Abstract
We consider the problem of defining a microcanonical thermofield double state at fixed energy and angular momentum from the gravitational path integral. A semiclassical approximation to this state is obtained by imposing a mixed boundary condition on an initial time surface. We analyze the corresponding boundary value problem and gravitational action. The overlap of this state with the canonical thermofield double state, which is interpreted as the Hartle-Hawking wavefunction of an eternal black hole in a mini-superspace approximation, is calculated semiclassically. The relevant saddlepoint is a higher-dimensional, rotating generalization of the wedge geometry that has been studied in two-dimensional gravity. Along the way we discuss a new corner term in the gravitational action that arises at a rotating horizon.
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Acknowledgments
We thank Jeevan Chandra, Scott Collier, Xi Dong, Yikun Jiang, David Kolchmeyer, Ho Tat Lam, Don Marolf, and Baur Mukhametzhanov for helpful discussions, and Yikun Jiang for collaboration in the early stages of this project. This work is supported by NSF grant PHY-2014071.
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Chua, W.Z., Hartman, T. Black hole wavefunctions and microcanonical states. J. High Energ. Phys. 2024, 54 (2024). https://doi.org/10.1007/JHEP06(2024)054
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DOI: https://doi.org/10.1007/JHEP06(2024)054