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1 
New approaches to spacetime singularities /Scott, Susan M. January 1991 (has links) (PDF)
Thesis (Ph. D.)University of Adelaide, Dept. of Physics and Mathematical Physics, 1992. / Includes bibliographical references.

2 
New classes of exact solutions for charged perfect fluids.Mthethwa, Thulani Richard. 28 March 2014 (has links)
We investigate techniques to generate new classes of exact solutions to the Einstein
Maxwell field equations which represent the gravitational field of charged perfect fluid
spherically symmetric distributions of matter. Historically, a large number of solutions
have been proposed but only a small number have been demonstrated to satisfy
elementary conditions for physical acceptability. Firstly we examine the case of the
constant density and constant electric field charged fluid sphere and show empirically
that such configurations of matter are unlikely to exist as basic physical requirements
are violated. We then make an ansatz relating the fluid's electric field intensity to
one of the gravitational potentials thereby simplifying the system of partial differential
equations. This prescription yields an algorithmic process to generate new classes of
exact solutions. We present a number of new solutions and comment on their viability
as stellar models. Graphical plots generated by symbolic software of the main dynamical
and geometrical quantities verify that one of our models is suitable to represent
a physically relevant distribution of charged matter in the form of a spherical shell.
In particular, positive definiteness of energy density and pressure are guaranteed, a
pressure free hypersurface denoting the boundary of the star exists, the sound speed
is shown to be subluminal and the energy conditions are satisfied everywhere in the
interior of the star. / Thesis (M.Sc.)University of KwaZuluNatal, Durban, 2012.

3 
New approaches to spacetime singularities / by Susan M. ScottScott, Susan M. (Susan Marjorie) January 1991 (has links)
Includes bibliographical references / vi, 128 leaves ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)University of Adelaide, Dept. of Physics and Mathematical Physics, 1992

4 
Singular behavior in T² symmetric spacetimes with cosmological constant /Clausen, Adam, January 2007 (has links)
Thesis (Ph. D.)University of Oregon, 2007. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 9598). Also available for download via the World Wide Web; free to University of Oregon users.

5 
The linear stability of the Schwarzschild spacetime in the harmonic gauge: odd partHung, PeiKen January 2018 (has links)
In this thesis, we study the odd solution of the linearlized Einstein equation on the Schwarzschild background and in the harmonic gauge. With the aid of ReggeWheeler quantities, we are able to estimate the odd part of Lichnerowicz d'Alembertian equation. In particular, we prove the solution decays to a linearlized Kerr solution except for the angular mode l=2.

6 
A hyperbolic tetrad approach to numerical relativity /Buchman, Luisa T. January 2003 (has links)
Thesis (Ph. D.)University of Washington, 2003. / Vita. Includes bibliographical references (p. 205211).

7 
Analysis of shearfree spherically symmetric charged relativistic fluids.Kweyama, Mandlenkosi Christopher. January 2011 (has links)
We study the evolution of shearfree spherically symmetric charged fluids
in general relativity. This requires the analysis of the coupled EinsteinMaxwell
system of equations. Within this framework, the master field equation to be
integrated is
yxx = f(x)y2 + g(x)y3
We undertake a comprehensive study of this equation using a variety of ap
proaches. Initially, we find a first integral using elementary techniques (subject
to integrability conditions on the arbitrary functions f(x) and g(x)). As a re
sult, we are able to generate a class of new solutions containing, as special
cases, the models of Maharaj et al (1996), Stephani (1983) and Srivastava
(1987). The integrability conditions on f(x) and g(x) are investigated in detail
for the purposes of reduction to quadratures in terms of elliptic integrals. We
also obtain a Noether first integral by performing a Noether symmetry analy
sis of the master field equation. This provides a partial group theoretic basis
for the first integral found earlier. In addition, a comprehensive Lie symmetry
analysis is performed on the field equation. Here we show that the first integral
approach (and hence the Noether approach) is limited { more general results
are possible when the full Lie theory is used. We transform the field equation
to an autonomous equation and investigate the conditions for it to be reduced
to quadrature. For each case we recover particular results that were found pre
viously for neutral fluids. Finally we show (for the first time) that the pivotal
equation, governing the existence of a Lie symmetry, is actually a fifth order
purely differential equation, the solution of which generates solutions to the
master field equation. / Thesis (Ph.D.)University of KwaZuluNatal, Westville, 2011.

