The Fluctuation-Dissipation Theorem and Dynamical Love Number in Schwarzschild Black Holes

@misc{giataganas2026fluctuationdissipation,
  title = {{The Fluctuation-Dissipation Theorem and Dynamical Love Number in Schwarzschild Black Holes}},
  author = {Dimitrios Giataganas and Alex Kehagias and Antonio Riotto},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.00545},
  eprint = {2611.00545},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.00545},
}

TY  - UNPB
TI  - The Fluctuation-Dissipation Theorem and Dynamical Love Number in Schwarzschild Black Holes
AU  - Dimitrios Giataganas
AU  - Alex Kehagias
AU  - Antonio Riotto
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.00545
UR  - https://arxiv.org/abs/2611.00545
AB  - We study the real-time response of a Schwarzschild black hole in the Hartle-Hawking state to an external massless scalar field. Using a complexified radial contour to represent the Schwinger-Keldysh closed time path, we describe dissipation, thermal fluctuations and conservative tidal response within a common framework. Before performing tidal matching, we derive the equilibrium fluctuation-dissipation relation directly from the radial construction for every scalar multipole at arbitrary real frequency. In the low-frequency tidal expansion, we recover the known relation between the logarithmic running of the conservative dynamical Love coefficient at order ω^2 and the leading dissipative response at order ω. We explain how the same leading absorptive coefficient enters both relations at low frequency and trace the unit coefficient of the running relation to the Schwarzschild horizon slope. In the Hartle-Hawking state, this common coefficient relates the logarithmic running directly to the zero-frequency thermal noise. Kubo-Martin-Schwinger analyticity determines the thermal noise from the dissipative response, whereas the near-zone radial equation and tidal matching determine the conservative logarithmic running.
ER  -