Abstract
We solve the Wheeler-DeWitt equation in the ‘cosmological interior’ (the past causal diamond of future infinity) of four dimensional dS-Schwarzschild spacetimes. Within minisuperspace there is a basis of solutions labelled by a constant c, conjugate to the mass of the black hole. We propose that these solutions are in correspondence with partition functions of a dual quantum mechanical theory where c plays the role of time. The quantum mechanical theory lives on worldtubes in the ‘static patch’ of dS-Schwarzschild, and the partition function is obtained by evolving the corresponding Wheeler-DeWitt wavefunction through the cosmological horizon, where a metric component gtt changes sign. We establish that the dual theory admits a symmetry algebra given by a central extension of the Poincaré algebra \( \mathfrak{e} \)(1, 1) and that the entropy of the dS black hole is encoded as an averaging of the dual partition function over the background gtt.
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Acknowledgments
It is a pleasure to acknowledge inspiring discussions with Dionysios Anninos, Diego Hofman, Albert Law and Ronak Soni. The work of S.A.H. is partially supported by Simons Investigator award #620869 and by STFC consolidated grant ST/T000694/1. M.J.B. was supported by a Gates Cambridge Scholarship (#OPP1144).
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Blacker, M.J., Hartnoll, S.A. Cosmological quantum states of de Sitter-Schwarzschild are static patch partition functions. J. High Energ. Phys. 2023, 25 (2023). https://doi.org/10.1007/JHEP12(2023)025
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DOI: https://doi.org/10.1007/JHEP12(2023)025