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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.06165 |
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Table of Contents:
- In this paper, we evaluate the one-loop partition function of a scalar field in the near-horizon geometry of the extremal Reissner Nordström black hole from an infinite product over quasinormal modes using the Denef-Hartnoll-Sachdev (DHS) formula. We show that the logarithmic divergent term of the one-loop partition function computed using the DHS formula agrees with the heat kernel method. Using the same formula, we also evaluate the one-loop partition function of a scalar field in the near-extremal Kerr-Newman black hole and observe that it reduces to the same in the near-horizon $AdS_2\times S^2$ geometry of the extremal Reissner Nordström black hole when the angular velocity at the horizon is tuned to $2πT_{BH}$ value. We observe that, for higher spin fields, the mode functions are not smooth at the horizon for certain quasinormal frequencies; therefore, we remove them to obtain the one-loop determinant.