Cylindrical Systems in General Relativity

Abstract

With the arrival of the era of gravitational wave astronomy, the strong gravitational field regime will be explored soon in various aspects. In this article, we provide a general review over cylindrical systems in Einstein's theory of general relativity. In particular, we first review the general properties, both local and global, of several important solutions of Einstein's field equations, including the Levi-Civita and Lewis solutions and their extensions to include the cosmological constant and matter fields, and pay particular attention to properties that represent the generic features of the theory, such as the formation of the observed extragalactic jets and gravitational Faraday rotation. We also review studies of cylindrical wormholes, gravitational collapse and Hoop conjecture, and polarizations of gravitational waves. In addition, by rigorously defining cylindrically symmetric spacetimes, we clarify various (incorrect) claims existing in the literature, regarding to the generality of such spacetimes.

revote-4, 1 table and 8 figures. Class. Quantum Grav. 37 (2020) 113002 (85pp)

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• Stable Charged Gravastar model in Cylindrically Symmetric Space-time
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• Cosmic stringlike objects in hybrid metric-Palatini gravity
• Stable Gravastar model in Cylindrically Symmetric Space-time
• Stationary cylindrical anisotropic fluid and new purely magnetic GR solutions
• First-order perturbations of Gödel-type metrics in non-dynamical Chern-Simons modified gravity
• New classes of exact interior nonvacuum solutions to the GR field equations for spacetimes sourced by a rigidly rotating stationary cylindrical anisotropic fluid
• Magnetic-induced Spontaneous Scalarization in Dynamcial Chern-Simons Gravity
• Some unusual wormholes in general relativity
• Reference frames in General Relativity and the galactic rotation curves
• Gravitomagnetism in the Lewis cylindrical metrics
• Spontaneous scalarization of self-gravitating magnetic fields
• Complexity Factor for Static Cylindrical System in Energy-momentum Squared Gravity
• Cylindrical spacetimes due to radial magnetic fields
• The Anholonomic Frame and Connection Deformation Method for constructing off-diagonal solutions in (modified) Einstein gravity and nonassociative geometric flows and Finsler-Lagrange-Hamilton theories
• Static and Dynamic Melvin Universes
• Spinors in cylindrically symmetric space-time
• The fundamental physical importance of generic off-diagonal solutions and Grigori Perelman entropy in the Einstein gravity theory
• Observable effect of quantized cylindrical gravitational waves
• Static Cylindrical Symmetric Solutions in the Einstein-Aether Theory
• An Invariant Characterization of the Levi-Civita Spacetimes
• A note on the Sagnac effect in general relativity as a Finslerian effect
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• Gravitational soliton solutions to self-coupled Klein-Gordon and Schrödinger equations
• General off-diagonal integrability of metric and nonmetric geometric flow and Finsler-Lagrange-Hamilton modified Einstein equations
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• Harvesting entanglement from the cylindrical gravitational wave spacetime
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• Three dimensional black bounces in $f(R)$ gravity
• AdS Black Hole with Cylindrical Symmetry
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