Radiating stars with exponential Lie symmetries

Abstract

We analyze the general model of a radiating star in general relativity. A group analysis of the under determined, nonlinear partial differential equation governing the model's gravitational potentials is performed. This analysis is an extension of previous group analyses carried out and produces new group invariant solutions. We find that the gravitational potentials depend on exponential functions owing to the choice of the Lie symmetry generator. The fundamental boundary equation to be solved is in general a Riccati equation. Several new exact families of solutions to the boundary condition are generated. Earlier models of Euclidean stars and generalized Euclidean stellar models are regained as special cases. Linear equations of state can be found for shear-free and shearing spacetimes.

14 pages, submitted for publication

References in corpus (4)

• Some analytical models of radiating collapsing spheres
• Generalized Euclidean stars with equation of state
• Thermal Behaviour of Euclidean Stars
• Radiating Gravitational Collapse with Shearing Motion and Bulk Viscosity Revisited

Cited by in corpus (5)

• Riccati equations for bounded radiating systems
• Lie Symmetries, Painlevé analysis and global dynamics for the temporal equation of radiating stars
• Non-existence of expansion-free dynamical stars with rotation and spatial twist
• Radiant gravitational collapse with anisotropy in pressures and bulk viscosity
• Exact Anti-Self-Dual four-manifolds with a Killing symmetry by similarity transformations