On the Near-Horizon Canonical Quantum Microstates from AdS2/CFT1 and Conformal Weyl Gravity
Abstract
:1. Introduction
- Christensen and Fulling [9], whose analysis of an anomalous energy momentum tensor to compute was first carried out by considering the most general solution to the conservation equation,
- Robinson and Wilczek (RW), who showed that anomalous two-dimensional chiral theories in the near horizon of black holes are rendered unitary by requiring the black hole to radiate at temperature [10,11,12,13]. RW’s analysis also provides a way for obtaining near-horizon two-dimensional analog black holes coupled to matter fields of parent four-dimensional pure gravity solutions [14].
- A general four-dimensional black hole does not necessary have a two-dimensional representation.
- Computation of the center depends on renormalization procedures of either the quantum CFT or the quantum energy momentum tensor.
- 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.
2. On the Weyl Rescaled Schwarzschild CFT
2.1. Geometry
2.2. Quantum Fields in WRSS Spacetime
2.3. Asymptotic Symmetries
2.4. Energy Momentum and Central Charge
2.5. Full Asymptotic Symmetry Group
2.6. and WRSS Thermodynamics
3. Canonical Microstates from the ASG and Conformal Weyl Gravity
3.1. CWG Geometry
3.2. Quantum Fields in CWGS
3.3. CWGS Asymptotic Symmetries
3.4. Energy Momentum and CWGS Central Charge
3.5. Full ASG for CWGS
3.6. and CWGS Thermodynamics
4. Discussion and Concluding Remarks
Acknowledgments
Author Contributions
Conflicts of Interest
Abbreviations
CFT | conformal field theory |
anti-de Sitter | |
RW | Robinson and Wilczek |
ASG | asymptotic symmetry group |
RN | Reissner-Nördstrom |
NHEK | near-horizon extremal Kerr |
CWG | conformal Weyl fravity |
ADM | Arnowitt, Deser and Misner |
RW2DA | Robinson and Wilczek two-dimensional analog |
WRSS | Weyl rescaled Schwarzschild spacetime |
EMT | energy momentum tensor |
NH | near horizon |
MUBC | modified Unruh Vacuum boundary conditions |
diffeomorphism | |
CWGS | conformal Weyl gravity solution |
CWDG | conformal Weyl dilaton gravity |
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1. | We employ the standard spacetime classification notation of [44]. |
2. | In [32] it was shown that terms above 00 decay exponentially fast in time by analyzing the asymptotic behavior of the field equation for an axisymmetric spacetime. |
3. | The factor is chosen to coincide with the normalization of (21) for the gravitational sector of the effective action. |
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Rodriguez, L.; Rodriguez, S. On the Near-Horizon Canonical Quantum Microstates from AdS2/CFT1 and Conformal Weyl Gravity. Universe 2017, 3, 56. https://doi.org/10.3390/universe3030056
Rodriguez L, Rodriguez S. On the Near-Horizon Canonical Quantum Microstates from AdS2/CFT1 and Conformal Weyl Gravity. Universe. 2017; 3(3):56. https://doi.org/10.3390/universe3030056
Chicago/Turabian StyleRodriguez, Leo, and Shanshan Rodriguez. 2017. "On the Near-Horizon Canonical Quantum Microstates from AdS2/CFT1 and Conformal Weyl Gravity" Universe 3, no. 3: 56. https://doi.org/10.3390/universe3030056