RECORD
Buchdahl limits in theories with regular black holes
General Relativity and Quantum Cosmology · Submitted 22 Dec 2025 · Published version
abstract compiled · 2026-10-20 · no language-model review
The authors' main claim We show, in particular, that stars in these theories may be more compact than in Einstein gravity.
The compiled record
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.
Open the compiled record
The abstract, sentence by sentence
We study generalizations of Buchdahl's compactness limits for perfect-fluid star solutions of $D$-dimensional Einstein gravity coupled to higher-curvature corrections. We focus on Quasi-topological theories involving infinite towers of terms for which the unique vacuum spherically symmetric solutions correspond to regular black holes. We solve analytically the problem of constant-density stars and find that the space of solutions is bounded by: configurations with divergent central-pressure, corresponding to the most compact stars; configurations which possess zero central-pressure; and configurations for which the sizes of the stars coincide with the inner-horizon radii of the would-be regular black holes. In the more general case of perfect-fluid stars for which the mean density decreases with increasing radius, we show that, for each density profile, maximum compactness is reached when the metric becomes singular at the center. Under certain additional conditions, we find a novel Buchdahl limit for the maximum compactness of stars, attained by a specific constant-density profile. We show, in particular, that stars in these theories may be more compact than in Einstein gravity. While the vacuum solutions of these theories are such that all curvature invariants take mass-independent maximum finite values, we argue that there exist ordinary matter stars with finite central pressures for which such bounds can be violated -- namely, arbitrarily high curvatures can be reached -- unless additional constraints, such as the dominant energy condition, are imposed on the fluid.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study generalizations of Buchdahl's compactness limits for perfect-fluid star solutions of $D$-dimensional Einstein gravity coupled to higher-curvature corrections. | contribution 0.94 | 0.90 | 0.05 | asserted 0.79 |
| s1 | We focus on Quasi-topological theories involving infinite towers of terms for which the unique vacuum spherically symmetric solutions correspond to regular black holes. | contribution 0.66 | 0.24 | 0.04 | asserted 0.97 |
| s2 | We solve analytically the problem of constant-density stars and find that the space of solutions is bounded by: configurations with divergent central-pressure, corresponding to the most compact stars; configurations which possess zero central-pressure; and configurations for which the sizes of the stars coincide with the inner-horizon radii of the would-be regular black holes. | result 0.99 | 0.96 | 0.23 | asserted 1.00 |
| s3 | In the more general case of perfect-fluid stars for which the mean density decreases with increasing radius, we show that, for each density profile, maximum compactness is reached when the metric becomes singular at the center. | result 0.99 | 0.95 | 0.18 | asserted 1.00 |
| s4 | Under certain additional conditions, we find a novel Buchdahl limit for the maximum compactness of stars, attained by a specific constant-density profile. | result 0.98 | 0.96 | 0.22 | asserted 0.99 |
| s5 | We show, in particular, that stars in these theories may be more compact than in Einstein gravity. | result 0.95 | 0.90 | 0.27 | hedged possibility 0.90 |
| s6 | While the vacuum solutions of these theories are such that all curvature invariants take mass-independent maximum finite values, we argue that there exist ordinary matter stars with finite central pressures for which such bounds can be violated -- namely, arbitrarily high curvatures can be reached -- unless additional constraints, such as the dominant energy condition, are imposed on the fluid. | result 0.49 | 0.71 | 0.39 | asserted 0.54 |
What was examined, and what was not
- arXiv listing abstract v2
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
We study generalizations of Buchdahl's compactness limits for perfect-fluid star solutions of $D$-dimensional Einstein gravity coupled to higher-curvature corrections. We focus on Quasi-topological theories involving infinite towers of terms for which the unique vacuum spherically symmetric solutions correspond to regular black holes. We solve analytically the problem of constant-density stars and find that the space of solutions is bounded by: configurations with divergent central-pressure, corresponding to the most compact stars; configurations which possess zero central-pressure; and configurations for which the sizes of the stars coincide with the inner-horizon radii of the would-be regular black holes. In the more general case of perfect-fluid stars for which the mean density decreases with increasing radius, we show that, for each density profile, maximum compactness is reached when the metric becomes singular at the center. Under certain additional conditions, we find a novel Buchdahl limit for the maximum compactness of stars, attained by a specific constant-density profile. We show, in particular, that stars in these theories may be more compact than in Einstein gravity. While the vacuum solutions of these theories are such that all curvature invariants take mass-independent maximum finite values, we argue that there exist ordinary matter stars with finite central pressures for which such bounds can be violated -- namely, arbitrarily high curvatures can be reached -- unless additional constraints, such as the dominant energy condition, are imposed on the fluid.
Human review
References
How the literature uses it
17 arXiv papers cite this in 32 sentences
Papers citing it · 16 sentences without a confident label
Compares with it 3 papers
-
The Bardeen spacetime could not be obtained as a solution to polynomial CQTGs in $d ≥5$ [ref] and to non-polynomial CQTGs in $d=4$ [ref] , but can be obtained as a solution to the extended QTGs in $d≥4$ discovered here.
All $2D$ generalised dilaton theories from $d\geq 4$ gravities · Example: $d$-dimensional Bardeen spacetime · 0.88
-
Another universal feature, which has been also observed in quasitopological theories [ref] , is the existence of solutions with an inner fluid core, the radius of which must not be larger than the corresponding radius of the inner horizon of the vacuum solutions associated with the deformation.
Effective geometrostatics of spherical stars beyond general relativity · Conclusions · 0.91
-
It is evident that $P_1 ≠P_2$, rendering the properties of this more complex and matter field model within the present gravitational framework distinct from isotropic perfect fluid in [ref] .
Proca-Maxwell System in an Infinite Tower of Higher-Derivative Gravity · Boundary Conditions and Physical Quantities · 0.80
Cites it as background 8 papers
-
Polynomial quasi-topological gravities [ref] are polynomial higher-curvature extensions of the Einstein-Hilbert action which possess second-order field equations on spherically symmetric backgrounds and admit single-function static spherically solutions characterized entirely by an algebraic equation involving a one-variable function, which can be derived from the reduced Lagrangian on this type of backgrounds [ref] .
Regular black holes from pure gravity in four dimensions · Introduction · 0.97
-
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
-
A compelling framework for analysing the resolution of black-hole singularities through a purely gravitational mechanism are polynomial curvature quasi-topological gravities, polynomial higher-curvature extensions of general relativity, which exist in $d≥5$ dimensions and among other properties feature second-order equations on spherically symmetric backgrounds [ref] .
Modified Friedmann equations and non-singular cosmologies in $d=4$ non-polynomial quasi-topological gravities · Introduction · 0.89
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.