2 research outputs found
Conformal symmetries and classification in shear-free spherically symmetric spacetimes.
No full textM. Sc. University of KwaZulu-Natal, Durban 2014.In this thesis we study the conformal geometry of static and non-static spherically
symmetric spacetimes. We analyse the general solution of the conformal Killing vector
equation subject to integrability conditions which place restrictions on the metric func-
tions. TheWeyl tensor is used to characterise the conformal geometry, and we calculate
the Weyl tensor components for the spherically symmetric line element. The accuracy
of our results is veri ed using Mathematica (Wolfram 2010) and Maple (2009). We
show that the standard result in the conformal motions for static spacetimes is in-
correct. This mistake is identi ed and corrected. Two nonlinear ordinary differential
equations are derived in the classi cation of static spacetimes. Both equations are
solved in general. Two nonlinear partial differential equations are derived in the classi-
cation of non-static spacetimes. The rst equation is solved in general and the second
equation admits a particular solution. Our treatment is the rst complete classi cation
of conformal motions in static and non-static spherically symmetric spacetimes using
the Weyl tensor
Conformal symmetry and applications to spherically symmetric spacetimes.
No full textDoctor of Philosophy in Applied Mathematics, University of KwaZulu-Natal, Westville, 2018.In this thesis we study static spherically symmetric spacetimes with a spherical conformal
symmetry and a nonstatic conformal factor. We analyse the general solution of
the conformal Killing vector equation subject to integrability conditions which impose
restrictions on the metric functions. The Weyl tensor is used to characterise the conformal
geometry. An explicit relationship between the gravitational potentials for both
conformally and nonconformally
at cases is obtained. The Einstein equations can then
be written in terms of a single gravitational potential. Previous results of conformally
invariant static spheres are special cases of our solutions. For isotropic pressure we can
find all metrics explicitly and show that the models always admit a barotropic equation
of state. We show that this treatment contains well known metrics such Schwarzschild
(interior), Tolman, Kuchowicz, Korkina and Orlyanskii, Patwardhan and Vaidya, and
Buchdahl and Land. For anisotropic pressures the solution of the
fluid equations is
found in general. We then consider an astrophysical application of conformal symmetries.
We investigate spherical exact models for compact stars with anisotropic pressures
and a conformal symmetry. We generate a new anisotropic solution to the Einstein
field equations. We demonstrate that this 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
