22 research outputs found
Lie symmetries for equations in conformal geometries
We seek exact solutions to the Einstein field equations which arise when two
spacetime geometries are conformally related. Whilst this is a simple method to
generate new solutions to the field equations, very few such examples have been
found in practice. We use the method of Lie analysis of differential equations
to obtain new group invariant solutions to conformally related Petrov type D
spacetimes. Four cases arise depending on the nature of the Lie symmetry
generator. In three cases we are in a position to solve the master field
equation in terms of elementary functions. In the fourth case special solutions
in terms of Bessel functions are obtained. These solutions contain known models
as special cases.Comment: 19 pages, To appear in J. Phys.
Spherical conformal models for compact stars
Abstract We consider spherical exact models for compact stars with anisotropic pressures and a conformal symmetry. The conformal symmetry condition generates an integral relationship between the gravitational potentials. We solve this condition to find a new anisotropic solution to the Einstein field equations. We demonstrate that the exact solution produces a relativistic model of a compact star. The model generates stellar radii and masses consistent with PSR J1614-2230, Vela X1, PSR J1903+327 and Cen X-3. A detailed physical examination shows that the model is regular, well behaved and stable. The mass–radius limit and the surface red shift are consistent with observational constraints