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

Mile Vrbica; Samuel Valach; Sa\v{s}o Grozdanov

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

Sašo Grozdanov, Samuel Valach, Mile Vrbica

High Energy Physics - Theory · Submitted 16 Mar 2026

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Finally, we demonstrate the validity and concrete limitations of the bouncing geodesic approach to the study of black hole singularities.

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arXiv ID2603.15598 (version 3)

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CitationMile Vrbica, Samuel Valach, Sa\v{s}o Grozdanov. "Bouncing geodesics, black hole singularities, and singularities of thermal correlators." arXiv:2603.15598 (2026). https://pith.science/paper/G7VNBK5A

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.94 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.34 · mentions code or data availability 0.02.

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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.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Bouncing geodesics have been used as valuable probes of black hole singularities.	background 1.00	0.05	0.04	asserted 1.00
s1	In the dual boundary theory, the presence of bouncing geodesics is encoded in the analytic structure of correlation functions.	background 0.94	0.12	0.08	asserted 1.00
s2	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.	interpretation 0.74	0.09	0.23	asserted 0.82
s3	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.	method 0.46	0.93	0.22	asserted 1.00
s4	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.	contribution 0.93	0.93	0.08	asserted 0.95
s5	We also present a general characterisation of bouncing geodesics and the associated singularities in correlation functions for arbitrary spacetimes.	contribution 0.98	0.94	0.13	asserted 0.98
s6	Furthermore, we compare the analytic structure of the correlators in position and momentum space and discuss explicit examples.	contribution 0.95	0.92	0.04	asserted 0.77
s7	Finally, we demonstrate the validity and concrete limitations of the bouncing geodesic approach to the study of black hole singularities.	contribution 0.59	0.94	0.30	asserted 1.00
s8	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.	result 0.78	0.94	0.22	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Original abstract

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.

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Cited by 13 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Bouncing and QNM convergence in Kerr
gr-qc 2026-11 accept novelty 7.0 of 10

The convergence region of QNM sums in Kerr is set by complex-time bouncing singularities, with prolate and oblate families giving different bounce radii and convergence boundaries.
Quantum gravity on the bulk cone
hep-th 2026-10 conditional novelty 7.0 of 10

Bulk-cone singularities predicted by classical holography are shown analytically to be absent in finite-G_N CFTs, and an explicit AdS_3 computation turns the would-be singularity into a smooth peak.
The Stringy Photon Sphere
hep-th 2026-10 accept novelty 7.0 of 10

String theory resolves the lightcone singularities in the Schwarzschild black hole S-matrix, producing a finite smoothed bump at real times and shifting singularities into the complex time plane.
Metric and dilaton information from high-overtone quasinormal modes of analytic Einstein-Maxwell-dilaton black holes
hep-th 2026-10 accept novelty 7.0 of 10

A neutral scalar probe with a dilaton-dependent mass profile allows high-overtone quasinormal-mode spectra to separately determine the metric exponents and the signed dilaton exponent of an Einstein–Maxwell–dilaton bl...
Stringy resolution of bouncing singularities
hep-th 2026-10 conditional novelty 7.0 of 10

The exact stringy reflection amplitude of the SL(2,R)_k/U(1) coset is an entire function of complex time, so the classical bouncing singularity at t = i pi is resolved nonperturbatively, with poles reappearing at ever...

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Fate of Bouncing Singularities at Finite $G_N$
hep-th 2026-09 conditional novelty 7.0 of 10

Bouncing singularities of thermal correlators are shown to be absent at finite Newton constant by analytic continuation of the thermal OPE to the second sheet.
Can one hear the shape of a black hole singularity?
hep-th 2026-09 accept novelty 7.0 of 10

Quasinormal mode dispersion at large overtone numbers reveals the Kasner exponents near a black hole singularity.
Spectral function, OPE, and QNMs detect different singular points of black branes with unequal R-charges
hep-th 2026-11 accept novelty 6.0 of 10

Spectral function, OPE coefficients, and QNM lines in STU black branes are each dominated by different singular points behind the horizon, forming a right triangle of optical times.
Smoothing the Bouncing-Geodesic Singularity in AdS/CFT
hep-th 2026-11 conditional novelty 6.0 of 10

Finite-c quantum corrections convert sharp complex-time singularity imprints of the black hole interior into smooth Gaussian profiles, while leaving short-distance, OPE-protected singularities intact.
A Matrix View of Holographic Null-State Equations in $d\geq 2$
hep-th 2026-11 conditional novelty 6.0 of 10

