1,720,971 research outputs found
Charge distribution in neutron stars.
Full text linkMaster of Science in Applied Mathematics, University of KwaZulu-Natal, Westville, 2017.In previous studies, people have shown that compact stars, like the neutron stars
and quark stars, can hold a lot of charge during their formation resulting in a large
mass and radius. It was also argued that when the charges leave the system due
to repulsion from the self created field, these might render a secondary collapse
to a charged black hole. In the present work, we have taken a particular type of
charge distribution, with varying parameters, such that changing these parameters
mimic the situation when the charge particles leaving the system. We have made
a systematic study of each stage of the charge distributions. Our results reveal that
when the charge distribution deviates slightly from the scenario where the charge
density is proportional to the mass density, then the system is no longer able to
retain the large mass and radius, and quickly attains a lower mass and radius
Non-circularity of beams in the CMB polarization power spectrum estimation.
Full text linkPh. D. University of KwaZulu-Natal, Durban 2013.Precise measurements of the Cosmic Microwave Background (CMB) anisotropies have been
one of the foremost concerns in modern cosmology as it provides valuable information on the
cosmology of the Universe. However, an accurate estimation of the CMB power spectrum faces
many challenges as the CMB experiments sensitivity increases. Furthermore, for the polarization
experiments, the precision of the measurements is complicated by the fact that the polarization
signal is very faint compared to the measured total intensity and could be impossible to detect
in the presence of high level of systematics. One of the most important source of errors in CMB
polarization experiment is the beam non-circularity (asymmetry). In addition, the non-uniform
and partial sky coverage resulting from the masking of the CMB foreground contaminants as well
as point sources bias the estimation of the power spectrum. Consequently, a reasonable estimation
of the power spectrum must account for, at least, the beam asymmetry and incomplete sky
coverage. Accurate estimation of the angular power spectrum can be done using the standard
optimal Maximum Likelihood (ML), although for high resolution CMB experiments with large
data set this method is unfeasible due to the enormous computation time involved in the process.
The focus of this research is to estimate the CMB temperature anisotropy T and E-
polarization cross-power spectrum and EE polarization power spectrum using a semi-analytical
framework, and tackle the computational challenge of the TE power spectrum estimation with
the pseudo-Cl estimator in the presence of the non-circular beam and cut-sky systematics. We
examine, in the first step, the estimation of the CMB TE power spectrum by only considering
the beam non-circularity with a complete sky, and give the error estimates of the power
spectrum. Then, we will consider the more general case that includes the effect of the beam
asymmetry and cut-sky as a result of the foreground removals across the Galactic plane. The
numerical implementation of the bias matrix presents a huge computational challenge. Our
ultimate goal is to speed-up the computation of the TE bias matrix that relates the true and
observed power spectra in the case of a full sky coverage using a non-circular beam. We adopt
a model of beams obtained from a perturbative expansion of the beam around a circular (axisymmetric)
one in harmonic space and compute the bias matrix by using an efficient algorithm
for rapid computation.
We show in this work that, in the case of non-circular beams and full sky survey, a fast
computation of the TE bias matrix can be performed in few seconds using a single CPU processor
by means of precomputations and insertion of symmetry relations in the initial analytical
expression of the TE bias matrix. We present as well in the last part of this research the first
analytical results of the EE bias matrix calculations in the case of a CMB experiment using
non-circular beams and incomplete sky coverage, and derive the corresponding results for the
non-circular beams and full sky limit
Some aspects of strong gravity effects on the electromagnetic field of a radio pulsar magnetosphere : solving the Maxwell’s equations.
Full text linkMaster of Science in Applied Mathematics. University of KwaZulu-Natal, Durban, 2019.The general relativistic (GR) effects of a neutron star play a substantial role on the physics
at the stellar surface. These neutron stars also host a very strong magnetic field and spin
with periods of a few seconds to as high as milliseconds. In order to account for the
motion of charged particles in the magnetosphere immediately outside the stellar surface,
it is essential to include the GR effects in the Maxwell’s equations. To account for the
frame dragging effects due to the stellar spin, we have, in this dissertation, considered a
3+1 decomposition of the spacetime and applied them to find the solutions to Maxwell’s
equations of an isolated neutron star in a vacuum, for different cases. In order to derive our
solutions we made use of the vector spherical harmonics in a curved spacetime. We first
considered an aligned dipole magnetic field from which we formed a general formalism for
the magnetic and electric fields for higher orders. We then considered an orthogonal dipole
magnetic field for which we solved only for the non-rotating case. In a realistic scenario
for a radio pulsar, the radio beams which originate from the pole caps of the magnetic
field, have a finite angle with the spin axis and hence it is necessary to find a model for
an oblique rotator. This study will be helpful in the future for the understanding of the
charged particle interaction at the pulsar pole caps and hence for the emission mechanism
of a radio pulsar
Models in isotropic coordinates with equation of state.
