Bouncing geodesics, black hole singularities, and singularities of thermal correlators
- 1University of Edinburgh
- 2University of Ljubljana
Abstract
A bstract Bouncing geodesics have been used as valuable probes of black hole singularities. In the dual boundary theory, the presence of bouncing geodesics is encoded in the analytic structure of correlation functions. Thus, when their existence is related to the presence of a black hole singularity, this presents a practical holographic framework to analyse, diagnose, and classify spacetimes with curvature singularities. To make this intuition precise, we use the Hadamard theory of hyperbolic differential equations to prove that both bulk and boundary retarded propagators diverge whenever two points can be connected by a null geodesic. We clarify why this statement remains valid beyond the geodesic regime (for operators of any dimension) and examine how holographic renormalisation modifies the structure of the dual propagator. We also present a general characterisation of bouncing geodesics and the associated singularities in correlation functions for arbitrary spacetimes. Furthermore, we compare the analytic structure of the correlators in position and momentum space and discuss explicit examples. Finally, we demonstrate the validity and concrete limitations of the bouncing geodesic approach to the study of black hole singularities. In particular, we show an explicit example of a black hole in the self-dual linear axion model, which has a curvature singularity despite the absence of bouncing geodesics.
Related
- Bouncing singularities and thermal correlators on line defects
- Exact thermal correlators at vanishing momenta and the black hole singularity
- Bouncing singularities in Schwarzschild: a geometric origin of the QNM convergence region
- Stringy resolution of bouncing singularities
- Fate of Bouncing Singularities at Finite GN
BibTeX
@article{grozdanov2026bouncing,
title = {{Bouncing geodesics, black hole singularities, and singularities of thermal correlators}},
author = {Sašo Grozdanov and Samuel Valach and Mile Vrbica},
journal = {Journal of High Energy Physics},
year = {2026},
month = aug,
doi = {10.1007/jhep08(2026)022},
url = {https://doi.org/10.1007/jhep08(2026)022},
note = {CC BY},
}
RIS
TY - JOUR
TI - Bouncing geodesics, black hole singularities, and singularities of thermal correlators
AU - Sašo Grozdanov
AU - Samuel Valach
AU - Mile Vrbica
PY - 2026
DA - 2026/08/05
JO - Journal of High Energy Physics
DO - 10.1007/jhep08(2026)022
UR - https://doi.org/10.1007/jhep08(2026)022
AB - A bstract Bouncing geodesics have been used as valuable probes of black hole singularities. In the dual boundary theory, the presence of bouncing geodesics is encoded in the analytic structure of correlation functions. Thus, when their existence is related to the presence of a black hole singularity, this presents a practical holographic framework to analyse, diagnose, and classify spacetimes with curvature singularities. To make this intuition precise, we use the Hadamard theory of hyperbolic differential equations to prove that both bulk and boundary retarded propagators diverge whenever two points can be connected by a null geodesic. We clarify why this statement remains valid beyond the geodesic regime (for operators of any dimension) and examine how holographic renormalisation modifies the structure of the dual propagator. We also present a general characterisation of bouncing geodesics and the associated singularities in correlation functions for arbitrary spacetimes. Furthermore, we compare the analytic structure of the correlators in position and momentum space and discuss explicit examples. Finally, we demonstrate the validity and concrete limitations of the bouncing geodesic approach to the study of black hole singularities. In particular, we show an explicit example of a black hole in the self-dual linear axion model, which has a curvature singularity despite the absence of bouncing geodesics.
SN - 1029-8479
SN - 1126-6708
SN - 1127-2236
ER -