Abstract
We compute the full asymptotic symmetry group of black holes belonging to the same equivalence class of solutions within the Conformal Weyl Gravity formalism. We do this within an $AdS_2/CFT_1$ correspondence and by performing a Robinson-Wilczek two dimensional reduction, thus enabling the construction of an effective quantum theory of the remaining field content. The resulting energy momentum tensors generate asymptotic Virasoro algebras, to $s$-wave, with calculable central extensions. These centers in conjunction with their proper regularized lowest Virasoro eigen-modes yield the Bekenstein-Hawking black hole entropy via the statistical Cardy formula. We also analyze quantum holomorphic fluxes of the dual CFTs in the near horizon, giving rise to finite Hawking temperatures weighted by the central charges of the respective black hole spacetimes. We conclude with a discussion and outlook for future work.
Highlights
Since the seminal work of Brown and Henneaux [1] and the Kerr/conformal field theory (CFT)correspondence [2,3], it has become universally accepted that most black holes exhibit a holographic dual description in terms of a conformal field theory of lesser dimensions
The auxiliary fields in the resulting conformal field theories (CFTs) require physical boundary conditions rendering them finite on either the black hole horizon, or at asymptotic infinity or both. Taking advantage of these facts to conformally map the Schwarzschild spacetime to one with global AdS2 × S2 topology in order to implement our CFT construction to compute the full asymptotic symmetry group provides us with a conformal window into what a full or complete Schwarzschild CFT construction may look like
We study the resulting quantum microstates within an AdS2 /CFT1 correspondence and compute its full asymptotic symmetry group (ASG)
Summary
Since the seminal work of Brown and Henneaux [1] and the Kerr/conformal field theory (CFT). The auxiliary fields in the resulting CFT require physical boundary conditions rendering them finite on either the black hole horizon, or at asymptotic infinity or both Taking advantage of these facts to (liberally) conformally map the Schwarzschild spacetime to one with global AdS2 × S2 topology in order to implement our CFT construction to compute the full asymptotic symmetry group provides us with a conformal window into what a full or complete Schwarzschild CFT construction may look like. The resulting two-dimensional black hole is pure AdS2 (not a non-null EM field) and we compute its full asymptotic symmetry group including lowest renormalized eigenmode This should complete the near-horizon quantum microstate study of the Weyl rescaled Schwarzschild geometry. We discuss a dimensional reduction of CWG and see what possible avenues there are for extracting the central extension directly from its action principle
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