8 
Applications of Lie symmetries to gravitating fluids.Msomi, Alfred Mvunyelwa. January 2011 (has links)
This thesis is concerned with the application of Lie's group theoretic method
to the Einstein field equations in order to find new exact solutions. We analyse
the nonlinear partial differential equation which arises in the study of non
static, nonconformally flat fluid plates of embedding class one. In order to find
the group invariant solutions to the partial differential equation in a systematic and comprehensive manner we apply the method of optimal subgroups.
We demonstrate that the model admits linear barotropic equations of state in
several special cases. Secondly, we study a shearfree spherically symmetric
cosmological model with heat flow. We review and extend a method of generating solutions developed by Deng. We use the method of Lie analysis as a
systematic approach to generate new solutions to the master equation. Also,
general classes of solution are found in which there is an explicit relationship
between the gravitational potentials which is not present in earlier models.
Using our systematic approach, we can recover known solutions. Thirdly, we
study generalised shearfree spherically symmetric models with heat flow in
higher dimensions. The method of Lie generates new solutions to the master equation. We obtain an implicit solution or we can reduce the governing equation to a Riccati equation. / Thesis (Ph.D.)University of KwaZuluNatal, Westville, 2011.

9 
New analytical stellar models in general relativity.Thirukkanesh, Suntharalingam. January 2009 (has links)
We present new exact solutions to the Einstein and EinsteinMaxwell field equations that model the interior of neutral, charged and radiating stars. Several new classes of solutions in static spherically symmetric interior spacetimes are found in the presence of charge. These correspond to isotropic matter with a specified electric field intensity. Our solutions are found by choosing different rational forms for one of the gravitational potentials and a particular form for the electric field. The models generated contain results found previously including Finch and Skea (1989) neutron stars, Durgapal and Bannerji (1983) dense stars, Tikekar (1990) superdense stars in the limit of vanishing charge. Then we study the general situation of a compact relativistic object with anisotropic pressures in the presence of the electromagnetic field. We assume the equation of state is linear so that the model may be applied to strange stars with quark matter and dark energy stars. Several new classes of exact solutions are found, and we show that the densities and masses are consistent with real stars. We regain as special cases the Lobo (2006) dark energy stars, the Sharma and Maharaj (2007) strange stars and the realistic isothermal universes of Saslaw et al (1996). In addition, we consider relativistic radiating stars undergoing gravitational collapse when the fluid particles are in geodesic motion. We transform the governing equation into Bernoulli, Riccati and confluent hypergeometric equations. These admit an infinite family of solutions in terms of simple elementary functions and special functions. Particular models contain the Minkowski spacetime and the Friedmann dust spacetime as limiting cases. Finally, we model the radiating star with shear, acceleration and expansion in the presence of anisotropic pressures. We obtain several classes of new solutions in terms of arbitrary functions in temporal and radial coordinates by rewriting the junction condition in the form of a Riccati equation. A brief physical analysis indicates that these models are physically reasonable. / Thesis (Ph.D.)University of KwaZuluNatal, Westville, 2009.

10 
Relativistic spherical stars.Mkhwanazi, Wiseman Thokozani. January 1993 (has links)
In this thesis we study spherically symmetric spacetimes which are static with a
perfect fluid source. The Einstein field equations, in a number of equivalent forms,
are derived in detail. The physical properties of a relativistic star are briefly reviewed.
We specify two particular choices for one of the gravitational potentials.
The behaviour of the remaining gravitational potential is governed by a second order
differential equation. This equation has solutions in terms of elementary functions
for some cases. The differential equation, in other cases, may be expressed as Bessel,
confluent hypergeometric and hypergeometric equations. In such instances the solution
is given in terms of special functions. A number of solutions to the Einstein
field equations are generated. We believe that these solutions may be used to model
realistic stars. Many of the solutions found are new and have not been published
previously. In some cases our solutions are generalisations of cases considered previously.
For some choices of the gravitational potential our solutions are equivalent to
wellknown results documented in the literature; in these cases we explicitly relate
our solutions to those published previously. We have utilised the computer package
MATHEMATICA Version 2.0 (Wolfram 1991) to assist with calculations, and to
produce figures to describe the gravitational field. In addition, we briefly investigate
the approach of specifying an equation of state relating the energy density and the
pressure. The solution of the Einstein field equations, for a linear equation of state,
is reduced to integrating Abel's equation of the second kind. / Thesis (M.Sc.)University of Natal, Durban, 1993.

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