2022 Articles

# Black hole scattering and partition functions

When computing the ideal gas thermal canonical partition function for a scalar outside a black hole horizon, one encounters the divergent single-particle density of states (DOS) due to the continuous nature of the normal mode spectrum. Recasting the Lorentzian field equation into an effective 1D scattering problem, we argue that the scattering phases encode non-trivial information about the DOS and can be extracted by “renormalizing” the DOS with respect to a reference. This defines a renormalized free energy up to an arbitrary additive constant. Interestingly, we discover that the 1-loop Euclidean path integral, as computed by the Denef-Hartnoll-Sachdev formula, fixes the reference free energy to be that on a Rindler-like region, and the renormalized DOS captures the quasinormal modes for the scalar. We support these claims with the examples of scalars on static BTZ, Nariai black holes and the de Sitter static patch. For black holes in asymptotically flat space, the renormalized DOS is captured by the phase of the transmission coefficient whose magnitude squared is the greybody factor. We comment on possible connections with recent works from an algebraic point of view.

## Subjects

## Files

- 13130_2022_Article_19401.pdf application/pdf 603 KB Download File

## Also Published In

- Title
- Journal of High Energy Physics
- DOI
- https://doi.org/10.1007/JHEP10(2022)039

## More About This Work

- Published Here
- July 22, 2024

## Related Items

- Identical to:
- Black hole scattering and partition functions

## Notes

Black Holes, Models of Quantum Gravity, Thermal Field Theory