Bouncing geodesics, black hole singularities, and singularities of thermal correlators

Grozdanov, Sašo (author), Valach, Samuel (author), Vrbica, Mile (author)

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.

• Language: English
• Keywords: cosmology, blak holes, gauge-gravity correspondence, spacetime singularities, thermal field theory
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2026
• Number of pages: 32 str.
• Numbering: Vol. 2026, art. no. 22
• PID: 20.500.12556/RUL-185528
• UDC: 539.1
• ISSN on article: 1029-8479
• DOI: 10.1007/JHEP08(2026)022
• COBISS.SI-ID: 287238147
• Publication date in RUL: 07.08.2026

Record is a part of a journal

• Title: The journal of high energy physics
• Shortened title: J. high energy phys.
• Publisher: SISSA
• ISSN: 1029-8479
• COBISS.SI-ID: 1314148

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: kozmologija, črne luknje, umeritveno-gravitacijska korespondenca, gravitacíjska síngularnost, teorija polja