Cylindrically Symmetric Relativistic Fluids: A Study Based on Structure Scalars

Abstract

The full set of equations governing the structure and the evolution of self--gravitating cylindrically symmetric dissipative fluids with anisotropic stresses, is written down in terms of scalar quantities obtained from the orthogonal splitting of the Riemann tensor (structure scalars), in the context of general relativity. These scalars which have been shown previously (in the spherically symmetric case) to be related to fundamental properties of the fluid distribution, such as: energy density, energy density inhomogeneity, local anisotropy of pressure, dissipative flux, active gravitational mass etc, are shown here to play also a very important role in the dynamics of cylindrically symmetric fluids. It is also shown that in the static case, all possible solutions to Einstein equations may be expressed explicitly through three of these scalars.

14 pages, Revtex4-1. Text has been shortened. Some erroneous conclusions about the nonexistence of specific static solutions have been removed.New references added, the "canonical" anisotropy tensor was introduced to avoid misunderstandings. Text changed to match the version accepted in Gen.Rel.Grav

References in corpus (13)

• Relativistic cosmology and large-scale structure
• Nonadiabatic charged spherical gravitational collapse
• On the Role of Electric Charge and Cosmological Constant in Structure Scalars
• Dynamics of viscous dissipative gravitational collapse: A full causal approach
• Dynamical laws of superenergy in General Relativity
• Shearfree Cylindrical Gravitational Collapse
• The inertia of heat and its role in the dynamics of dissipative collapse
• Dynamics of Non-adiabatic Charged Cylindrical Gravitational Collapse
• Why does gravitational radiation produce vorticity?
• Dynamics of Charged Plane Symmetric Gravitational Collapse
• Charged Perfect Fluid Cylindrical Gravitational Collapse
• Levi-Civita spacetimes in multidimensional theories
• Levi-Civita cylinders with fractional angular deficit

Cited by in corpus (40)

• Causes of Irregular Energy Density in $f(R,T)$ Gravity
• Complexity factors for axially symmetric static sources
• Influence of Modification of Gravity on the Complexity Factor of Static Spherical Structures
• Complexity Factor For Static Anisotropic Self-Gravitating Source in $f(R)$ Gravity
• Dissipative collapse of axially symmetric, general relativistic, sources: A general framework and some applications
• Stability Analysis of Stellar Radiating Filaments
• Quasi-static evolution of axially and reflection symmetric large-scale configuration
• New Definition of Complexity Factor in $f(R,T,R_{\mu \nu }{T}^{\mu \nu })$ Gravity
• Structure Scalars for Charged Cylindrically Symmetric Relativistic Fluids
• The Measure of Complexity in Charged Celestial Bodies in $f(R,T,R_{\mu \nu }{T}^{\mu \nu })$ Gravity
• Axially symmetric static sources: A general framework and some analytical solutions
• Complexity analysis of Cylindrically Symmetric Self-gravitating Dynamical System in $f(R,T)$ Theory of Gravity
• Orthogonal splitting of the Riemann curvature tensor and its implications in modeling compact stellar structures
• Interpretation of complexity for spherically symmetric fluid composition within the context of modified gravity theory
• Spatially Hyperbolic Gravitating Sources in $\Lambda$-Dominated Era
• Stability of Anisotropic Cylinder with Zero Expansion
• Higher Dimensional Inhomogeneous Perfect Fluid Collapse in \emph{f(R)} Gravity
• Dynamics of Charged Bulk Viscous Collapsing Cylindrical Source With Heat Flux
• Models of Collapsing and Expanding Anisotropic Gravitating Source in $f(R,T)$ Theory of Gravity
• Evolution of Cluster of Stars in f(R) Gravity
• Complexity for Dynamical Anisotropic Sphere in f(G,T) Gravity
• Quasi Static Evolution of Compact Objects in Modified Gravity
• Influence of Electromagnetic Field on Hyperbolically Symmetric Source
• Gravitational Binding Energy in Charged Cylindrical Symmetry
• Gravitational collapse of cylindrical anisotropic fluid: A source of gravitational waves
• Dynamics of Charged Viscous Dissipative Cylindrical Collapse With Full Causal Approach
• A cylindrically symmetric, static anisotropic fluid spacetime and the naked singularity
• On the Relativistic anisotropic configurations
• The theory of gravitation: A tale of many questions and few answers
• Collapsing dynamics of relativistic fluid in modified gravity admitting a conformal Killing vector
• Cylindrical symmetric, non-rotating and non-static or static black hole solutions and the naked singularities
• Gravitational collapse of dissipative fluid as a source of gravitational waves
• Cylindrically symmetric models of gravitational collapse to black holes: a short review
• Static and Dynamic Melvin Universes
• Study of Complexity Factor and Stability of Dynamical Systems in $f(G)$ Gravity
• What makes a shear-free spherical perfect fluid be inhomogeneous with tidal effects?
• Stability of Relativistic Spheres Powered by Energy Profile in Einstein Gauss-Bonnet Gravity
• Black holes/naked singularities in four-dimensional non-static space-time and the energy-momentum distributions
• Generating anisotropic models for relativistic stellar objects
• Relativistic Bessel Cylinders