In this letter, we show the Unruh temperature of the photon sphere for an AdS4-Schwarzschild black hole can be determined holographically from the retarded Green's function and is proportional to its circumference according to a boundary observer. We then sharpen the conjecture that the photon sphere, as seen by a boundary observer, is the spatial Fourier transform of the response function. The conjecture is found to be in excellent agreement with our numerics after certain long-lived excitations -- associated with geodesics traveling between boundary points -- are removed from the response, which is then controlled by the short-lived excitations of the AdS black hole.
Cite
@article{arxiv.2310.16034,
title = {The Photon Sphere and Response Functions in Holography},
author = {Marcos Riojas and Hao-Yu Sun},
journal= {arXiv preprint arXiv:2310.16034},
year = {2024}
}
Comments
6 pages, 5 figures. Simplified Abstract. Correction added to Equation 20. Included additional citations. Corrected a dotted line in Figure 2. The definition of the impact parameter is now self-consistent in Figure 4. Larger labels in Figure 5