General Relativity and Quantum Cosmology · arXiv:1001.0359 v2 · submitted 3 Jan 2010
Circular Orbits in Extremal Reissner Nordstrom Spacetimes
The paper says
“Extremization of the effective potential for null circular orbits shows the existence of a stable circular geodesic in the extremal spacetime, precisely {\it on} the event horizon, which coincides with its null geodesic generator.”
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Abstract
Circular null geodesic orbits, in extremal Reissner-Nordstrom spacetimes, are examined with regard to their stability, and compared with similar orbits in the near-extremal situation. Extremization of the effective potential for null circular orbits shows the existence of a stable circular geodesic in the extremal spacetime, precisely {\it on} the event horizon, which coincides with its null geodesic generator. Such an orbit also emerges as a global minimum of the effective potential for circular {\it timelike} orbits. This type of geodesic is of course absent in the corresponding near-extremal spacetime, as we show here, testifying to differences between the extremal limit of a generic RN spacetime and the exactly extremal geometry.
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abstract compiled · 2026-09-23 · no language-model review
How the main claim is stated: asserted 1.00
What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.20 · human participants 0.01 · controlled comparison 0.41 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.87 · mentions code or data availability 0.02
The abstract, sentence by sentence
This table labels the abstract only (arXiv listing abstract v2). The number is the probability the classifier gave the label.
| Sentence | Role | The authors' own work | States the main conclusion | Strength |
|---|---|---|---|---|
| Circular null geodesic orbits, in extremal Reissner-Nordstrom spacetimes, are examined with regard to their stability, and compared with similar orbits in the near-extremal situation. | contribution 0.86 | 0.84 | 0.08 | asserted 0.63 |
| Extremization of the effective potential for null circular orbits shows the existence of a stable circular geodesic in the extremal spacetime, precisely {\it on} the event horizon, which coincides with its null geodesic generator. | result 1.00 | 0.90 | 0.72 | asserted 1.00 |
| Such an orbit also emerges as a global minimum of the effective potential for circular {\it timelike} orbits. | result 1.00 | 0.82 | 0.20 | asserted 1.00 |
| This type of geodesic is of course absent in the corresponding near-extremal spacetime, as we show here, testifying to differences between the extremal limit of a generic RN spacetime and the exactly extremal geometry. | interpretation 0.56 | 0.88 | 0.21 | asserted 1.00 |
What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00
What was examined, and what was not
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- arXiv listing abstract v2
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- P abstract
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- T body sentences
- C citations
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How the labels were made
Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,738 input tokens, $0.0002 reported.
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Cited by 6 Pith papers
Reviewed papers on Pith that cite this one. The full citation record
- Astrophysical hints for magnetic black holes hep-ph · Sep 2020
- Photon Spheres and Sonic Horizons in Black Holes from Supergravity and Other Theories gr-qc · Aug 2016
- Motion of charged test particles in Reissner--Nordstr\"om spacetime gr-qc · Mar 2011
- Joule-Thomson Effect and Geodesic Structure of Charged AdS Black Holes in f(R,T) Coupled with Nonlinear Electrodynamics gr-qc · Jul 2026
- Islands and Page curves of Reissner-Nordstr\"om black holes hep-th · Jan 2021
- Circular motion of neutral test particles in Reissner-Nordstr\"om spacetime astro-ph.HE · Dec 2010
How the literature uses it
20 arXiv papers cite this in 28 sentences
Papers citing it · 23 sentences without a confident label
Compares with it 2 papers
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This seems to be in conflict with the previous result of [ref] by Pradhan and Majumdar, since in that work it is shown that an extremal asymptotically flat Reissner-Nordström black hole does have a (stable) photon orbit on its event horizon.
Lux in obscuro: Photon Orbits of Extremal Black Holes Revisited · Black Holes and Their Photon Orbits · 0.84
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These results are similar to those obtained in the RN geometry [ref] .
Electrically charged regular black holes in nonlinear electrodynamics: light rings, shadows and gravitational lensing · Light rings (LRs) in the effective geometry · 1.00
Cites it as background 3 papers
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The occurrence of photon spheres in extremal black holes has been extensively studied, for example in [ref] , and we shall not consider this case further here.
Photon Spheres and Sonic Horizons in Black Holes from Supergravity and Other Theories · Photon spheres · 1.00
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There have been extensive theoretical studies on stable orbits for test particles, in asymptotically flat Reisnner-Nordstrom spacetimes [ref] , as well as some studies in Reisnner-Nordstrom spacetimes with a non-zero cosmological constant [ref] .
Astrophysical hints for magnetic black holes · Stable circular orbits near MBHs · 0.98
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Trajectories of test particles in the RN spacetime have been studied extensively (some recent works can be found in e.g. [ref] ).
Displaced orbits and electric-magnetic black hole binaries · Introduction · 1.00
What it cites · 5 sentences without a confident label
Cites as support 1 paper
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Our analysis reinforces earlier assertions in the literature [ref] , [ref] that the extremal limit of a generic charged black hole is not necessarily the extremal black hole spacetime.
Extremal limits and black hole entropy · Outlook · 0.99
Cites as background 2 papers
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One aspect related to black hole thermodynamics is the definition of the so-called Entropy Function [ref] used widely nowadays to match the `macroscopic' entropy of a class of extremal black holes emerging in the supergravity limit of string theories, to the `microscopic' entropy obtained from counting of string states [ref] .
Quantum Entropy Function from AdS(2)/CFT(1) Correspondence · Introduction · 0.97
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One aspect related to black hole thermodynamics is the definition of the so-called Entropy Function [ref] used widely nowadays to match the `macroscopic' entropy of a class of extremal black holes emerging in the supergravity limit of string theories, to the `microscopic' entropy obtained from counting of string states [ref] .
Classical Models of Subatomic Particles · Introduction · 0.97
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