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Black hole Near Horizons through the Looking Glass
High Energy Physics - Theory · Submitted 23 Feb 2026
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Our encyclopedia of examples establishes the notion of SC geometries as near-horizon geometries of non-extremal black objects, paving the way for a detailed, intricate future analysis of the quantum aspects of this geometry.
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The abstract, sentence by sentence
We show that the near horizon of a generic non-extremal black hole (BH) can be understood in terms of a Carrollian geometry with two null directions, also called a String-Carroll (SC) geometry. The base space of this fibre-bundle structure is a sphere (or a plane for a black brane) and the fibre is the two-dimensional Rindler spacetime. We launch a detailed study of probes in this geometry. We study particle geodesics and scalar fields. The first part of the paper constructs geodesics and probe scalar fields directly in the SC geometry. We then look at a wide class of examples, including the Schwarzschild BH and the Kerr BH in asymptotically flat spacetimes, the BTZ BH and the black brane in AdS spacetimes, as well as Lifshitz black holes and construct the explicit maps to the SC geometry to obtain results specific to each case. These results are reproduced by considering the probe particles and fields in the original BH background and taking the near-horizon limit of the solutions. Our encyclopedia of examples establishes the notion of SC geometries as near-horizon geometries of non-extremal black objects, paving the way for a detailed, intricate future analysis of the quantum aspects of this geometry.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We show that the near horizon of a generic non-extremal black hole (BH) can be understood in terms of a Carrollian geometry with two null directions, also called a String-Carroll (SC) geometry. | result 0.66 | 0.92 | 0.76 | asserted 1.00 |
| s1 | The base space of this fibre-bundle structure is a sphere (or a plane for a black brane) and the fibre is the two-dimensional Rindler spacetime. | result 0.74 | 0.68 | 0.11 | asserted 1.00 |
| s2 | We launch a detailed study of probes in this geometry. | contribution 0.98 | 0.88 | 0.03 | asserted 0.65 |
| s3 | We study particle geodesics and scalar fields. | contribution 0.86 | 0.92 | 0.03 | asserted 0.79 |
| s4 | The first part of the paper constructs geodesics and probe scalar fields directly in the SC geometry. | method 0.69 | 0.93 | 0.05 | asserted 0.93 |
| s5 | We then look at a wide class of examples, including the Schwarzschild BH and the Kerr BH in asymptotically flat spacetimes, the BTZ BH and the black brane in AdS spacetimes, as well as Lifshitz black holes and construct the explicit maps to the SC geometry to obtain results specific to each case. | contribution 0.61 | 0.93 | 0.08 | asserted 0.99 |
| s6 | These results are reproduced by considering the probe particles and fields in the original BH background and taking the near-horizon limit of the solutions. | result 0.77 | 0.87 | 0.13 | asserted 1.00 |
| s7 | Our encyclopedia of examples establishes the notion of SC geometries as near-horizon geometries of non-extremal black objects, paving the way for a detailed, intricate future analysis of the quantum aspects of this geometry. | interpretation 0.54 | 0.87 | 0.68 | asserted 0.99 |
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The paper
Original abstract
We show that the near horizon of a generic non-extremal black hole (BH) can be understood in terms of a Carrollian geometry with two null directions, also called a String-Carroll (SC) geometry. The base space of this fibre-bundle structure is a sphere (or a plane for a black brane) and the fibre is the two-dimensional Rindler spacetime. We launch a detailed study of probes in this geometry. We study particle geodesics and scalar fields. The first part of the paper constructs geodesics and probe scalar fields directly in the SC geometry. We then look at a wide class of examples, including the Schwarzschild BH and the Kerr BH in asymptotically flat spacetimes, the BTZ BH and the black brane in AdS spacetimes, as well as Lifshitz black holes and construct the explicit maps to the SC geometry to obtain results specific to each case. These results are reproduced by considering the probe particles and fields in the original BH background and taking the near-horizon limit of the solutions. Our encyclopedia of examples establishes the notion of SC geometries as near-horizon geometries of non-extremal black objects, paving the way for a detailed, intricate future analysis of the quantum aspects of this geometry.
