes in Mink3 have received less attention than their (A)dS cousins.

“Though they were the first exact three-dimensional braneworld black hole solution to be discovered [23], quantum black holes in Mink 3 have received less attention than their (A)dS cousins [22].”

This theorem, and the dearth of evidence of exact static black holes localizing in the RS-II construction circa 2002, in part motivated Tanaka and Emparan, Fabbri, and Kaloper to conjecture higher-dimensional braneworld black holes must be time-dependent.

“This theorem, and the dearth of evidence of exact static black holes localizing in the RS-II construction (circa 2002), in part motivated Tanaka [34] and Emparan, Fabbri, and Kaloper [22] to conjecture higher-dimensional braneworld black holes must be time-dependent (see also [198]).”

Hawking radiation from the brane perspective corresponds to bulk gravitational bremsstrahlung.

“Thus, Hawking radiation from the brane perspective corresponds to bulk gravitational bremsstrahlung [22].”

According to the conjecture, the braneworld black hole must be a solution to the semi-classical theory sourced by the CFT stress-tensor in some quantum state.

“Now, according to the conjecture [22], the braneworld black hole must be a solution to the semi-classical theory sourced by the CFT stress-tensor ⟨T ij ⟩ in some quantum state.”

Other bulk black solutions evaporate due to a Gregory-Laflamme instability, as originally suggested in [22,34].

“Indeed, while some bulk black holes get stuck on the brane and never shrink ('black droplets') [71] and hence dynamically stable, there are other bulk black solutions that evaporate due to a Gregory-Laflamme instability [72], as originally suggested in [22,34].”