Noether and Lie symmetries for charged perfect fluids

Abstract

We study the underlying nonlinear partial differential equation that governs the behaviour of spherically symmetric charged fluids in general relativity. We investigate the conditions for the equation to admit a first integral or be reduced to quadratures using symmetry methods for differential equations. A general Noether first integral is found. We also undertake a comprehensive group analysis of the underlying equation using Lie point symmetries. The existence of a Lie symmetry is subject to solving an integro-differential equation in general; we investigate the conditions under which it can be reduced to quadratures. Earlier results for uncharged fluids and particular first integrals for charged matter are regained as special cases of our treatment.

17 pages, To appear in Class. Quantum Grav

References in corpus (7)

• Charged anisotropic matter with linear equation of state
• Nonadiabatic charged spherical gravitational collapse
• Dynamics of viscous dissipative gravitational collapse: A full causal approach
• Analytical models for quark stars
• Gravitational collapse of spherically symmetric plasmas in Einstein-Maxwell spacetimes
• Spherically Symmetric Gravitational Collapse of General Fluids
• Charged seven-dimensional spacetimes with spherically symmetric extra-dimensions

Cited by in corpus (9)

• Geodesic models generated by Lie symmetries
• Generalized Euclidean stars with equation of state
• Temporal evolution of a radiating star via Lie symmetries
• New charged shear-free relativistic models with heat flux
• A fifth order differential equation for charged perfect fluids
• Classification of the Lie and Noether point symmetries for the Wave and the Klein-Gordon equations in pp-wave spacetimes
• Exact solution of the Einstein-Skyrme model in a Kantowski-Sachs spacetime
• Similarity Solutions For The Complex Burgers' Hierarchy
• New analytic solutions in $f\left(R\right)$-Cosmology from Painlevé analysis