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Regular Geometries from Singular Matter in Quasi-Topological Gravity
General Relativity and Quantum Cosmology · Submitted 10 Mar 2026 · Published version
abstract compiled · 2026-10-20 · no language-model review
The authors' main claim Overall, our results highlight subtleties in coupling quasi-topological gravity to matter and suggest Markov's hypothesis as a potential selection criterion for resummed gravity-matter effective theories.
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The abstract, sentence by sentence
Vacuum quasi-topological gravity with infinitely many terms in the action satisfies Markov's limiting curvature hypothesis: the spherically symmetric solutions are regular and all curvature invariants are bounded by solution-independent scales. We study how this picture changes when the theory is coupled to matter. We find that minimally coupled matter spoils the scaling properties of the vacuum equations that lead to the validity of Markov's hypothesis, but the corresponding geometries often remain regular. We make this precise by developing a set of sufficient conditions on general static, spherically symmetric stress-tensors such that the corresponding solutions have bounded curvature. These conditions cover regular matter sectors but also singular matter profiles that are sufficiently singular in a sense we quantify. Our conclusions hold independently of the matter field equations and include configurations in which matter exhibits divergent energy density and pressure at finite radius or at Killing horizons, results that may have implications for mass inflation in these models. We then explore non-minimal couplings, focusing on theories with infinite towers of higher-curvature and electromagnetic terms in the action. In this class, Markov's hypothesis can be restored: we present theories admitting a universal upper bound on curvature, independent of the mass and charge. Overall, our results highlight subtleties in coupling quasi-topological gravity to matter and suggest Markov's hypothesis as a potential selection criterion for resummed gravity-matter effective theories.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Vacuum quasi-topological gravity with infinitely many terms in the action satisfies Markov's limiting curvature hypothesis: the spherically symmetric solutions are regular and all curvature invariants are bounded by solution-independent scales. | background 0.97 | 0.25 | 0.16 | asserted 1.00 |
| s1 | We study how this picture changes when the theory is coupled to matter. | contribution 0.76 | 0.41 | 0.02 | unclear 0.72 |
| s2 | We find that minimally coupled matter spoils the scaling properties of the vacuum equations that lead to the validity of Markov's hypothesis, but the corresponding geometries often remain regular. | result 1.00 | 0.96 | 0.27 | asserted 0.98 |
| s3 | We make this precise by developing a set of sufficient conditions on general static, spherically symmetric stress-tensors such that the corresponding solutions have bounded curvature. | method 0.53 | 0.96 | 0.12 | asserted 1.00 |
| s4 | These conditions cover regular matter sectors but also singular matter profiles that are sufficiently singular in a sense we quantify. | result 0.84 | 0.92 | 0.10 | asserted 1.00 |
| s5 | Our conclusions hold independently of the matter field equations and include configurations in which matter exhibits divergent energy density and pressure at finite radius or at Killing horizons, results that may have implications for mass inflation in these models. | result 0.68 | 0.91 | 0.16 | hedged possibility 0.51 |
| s6 | We then explore non-minimal couplings, focusing on theories with infinite towers of higher-curvature and electromagnetic terms in the action. | contribution 0.98 | 0.84 | 0.04 | unclear 0.51 |
| s7 | In this class, Markov's hypothesis can be restored: we present theories admitting a universal upper bound on curvature, independent of the mass and charge. | result 0.99 | 0.93 | 0.22 | asserted 0.83 |
| s8 | Overall, our results highlight subtleties in coupling quasi-topological gravity to matter and suggest Markov's hypothesis as a potential selection criterion for resummed gravity-matter effective theories. | interpretation 1.00 | 0.61 | 0.68 | hedged possibility 0.97 |
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Original abstract
Vacuum quasi-topological gravity with infinitely many terms in the action satisfies Markov's limiting curvature hypothesis: the spherically symmetric solutions are regular and all curvature invariants are bounded by solution-independent scales. We study how this picture changes when the theory is coupled to matter. We find that minimally coupled matter spoils the scaling properties of the vacuum equations that lead to the validity of Markov's hypothesis, but the corresponding geometries often remain regular. We make this precise by developing a set of sufficient conditions on general static, spherically symmetric stress-tensors such that the corresponding solutions have bounded curvature. These conditions cover regular matter sectors but also singular matter profiles that are sufficiently singular in a sense we quantify. Our conclusions hold independently of the matter field equations and include configurations in which matter exhibits divergent energy density and pressure at finite radius or at Killing horizons, results that may have implications for mass inflation in these models. We then explore non-minimal couplings, focusing on theories with infinite towers of higher-curvature and electromagnetic terms in the action. In this class, Markov's hypothesis can be restored: we present theories admitting a universal upper bound on curvature, independent of the mass and charge. Overall, our results highlight subtleties in coupling quasi-topological gravity to matter and suggest Markov's hypothesis as a potential selection criterion for resummed gravity-matter effective theories.
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How the literature uses it
11 arXiv papers cite this in 15 sentences
Papers citing it · 10 sentences without a confident label
Cites it as background 4 papers
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A particularly interesting recent development in the theory of regular black holes arises in the context of quasi-topological gravity (QTG) [ref] ,.
Charged Black Holes in Quasi-Topological Gravity Coupled to Born-Infeld Nonlinear Electrodynamics · Introduction · 0.96
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Some first investigations of FLRW cosmological sectors for these types of theories have been performed in [ref] , see also [ref] for results concerning polynomial curvature quasi-topological gravities in higher dimensions which are relevant to our discussion, as the reduced theories belong to the same subclass of two-dimensional Horndeski theories.
Modified Friedmann equations and non-singular cosmologies in $d=4$ non-polynomial quasi-topological gravities · Introduction · 0.83
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See, however, [ref] for complementary analyses addressing conditions for curvature scalar regularity and geodesic completeness in such theories in the presence of matter.
Formation of extremal regular black holes · Application of singularity theorems beyond general relativity · 0.93
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