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Keywords = geodesic incompleteness

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27 pages, 1600 KB  
Review
A Primer on Spacetime Singularities I: Mathematical Framework
by Jean-Pierre Luminet
Universe 2025, 11(8), 272; https://doi.org/10.3390/universe11080272 - 17 Aug 2025
Viewed by 3241
Abstract
This article presents a comprehensive and rigorous overview of spacetime singularities within the framework of classical General Relativity. Singularities are defined through the failure of geodesic completeness, reflecting the limits of predictability in spacetime evolution. This paper reviews the mathematical structures involved, including [...] Read more.
This article presents a comprehensive and rigorous overview of spacetime singularities within the framework of classical General Relativity. Singularities are defined through the failure of geodesic completeness, reflecting the limits of predictability in spacetime evolution. This paper reviews the mathematical structures involved, including differentiability classes of the metric, and explores key constructions such as Geroch’s and Schmidt’s formulations of singular boundaries. A detailed classification of singularities—quasi-regular, non-scalar, and scalar—is proposed, based on the behavior of curvature tensors along incomplete curves. The limitations of previous approaches, including the cosmic censorship conjecture and extensions beyond General Relativity, are critically examined. This work also surveys the major singularity theorems of Penrose and Hawking, emphasizing their implications for gravitational collapse and cosmology. By focusing exclusively on the classical regime, this article lays a solid foundation for the systematic study of singular structures in relativistic spacetimes. Full article
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19 pages, 7154 KB  
Article
A Heuristic Exploration of Zonal Flow-like Structures in the Presence of Toroidal Rotation in a Non-Inertial Frame
by Xinliang Xu, Yihang Chen, Yulin Zhou, Zhanhui Wang, Xueke Wu, Bo Li, Jiang Sun, Junzhao Zhang and Da Li
Plasma 2025, 8(3), 29; https://doi.org/10.3390/plasma8030029 - 22 Jul 2025
Viewed by 651
Abstract
The mechanisms by which rotation influences zonal flows (ZFs) in plasma are incompletely understood, presenting a significant challenge in the study of plasma dynamics. This research addresses this gap by investigating the role of non-inertial effects—specifically centrifugal and Coriolis forces—on Geodesic Acoustic Modes [...] Read more.
The mechanisms by which rotation influences zonal flows (ZFs) in plasma are incompletely understood, presenting a significant challenge in the study of plasma dynamics. This research addresses this gap by investigating the role of non-inertial effects—specifically centrifugal and Coriolis forces—on Geodesic Acoustic Modes (GAMs) and ZFs in rotating tokamak plasmas. While previous studies have linked centrifugal convection to plasma toroidal rotation, they often overlook the Coriolis effects or inconsistently incorporate non-inertial terms into magneto-hydrodynamic (MHD) equations. In this work, we derive self-consistent drift-ordered two-fluid equations from the collisional Vlasov equation in a non-inertial frame, and we modify the Hermes cold ion code to simulate the impact of rotation on GAMs and ZFs. Our simulations reveal that toroidal rotation enhances ZF amplitude and GAM frequency, with Coriolis convection playing a critical role in GAM propagation and the global structure of ZFs. Analysis of simulation outcomes indicates that centrifugal drift drives parallel velocity growth, while Coriolis drift facilitates radial propagation of GAMs. This work may provide valuable insights into momentum transport and flow shear dynamics in tokamaks, with implications for turbulence suppression and confinement optimization. Full article
(This article belongs to the Special Issue New Insights into Plasma Theory, Modeling and Predictive Simulations)
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25 pages, 513 KB  
Article
Non-Minimally Coupled Electromagnetic Fields and Observable Implications for Primordial Black Holes
by Susmita Jana and S. Shankaranarayanan
Universe 2024, 10(7), 270; https://doi.org/10.3390/universe10070270 - 22 Jun 2024
Cited by 10 | Viewed by 1699
Abstract
General relativity (GR) postulates have been verified with high precision, yet our understanding of how gravity interacts with matter fields remains incomplete. Various modifications to GR have been proposed in both classical and quantum realms to address these interactions within the strong gravity [...] Read more.
General relativity (GR) postulates have been verified with high precision, yet our understanding of how gravity interacts with matter fields remains incomplete. Various modifications to GR have been proposed in both classical and quantum realms to address these interactions within the strong gravity regime. One such approach is non-minimal coupling (NMC), where the space-time curvature (scalar and tensor) interacts with matter fields, resulting in matter fields not following the geodesics. To probe the astrophysical implications of NMC, in this work, we investigate non-minimally coupled electromagnetic (EM) fields in the presence of black holes. Specifically, we show that primordial black holes (PBHs) provide a possible tool to constrain the NMC parameter. PBHs represent an intriguing cosmological black hole class that does not conform to the no-hair theorem. We model the PBH as a Sultana–Dyer black hole and compare it with Schwarzschild. We examine observables such as the radius of the photon sphere, critical impact parameter, and total deflection angles for non-minimally coupled photons for Schwarzschild and Sultana–Dyer black holes. Both the black hole space-times lead to similar constraints on the NMC parameter. For a PBH of mass M=105 M, the photon sphere will not be formed for one mode. Hence, the photons forming the photon sphere will be highly polarized, potentially leading to observable implications. Full article
(This article belongs to the Collection Open Questions in Black Hole Physics)
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7 pages, 246 KB  
Article
Geodesic Incompleteness and Partially Covariant Gravity
by Ignatios Antoniadis and Spiros Cotsakis
Universe 2021, 7(5), 126; https://doi.org/10.3390/universe7050126 - 2 May 2021
Cited by 2 | Viewed by 1894
Abstract
We study the issue of length renormalization in the context of fully covariant gravity theories as well as non-relativistic ones such as Hořava–Lifshitz gravity. The difference in their symmetry groups implies a relation among the lengths of paths in spacetime in the two [...] Read more.
We study the issue of length renormalization in the context of fully covariant gravity theories as well as non-relativistic ones such as Hořava–Lifshitz gravity. The difference in their symmetry groups implies a relation among the lengths of paths in spacetime in the two types of theory. Provided that certain asymptotic conditions hold, this relation allows us to transfer analytic criteria for the standard spacetime length to be finite and the Perelman length to be likewise finite, and therefore formulate conditions for geodesic incompleteness in partially covariant theories. We also discuss implications of this result for the issue of singularities in the context of such theories. Full article
9 pages, 284 KB  
Article
Non-Geodesic Incompleteness in Poincaré Gauge Gravity
by José Alberto Ruiz Cembranos, Jorge Gigante Valcarcel and Francisco J. Maldonado Torralba
Entropy 2019, 21(3), 280; https://doi.org/10.3390/e21030280 - 14 Mar 2019
Cited by 7 | Viewed by 3464
Abstract
In this work, we review the study of singularities in Poincaré gauge theories of gravity. Since one of the most recent studies used the appearance of black hole regions of arbitrary dimension as an indicator of singular behavior, we also give some explicit [...] Read more.
In this work, we review the study of singularities in Poincaré gauge theories of gravity. Since one of the most recent studies used the appearance of black hole regions of arbitrary dimension as an indicator of singular behavior, we also give some explicit examples of these structures and study how particles behave around them. Full article
(This article belongs to the Special Issue Modified Gravity: From Black Holes Entropy to Current Cosmology II)
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