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References
How the literature uses it
4 arXiv papers cite this in 8 sentences
Papers citing it · 5 sentences without a confident label
Cites it as support 1 paper
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These include membrane paradigm [ref] - [ref] , as well as related fluid/gravity correspondence in AdS/CFT [ref] , [ref] , the near horizon conformal symmetry with analogous structure of a single copy of the “near-horizon Virasoro algebra” [ref] - [ref] , as noticed in [ref] , Kerr/CFT correspondence [ref] , Carrolian description of near horizon physics [ref] - [ref] , which may provide a natural holographic framework for non-extremal black holes, even beyond the AdS setting.
Modular quantization and black holes · Discussion · 0.99
Cites it as background 2 papers
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This framework has been developed in recent work on strings and probes near non extremal black hole horizons [ref] .
Emergence of Lorentzian geometry from string Carroll geometry · Introduction · 0.86
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Carrollian geometries have been studied in various areas of theoretical physics, ranging from physics on null hypersurfaces and black-hole-horizon dynamics to string theory and holography (see [ref] and references therein).
Stationary solutions in the small-$c$ expansion of GR · Introduction · 1.00
What it cites · 65 sentences without a confident label
Uses the method or tool of 4 papers
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Following the works of [ref] , we expand [ref] in analytical powers of $c^2$ for a general Lorentzian metric which has a small $c^2$ expansion of the form [ref].
Strings near black holes are Carrollian · Near-horizon expansion of the action · 0.91
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Following the works of [ref] , we expand [ref] in analytical powers of $c^2$ for a general Lorentzian metric which has a small $c^2$ expansion of the form [ref].
Strings near black holes are Carrollian -- Part II · Near-horizon expansion of the action · 0.91
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As shown in [ref] , any d+1-dimensional Lorentzian metric $g_μν$ and its inverse can be decomposed in terms of pre-Carrollian variables as [equation] such that, [equation] Here, $Π_$ is a non-degenerate metric in the transverse space.
Carroll Expansion of General Relativity · Particle Carroll Expansion · 0.89
Compares with 2 papers
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These propagators bear a striking resemblance to Carrollian propagators [ref] even though the near-horizon is not a Carrollian manifold, but a String Carroll manifold.
Carroll stories · Scalar fields: What is universal and what is not? · 0.90
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These propagators bear a striking resemblance to Carrollian propagators [ref] even though the near-horizon is not a Carrollian manifold, but a String Carroll manifold.
Scattering Amplitudes: Celestial and Carrollian · Scalar fields: What is universal and what is not? · 0.90
Cites as support 1 paper
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This is corroborated by the fact that the Lifshitz metric can be recast via $ρ∼r^z$ as [equation] These can be obtained independently as solutions in auxiliary 2-dim dilaton gravity theories [ref] .
Cosmological singularities and 2-dimensional dilaton gravity · Interlude: a quick review of Lifshitz spacetimes · 0.96
Cites as background 19 papers
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Here, e.g. in the context of four dimensional black holes, it is known that the geometry becomes $AdS_2 ×S^2$ [ref] , where it is understood that in the general case, the sphere is non-trivially fibred on the $AdS_2$ .
Classification of near-horizon geometries of extremal black holes · Introduction · 0.84
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A $d$-dimensional Carrollian manifold is a smooth manifold with a degenerate metric $h_μν$ and a nowhere-vanishing vector field $θ^μ$ that generates the kernel of the metric [ref] , i.e. [equation] For flat Carroll manifolds, the isometries of this doublet [equation] generates the Carroll algebra: [equation] Notice that this is generically infinite dimensional for all spacetime dimensions.
Conformal Carroll groups · Carroll symmetries · 0.91
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We refer the reader to the recent review [ref] for an overview of the recent developments and further references to the literature, to [ref] for a review aimed particularly at flat holography from the Carroll perspective, and to [ref] for a nice geometric overview of Carroll symmetries.
Foundations of Carrollian Geometry · Introduction · 1.00
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