The null-state-type CFT equations from black hole holography can be encoded as determinants of banded finite matrices built from sl2 generators, for all levels in d=2 and d=4.
Quasinormal modes, complex null geodesics and singularity resolution in regular AdS black holes
hep-th 2026-10 conditional novelty 6.0 of 10

For regular AdS black holes, the CFT two-point function singularity from a null geodesic bouncing off the singularity is replaced by a bump associated with a complex null geodesic.
A signature of the timelike singularity in holography
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For a charged AdS5 black brane, the vacuum-subtracted spectral density has a predicted exponentially small tail governed by the complex time of a null geodesic reflecting off the timelike singularity, with a universal...
Asymptotic expansion of cavity Quasi-Normal Modes in Schwarzschild de-Sitter black hole
gr-qc 2026-09 conditional novelty 5.0 of 10

The paper derives the n^{-1/2} and n^{-1} corrections to the large-overtone cavity quasi-normal frequencies of a scalar in Schwarzschild-de Sitter and verifies them with a Frobenius-series numerical solution.

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8 arXiv papers cite this in 27 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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More recently, in [ref] , it was found that these “bouncing singularities” are directly visible on the principal sheet of a particular sector of the dual propagator for any finite conformal operator dimension (bulk probe mass) and can be effectively analysed using the operator product expansion (OPE) techniques [ref] .[For more details on these holographic computations and the OPE techniques, see also [ref] .] Since then, various other approaches were used to examine these bouncing singularities, using momentum space approaches and the WKB approximation [ref] , bulk phase-shift computations [ref] and properties of quasinormal modes [ref] , see also [ref] for relevant discussion and applications.

Bouncing Geodesics, Singularities, and the Cavity Thermal Product Formula in Asymptotically Flat and de Sitter Black Holes · Bouncing Geodesics · 0.82
Bouncing singularities is a development drawn from the AdS/CFT literature, where such singularities appear in analytic continuations of thermal correlation functions [ref] and for which there has been considerable recent interest [ref] .

Bouncing singularities in Schwarzschild: a geometric origin of the QNM convergence region · Introduction · 0.85
The recent paper [ref] explores the analytic structure of the correlator, while [ref] examines the connection to the bouncing geodesic.[In a related vein [ref] study the connection to bulk-cone singularities, which were originally motivated as diagnostics of horizon formation and gravitational time delay in [ref] .]

Exact holographic thermal spectral functions: OPE, non-perturbative corrections, and black hole singularity · Introduction and summary of results · 0.88

What it cites · 70 sentences without a confident label

Uses the method or tool of 1 paper

In Section [ref], we follow the approach of [ref] and discuss the bouncing singularities directly from the structure of QNMs.

A thermal product formula · Introduction and summary · 0.99

Cites as support 13 papers

The idea is as follows: Firstly, as motivated by a recent WKB analysis[Importantly, unlike in the Wightman function, [ref] found that the bouncing singularities in AdS-Schwarzschild spacetime should be present on the principal sheet of the retarded propagator.] [ref] and their privileged role in (causal) linear response theory, we identify the boundary retarded thermal correlator as the cleanest and most suitable object for the study of singularities.

Imprint of the black hole singularity on thermal two-point functions · Introduction and summary · 0.99
Indeed, as was shown in [ref] , there exists a corresponding singularity in the dual propagator.

2511.09638 · Definitions and existence · 1.00
Indeed, as was shown in [ref] , there exists a corresponding singularity in the dual propagator.

2511.09616 · Definitions and existence · 1.00

Cites as background 12 papers

A fruitful line of research addressing this question has focused on the so-called bouncing geodesics as probes of both the black hole interiors and spacetime singularities [ref] .

The Black Hole Singularity in AdS/CFT · Introduction and summary · 0.87
A fruitful line of research addressing this question has focused on the so-called bouncing geodesics as probes of both the black hole interiors and spacetime singularities [ref] .

Excursions beyond the horizon: Black hole singularities in Yang-Mills theories (I) · Introduction and summary · 0.87
In principle, the gauge/gravity duality (holography) [ref] is (tautologically) supposed to provide us all possible insights into the physics of singularities.

Gauge Theory Correlators from Non-Critical String Theory · Introduction and summary · 0.97

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