Static models with conformal symmetry

Abstract

We study static spherically symmetric spacetimes with a spherical conformal symmetry and a nonstatic conformal factor associated with the conformal Killing field. With these assumptions we find an explicit relationship relating two metric components of the metric tensor field. This leads to the general solution of the Einstein field equations with a conformal symmetry in a static spherically symmetric spacetime. For perfect fluids we can find all metrics explicitly and show that the models always admit a barotropic equation of state. Contained within this class of spacetimes are the well known metrics of (interior) Schwarzschild, Tolman, Kuchowicz, Korkina and Orlyanskii, Patwardhan and Vaidya, and Buchdahl and Land. The isothermal metric of Saslaw et al also admits a conformal symmetry. For imperfect fluids an infinite family of exact solutions to the field equations can be generated.

Static conformal models for anisotropic charged fluids

“…Conformally flat spacetimes and nonconformally flat spacetimes with the static assumption were also studied by Grøn and Johannesen [11] and Herrera et al [12]. In a general treatment Manjonjo et al [13] showed that an explicit functional relation relates the two metric components of the gravitational field. This relationship can be exploited to find new solutions to the Einstein field equations and model relativistic stars.…”

“…The work done by various authors can then be shown to be only special cases of the work done here. Manjonjo et al [13] considered the case of the conformal symmetry in the presence of anisotropic pressures. We extend this work to include the electromagnetic field.…”

Spherical conformal models for compact stars

“…Manjonjo et al [9] used the Weyl tensor to find conformally flat and non-conformally flat static metrics with conformal symmetries. In a subsequent paper Manjonjo et al [10] showed that a conformal symmetry generates an explicit relationship relating the gravitational potentials in general; isotropic and anisotropic matter distributions can then be found with a conformal Killing vector. These studies may be used to model stellar systems in relativistic astrophysics.…”

Linear and Riccati equations in generating functions for stellar models in general relativity

“…where L K is the Lie derivative operator and ψ (t, r) is the conformal factor. This implies the equation [5] 2ν…”

“…Solutions with LEOS and known m are given in [44], [45], [46], [47]. 5 The tangential pressure and the anisotropic factor Eq (4) is an expression for p t and can be written as a linear equation for y…”