Abstract
We propose a 1+1 dimensional CFT dual structure for quantum gravity and matter on the extended 2+1 dimensional BTZ black hole, realized as a quotient of the Poincare patch of AdS$_3$. The quotient spacetime includes regions beyond the singularity, "whiskers", containing timelike and lightlike closed curves, which at first sight seem unphysical. The spacetime includes the usual AdS-asymptotic boundaries outside the horizons as well as boundary components inside the whiskers. We show that local boundary correlators with some endpoints in the whisker regions: (i) are a protected class of amplitudes, dominated by effective field theory even when the associated Witten diagrams appear to traverse the singularity, (ii) describe well-defined diffeomorphism-invariant quantum gravity amplitudes in BTZ, (iii) sharply probe some of the physics inside the horizon but outside the singularity, and (iv) are equivalent to correlators of specific non-local CFT operators in the standard thermofield entangled state of two CFTs. In this sense, the whisker regions can be considered as purely auxiliary spacetimes in which these useful non-local CFT correlators can be rendered as local boundary correlators, and their diagnostic value more readily understood. Our results follow by first performing a novel reanalysis of the Rindler view of standard AdS/CFT duality on the Poincare patch of AdS, followed by exploiting the simple quotient structure of BTZ which turns the Rindler horizon into the BTZ black hole horizon. While most of our checks are within gravitational effective field theory, we arrive at a fully non-perturbative CFT proposal to probe the UV-sensitive approach to the singularity.
Highlights
A century after the discovery of the Schwarzschild metric, ds2 = 1 − rS r dt2 − dr2 rS r − r2 dθ2 + sin2 θ dφ2 (1.1)black holes remain a source of mystery and fascination
We propose a 1 + 1 dimensional conformal field theory (CFT) dual structure for quantum gravity and matter on the extended 2 + 1 dimensional BTZ black hole, realized as a quotient of the Poincare patch of AdS3
We show that local boundary correlators with some endpoints in the whisker regions: (i) are a protected class of amplitudes, dominated by effective field theory even when the associated Witten diagrams appear to traverse the singularity, (ii) describe well-defined diffeomorphism-invariant quantum gravity amplitudes in BTZ, (iii) sharply probe some of the physics inside the horizon but outside the singularity, and (iv) are equivalent to correlators of specific non-local CFT operators in the standard thermofield entangled state of two CFTs
Summary
Black holes remain a source of mystery and fascination. In theoretical physics, they provide key insights for our most ambitious attempts to unify gravity, relativity and quantum mechanics. Pure 2 + 1-dimensional general relativity does not contain propagating gravitons, it does have gravitational fluctuations and backreactions, and coupled to propagating matter the EFT is non-renormalizable as in higher dimensions (it may be a compactification of higher dimensions, and contain propagating Kaluza-Klein gravitons), requiring UV completion It shares with higher-dimensional eternal AdS Schwarzschild black holes, the central consequence of AdS/CFT duality: as an object inside AdSglobal the black hole inherits a holographic dual in terms of a “hot” conformal field theory (CFT) (for BTZ, a 1 + 1 CFT on a spatial circle), the CFT temperature being dual to the BTZ Hawking temperature. Since the interior of the horizon is a cosmological spacetime, finding the non-local CFT operators can be thought of as giving the holographic description of a quantum cosmology with singularity, a signficant step beyond the more familiar holography of static AdS
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