Gen Relativ Gravit (2006) 38:1723–1726 DOI 10.1007/s10714-006-0353-7 LETTER Equation of state for anisotropic spheres S. D. Maharaj · M. Chaisi Received: 12 January 2006 / Accepted: 19 September 2006 / Published online: 5 October 2006 © Springer Science+Business Media, LLC 2006 Abstract We present a new class of exact interior solutions for anisotropic spheres to the Einstein field equations with a prescribed energy density. This category of solutions has similar energy density profiles to the models of Chaisi and Maharaj (Gen. Rel. Grav. 37, 1177–1189, 2005) whose approach we follow in the integration process. A distinguishing feature of the solutions presented is that they satisfy a barotropic equation of state linearly relating the radial pressure to the energy density. Keywords Anisotropic relativistic stars · Exact solutions · Compact spheres Since the pioneering work of Bowers and Liang [1] on anisotropic stars many researchers, in recent years, have studied anisotropic matter in the context of general relativity; these include the investigations of Dev and Gleiser [2, 3], Mak and Harko [4, 5] and Herrera et al. [6, 7] in different relativistic astrophys- ical situations. This research has been motivated on the grounds that anisot- ropy affects the critical mass, surface redshift and stability of highly compact relativistic bodies. Anisotropic matter appears to be a vital ingredient in the modelling of boson stars and strange matter with densities higher than neutron stars as pointed out by Mak and Harko [4] and Sharma and Mukherjee [8] S. D. Maharaj (B) · M. Chaisi Astrophysics and Cosmology Research Unit, School of Mathematical Sciences, University of KwaZulu-Natal, Durban 4041, South Africa e-mail: maharaj@ukzn.ac.za M. Chaisi Department of Mathematics and Computer Science, National University of Lesotho, Roma 180, Lesotho e-mail: m.chaisi@nul.ls