Rod Halburd 2001 Class. Quantum Grav. 18 11 doi:10.1088/0264-9381/18/1/302
Rod Halburd
Show affiliationsIt is known that charged relativistic shear-free fluid spheres are described by the equation yxx = f(x)y2 + g(x)y3, where f and g are arbitrary functions of x only and y is a function of x and an external parameter t. Necessary and sufficient conditions on f and g are obtained such that this equation possesses the Painlevé property. In this case the general solution y is given in terms of solutions of the first or second Painlevé equation (or their autonomous versions) and solutions of their linearizations. In the autonomous case we recover the solutions of Wyman, Chatterjee and Sussman and a large class of (apparently new) solutions involving elliptic integrals of the second kind. Solutions arising from the special Airy function solutions of the second Painlevé equation are also given. It is noted that, as in the neutral case, a three-parameter family of choices of f and g are described by solutions of an equation of Chazy type.
04.40.Nr Einstein-Maxwell spacetimes, spacetimes with fluids, radiation or classical fields
33C10 Bessel and Airy functions, cylinder functions, 0F1
34M55 Painlevé and other special equations; classification, hierarchies; isomonodromic deformations
Issue 1 (7 January 2001)
Received 3 May 2000
Rod Halburd 2001 Class. Quantum Grav. 18 11
G J Kramer et al 2004 Plasma Phys. Control. Fusion 46 695
Eric Akkermans and Sankalpa Ghosh 2004 J. Phys. B: At. Mol. Opt. Phys. 37 S127
L F Marsal et al 1996 Semicond. Sci. Technol. 11 1209
V N Rudenko et al 2003 Class. Quantum Grav. 20 317
Kyung Joong Kim et al 2006 Metrologia 43 L28
Bhinyo Panijpan et al 2009 Phys. Educ. 44 599
A Kaye 1966 Br. J. Appl. Phys. 17 803
Chen Jie-Fei et al 2008 Chinese Phys. Lett. 25 747
C E G R Alves et al 2009 J. Radiol. Prot. 29 507