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Relevant bibliographies by topics / Geodesically complete structure

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Journal articles

Academic literature on the topic 'Geodesically complete structure'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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Journal articles on the topic "Geodesically complete structure"

1

Mahamane, Saminou Ali, Hassirou Mouhamadou, and Mahaman Bazanfare. "Geodesically Complete Lie Algebroid." British Journal of Mathematics & Computer Science 22, no. 5 (2017): 1–12. https://doi.org/10.9734/BJMCS/2017/34009.

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In this paper we introduce the notion of geodesically complete Lie algebroid. We give a Riemannian distance on the connected base manifold of a Riemannian Lie algebroid. We also prove that the distance is equivalent to natural one if the base manifold was endowed with Riemannian metric. We obtain Hopf Rinow type theorem in the case of transitive Riemannian Lie algebroid, and give a characterization of the connected base manifold of a geodesically complete Lie algebroid.

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2

Friedrich, Helmut. "On the existence ofn-geodesically complete or future complete solutions of Einstein's field equations with smooth asymptotic structure." Communications in Mathematical Physics 107, no. 4 (1986): 587–609. http://dx.doi.org/10.1007/bf01205488.

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ROSALES, J. L. "VACUUM DECAY VIA LORENTZIAN WORMHOLES." International Journal of Modern Physics A 13, no. 07 (1998): 1191–99. http://dx.doi.org/10.1142/s0217751x98000548.

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We speculate about the space–time description due to the presence of Lorentzian worm-holes (handles in space–time joining two distant regions or other universes) in quantum gravity. The semiclassical rate of production of these Lorentzian wormholes in Reissner–Nordström space–times is calculated as a result of the spontaneous decay of vacuum due to a real tunneling configuration. In the magnetic case it only depends on the value of the field theoretical fine structure constant. We predict that the quantum probability corresponding to the nucleation of such geodesically complete space–times sho

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Barletta, Elisabetta, Sorin Dragomir, and Francesco Esposito. "On the Canonical Foliation of an Indefinite Locally Conformal Kähler Manifold with a Parallel Lee Form." Mathematics 9, no. 4 (2021): 333. http://dx.doi.org/10.3390/math9040333.

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We study the semi-Riemannian geometry of the foliation F of an indefinite locally conformal Kähler (l.c.K.) manifold M, given by the Pfaffian equation ω=0, provided that ∇ω=0 and c=∥ω∥≠0 (ω is the Lee form of M). If M is conformally flat then every leaf of F is shown to be a totally geodesic semi-Riemannian hypersurface in M, and a semi-Riemannian space form of sectional curvature c/4, carrying an indefinite c-Sasakian structure. As a corollary of the result together with a semi-Riemannian version of the de Rham decomposition theorem any geodesically complete, conformally flat, indefinite Vais

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Majumder, Bivash, Maxim Khlopov, Saibal Ray, and Goutam Manna. "Geodesic Structure of Generalized Vaidya Spacetime through the K-Essence." Universe 9, no. 12 (2023): 510. http://dx.doi.org/10.3390/universe9120510.

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This article investigates the radial and non-radial geodesic structures of the generalized K-essence Vaidya spacetime. Within the framework of K-essence geometry, it is important to note that the metric does not possess conformal equivalence to the conventional gravitational metric. This study employs a non-canonical action of the Dirac–Born–Infeld kind. In this work, we categorize the generalized K-essence Vaidya mass function into two distinct forms. Both the forms of the mass functions have been extensively utilized to analyze the radial and non-radial time-like or null geodesics in great d

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BASMAJIAN, ARA, and DRAGOMIR ŠARIĆ. "Geodesically Complete Hyperbolic Structures." Mathematical Proceedings of the Cambridge Philosophical Society 166, no. 2 (2017): 219–42. http://dx.doi.org/10.1017/s0305004117000792.

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AbstractIn the first part of this work we explore the geometry of infinite type surfaces and the relationship between its convex core and space of ends. In particular, we give a geometric proof of a Theorem due to Alvarez and Rodriguez that a geodesically complete hyperbolic surface is made up of its convex core with funnels attached along the simple closed geodesic components and half-planes attached along simple open geodesic components. We next consider gluing infinitely many pairs of pants along their cuffs to obtain an infinite hyperbolic surface. We prove that there always exists a choic

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7

Carballo-Rubio, Raúl, Francesco Di Filippo, Stefano Liberati, and Matt Visser. "Geodesically complete black holes in Lorentz-violating gravity." Journal of High Energy Physics 2022, no. 2 (2022). http://dx.doi.org/10.1007/jhep02(2022)122.

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Abstract We present a systematic study of the geometric structure of non-singular spacetimes describing black holes in Lorentz-violating gravity. We start with a review of the definition of trapping horizons, and the associated notions of trapped and marginally trapped surfaces, and then study their significance in frameworks with modified dispersion relations. This leads us to introduce the notion of universally marginally trapped surfaces, as the direct generalization of marginally trapped surfaces for frameworks with infinite signal velocities (Hořava-like frameworks), which then allows us

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8

Galloway, Gregory, and Eric Ling. "Rigidity Aspects of Penrose’s Singularity Theorem." Communications in Mathematical Physics 406, no. 2 (2025). https://doi.org/10.1007/s00220-024-05210-4.

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AbstractIn this paper, we study rigidity aspects of Penrose’s singularity theorem. Specifically, we aim to answer the following question: if a spacetime satisfies the hypotheses of Penrose’s singularity theorem except with weakly trapped surfaces instead of trapped surfaces, then what can be said about the global spacetime structure if the spacetime is null geodesically complete? In this setting, we show that we obtain a foliation of MOTS which generate totally geodesic null hypersurfaces. Depending on our starting assumptions, we obtain either local or global rigidity results. We apply our ar

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9

Chen, Bin, Haowei Sun, and Jie Xu. "Geodesics in Carrollian Reissner-Nordström black holes." Physical Review D 110, no. 12 (2024). https://doi.org/10.1103/physrevd.110.125016.

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In this work, we study the geodesics in different Carrollian limits of RN (Reissner-Nordström) black holes, considering the motions of both neutral and charged particles. We use the geodesic equations in the weak Carrollian structure and analyze the corresponding trajectories projected onto the absolute space, and find that the geodesics are well defined. In particular, we examine the electric-electric and magnetic-electric limit of the RN black hole, focusing on their geodesic structures. We find that the global structures of the usual RN black holes get squeezed under the ultrarelativistic l

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10

Bauer, Martin, Patrick Heslin, and Cy Maor. "Completeness and Geodesic Distance Properties for Fractional Sobolev Metrics on Spaces of Immersed Curves." Journal of Geometric Analysis 34, no. 7 (2024). http://dx.doi.org/10.1007/s12220-024-01652-3.

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AbstractWe investigate the geometry of the space of immersed closed curves equipped with reparametrization-invariant Riemannian metrics; the metrics we consider are Sobolev metrics of possible fractional-order $$q\in [0,\infty )$$ q ∈ [ 0 , ∞ ) . We establish the critical Sobolev index on the metric for several key geometric properties. Our first main result shows that the Riemannian metric induces a metric space structure if and only if $$q>1/2$$ q > 1 / 2 . Our second main result shows that the metric is geodesically complete (i.e., the geodesic equation is globally well posed) if $$q&

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