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Geodesic completeness, curvature singularities and infinite tidal forces

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Xiaotian Zhang, Sijie Gao

General Relativity and Quantum Cosmology · Submitted 7 Jul 2025

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

The authors' main claim Therefore, no particle can actually reach the curvature singularity even if the metric is well defined at that point.

how it is stated · asserted 1.00 read the record →

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arXiv ID2507.04616 (version 4)
Pith IDJ6I2GZFH, Pith's permanent record of this paper and its review
CitationSijie Gao, Xiaotian Zhang. "Geodesic completeness, curvature singularities and infinite tidal forces." arXiv:2507.04616 (2025). https://pith.science/paper/J6I2GZFH
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 9,535 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.16 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.12 · compares with prior results 0.85 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v4. Results and the main claim are underlined; .

We report some new findings regarding the subtle relations among geodesic completeness, curvature singularities and tidal forces. It is well known that any particle may be torn up near a singularity at the center of a black hole due to the divergent tidal force. However, we find that singularity is not the only cause of tidal force divergence. Even on the surface of the Earth, the tidal force experienced by a particle could be arbitrarily large if the particle moves arbitrarily close to the speed of light in a nonradial direction. Moreover, we find that the maximum tidal force always occurs along the radial direction, regardless of the particle's motion. Usually, a curvature singularity implies geodesic incompleteness since in many cases the metric cannot be defined at the location of the singularity. Counterexamples have been found in recent years, suggesting that geodesics could pass through curvature singularities. By taking into account the fact that any real particle is an extended body, we calculate the tidal force acting on the particle in a static and spherically symmetric spacetime. We explicitly show that an infinite tidal force always occurs near such a singularity. Therefore, no particle can actually reach the curvature singularity even if the metric is well defined at that point. We also demonstrate that the tidal acceleration along a null geodesic at the coordinate origin is divergent. Finally, we examine a wormhole solution which possesses a curvature singularity at its throat and was previously asserted to be geodesically complete in the literature. However, we prove that no metric can be defined at the throat and thus the spacetime is geodesically incomplete. we also show that the tidal forces experienced by any particle near the singularity are divergent.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We report some new findings regarding the subtle relations among geodesic completeness, curvature singularities and tidal forces. contribution 0.97 0.78 0.04 asserted 0.85
s1 It is well known that any particle may be torn up near a singularity at the center of a black hole due to the divergent tidal force. background 1.00 0.03 0.03 hedged possibility 0.71
s2 However, we find that singularity is not the only cause of tidal force divergence. result 0.89 0.94 0.19 asserted 1.00
s3 Even on the surface of the Earth, the tidal force experienced by a particle could be arbitrarily large if the particle moves arbitrarily close to the speed of light in a nonradial direction. result 0.99 0.86 0.10 hedged possibility 0.91
s4 Moreover, we find that the maximum tidal force always occurs along the radial direction, regardless of the particle's motion. result 1.00 0.90 0.09 asserted 1.00
s5 Usually, a curvature singularity implies geodesic incompleteness since in many cases the metric cannot be defined at the location of the singularity. background 1.00 0.05 0.04 asserted 0.69
s6 Counterexamples have been found in recent years, suggesting that geodesics could pass through curvature singularities. background 0.96 0.05 0.03 hedged possibility 0.92
s7 By taking into account the fact that any real particle is an extended body, we calculate the tidal force acting on the particle in a static and spherically symmetric spacetime. method 0.92 0.94 0.04 asserted 0.99
s8 We explicitly show that an infinite tidal force always occurs near such a singularity. result 1.00 0.94 0.19 asserted 1.00
s9 Therefore, no particle can actually reach the curvature singularity even if the metric is well defined at that point. interpretation 0.68 0.86 0.50 asserted 1.00
s10 We also demonstrate that the tidal acceleration along a null geodesic at the coordinate origin is divergent. result 0.99 0.93 0.07 asserted 1.00
s11 Finally, we examine a wormhole solution which possesses a curvature singularity at its throat and was previously asserted to be geodesically complete in the literature. contribution 0.90 0.59 0.05 asserted 0.95
s12 However, we prove that no metric can be defined at the throat and thus the spacetime is geodesically incomplete. we also show that the tidal forces experienced by any particle near the singularity are divergent. result 0.99 0.94 0.19 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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not examined
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  • references and citing sentences
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  • C citations
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We report some new findings regarding the subtle relations among geodesic completeness, curvature singularities and tidal forces. It is well known that any particle may be torn up near a singularity at the center of a black hole due to the divergent tidal force. However, we find that singularity is not the only cause of tidal force divergence. Even on the surface of the Earth, the tidal force experienced by a particle could be arbitrarily large if the particle moves arbitrarily close to the speed of light in a nonradial direction. Moreover, we find that the maximum tidal force always occurs along the radial direction, regardless of the particle's motion. Usually, a curvature singularity implies geodesic incompleteness since in many cases the metric cannot be defined at the location of the singularity. Counterexamples have been found in recent years, suggesting that geodesics could pass through curvature singularities. By taking into account the fact that any real particle is an extended body, we calculate the tidal force acting on the particle in a static and spherically symmetric spacetime. We explicitly show that an infinite tidal force always occurs near such a singularity. Therefore, no particle can actually reach the curvature singularity even if the metric is well defined at that point. We also demonstrate that the tidal acceleration along a null geodesic at the coordinate origin is divergent. Finally, we examine a wormhole solution which possesses a curvature singularity at its throat and was previously asserted to be geodesically complete in the literature. However, we prove that no metric can be defined at the throat and thus the spacetime is geodesically incomplete. we also show that the tidal forces experienced by any particle near the singularity are divergent.

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2 arXiv papers cite this in 2 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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What it cites · 12 sentences without a confident label

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