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Dynamical systems approach to relativistic spherically symmetric static perfect fluid models

J Mark Heinzle1, Niklas Röhr2 and Claes Uggla2

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We investigate relativistic spherically symmetric static perfect fluid models with barotropic equations of state that are asymptotically polytropic and linear at low and high pressures, respectively. We generalize standard work on Newtonian polytropes to a relativistic setting and to a much larger class of equations of state. This is accomplished by introducing dimensionless variables that are asymptotically homology invariant in the low pressure regime, which yields a reformulation of the field equations into a regular dynamical system on a three-dimensional compact state space. A global picture of the solution space is thus obtained which makes it possible to derive qualitative features and to prove theorems about mass–radius properties. Moreover, the framework is also suited for numerical computations, as illustrated by several numerical examples, e.g., the ideal neutron gas and examples that involve phase transitions.


PACS

04.40.Nr Einstein-Maxwell spacetimes, spacetimes with fluids, radiation or classical fields

04.20.Jb Exact solutions

MSC

83C15 Exact solutions

Subjects

Gravitation and cosmology

Dates

Issue 21 (7 November 2003)

Received 14 April 2003, in final form 11 August 2003

Published 26 September 2003



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