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