A generalisation of the Buchdahl transformation and perfect fluid solutions

Perfect fluid solutions in general relativity are examined. The pressure isotropy relation possesses a discrete symmetry in the derivatives of the metric functions. It is shown that a generalisation of Buchdahl's original transformation (Aust. J. Phys.; 9: 13 (1956)) allows new physically reasonable solutions to be obtained from known solutions. An example is given. Previously noticed first by Buchdahl, and later by Glass and Goldman (J. Math. Phys.; 19: 856 (1978)), this symmetry was thought to lead only to unphysical solutions. (author)