Full text linkPh. D. University of KwaZulu-Natal, Durban 2014.In this thesis we consider spacetimes which are static and spherically symmetric related
to the Einstein and Einstein-Maxwell system of equations in isotropic coordinates. We
study both neutral and charged matter distributions with isotropic and anisotropic
pressures, respectively. Our aim is to model relativistic stellar models. A known
transformation that has been utilised by other researchers is applied to rewrite the
field equations in equivalent forms. We produce new models to the Einstein system
of equations with isotropic pressures by developing an algorithm that generates new
classes of exact solutions if a particular seed solution is known. By applying the
algorithm to the field equations and the condition of pressure isotropy we obtain a
nonlinear Bernoulli equation which can be integrated. We also consider charged matter
distributions with anisotropic pressures by introducing barotropic equations of state.
Both linear and quadratic equations of state are considered and new exact solutions
of the Einstein-Maxwell system are found. This is achieved by specifying a particular
form for one of the metric functions and the electric field intensity. We select particular
parameter values to regain the masses of known stars. For the linear equation of state
we regain masses of the stars PSR J1614-2230, Vela X-1, PSR J1903+327, 4U 1820-30
and SAX J1808.4-3658. The masses for the stars PSR J1614-2230, 4U 1608-52, PSR
J1903+327, EXO 1745-248 and SAX J1808.4-3658 are generated when a quadratic
equation of state is imposed. Extensive physical analyses for the stars PSR J1614-2230
and PSR J1903+327 indicate that our models are well behaved
Exact solutions for relativistic models.
Full text linkThesis (M.Sc.)-University of KwaZulu-Natal, Westville, 2011.In this thesis we study spherically symmetric spacetimes related to the Einstein field equations. We consider only neutral matter and apply the Einstein field equations with isotropic pressures. Our object is to model relativistic stellar systems. We express the Einstein field equations and the condition of pressure isotropy in terms of Schwarzschild coordinates and isotropic coordinates. For Schwarzschild coordinates we consider the
transformations due to Buchdahl (1959), Durgapal and Bannerji (1983), Fodor (2000) and Tewari and Pant (2010). The condition of pressure isotropy is integrated and new exact solutions of the field equations are obtained utilizing the transformations of Buchdahl (1959) and Tewari and Pant (2010). These exact solutions are given in terms of elementary functions. For isotropic coordinates we can express the condition of pressure isotropy as a Riccati equation or a linear equation. An algorithm is developed that produces a new solution if a particular solution is known. The transformations reduce to a nonlinear Bernoulli equation in most instances. There are fundamentally three new classes of solutions to the condition of pressure isotropy
New families of exact solutions for compact stars.
Full text linkDoctoral degree. University of KwaZulu-Natal, Durban.In this thesis we present new families of exact solutions to the Einstein and Einstein-
Maxwell eld equations which are relevant in the description of highly compact stellar
objects. We rst impose a linear equation of state to generate exact solutions in
terms of elementary functions which contain earlier quark models, including those
of Thirukkanesh and Maharaj (Class. Quantum Grav. 25, 235001 (2008)) and
Mafa Takisa and Maharaj (Astrophys. Space Sci. 354, 463 (2013)). Secondly, we
nd exact solutions in terms of elementary functions, Bessel and modi ed Bessel
functions through the Finch and Skea geometry which satisfy all criteria for physical
acceptability. From these models we regain the uncharged model of Finch and Skea
(Class. Quantum Grav. 6, 467 (1989)) and the charged model of Hansraj and
Maharaj (Int. J. Mod. Phys. D 15, 1311 (2006)) as particular cases. Thirdly, we nd
new exact stellar models by imposing a symmetry condition on spacetime, namely
a conformal Killing vector. We nd solutions to the eld equations with the help of
the gravitational potentials related explicitly by the conformal vector established by
Manjonjo et al (Eur. Phys. J. Plus 132, 62 (2017)). For each approach, we select
a particular model to study the physical features and then masses and radii with
accurate ranges consistent with observed numerical values of compact objects such
as SAX J1808.4-3658, LMC X-4, SMC X-1, EXO 1785, Cen X-3, 4U1820-30, PSR
J1903+327, Vela X-1 and PSR J1614-2230 are generated. The physical features in
all cases are studied comprehensively, and we show that our solutions are stable, well
behaved and have realistic physical features
New models for quark stars with charge and anisotropy.
Full text linkPh. D. University of KwaZulu-Natal, Durban 2014.We find new classes of exact solutions for the Einstein-Maxwell field equations. The
solutions are obtained by considering charged anisotropic matter with a linear equation
of state consistent with quark stars. The field equations are integrated by specifying
forms for the measure of anisotropy and one of the gravitational potentials which are
physically reasonable. A general feature of our models is that isotropic pressures are
regained when certain parameters vanish; this behaviour is missing in most previous
treatments. Particular models found in our results generalize the models of Mak and
Harko, Komathiraj and Maharaj, Misner and Zapolsky, and the earlier results of Einstein.
The graphical and physical analyses indicate that the gravitational potentials,
the matter variables, the electric field and the mass are well behaved. In performing
physical analysis we regain masses and radii of stellar objects consistent with observations.
It is also shown that other masses and radii may be generated which are in
acceptable ranges consistent with observed values of stellar objects. In particular we
have established that our model is consistent with the stellar object SAXJ1808.4-3658.
A study of the mass-radius relation indicates the effect of the electromagnetic field and
anisotropy on the mass of the relativistic star
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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