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Extensions to general relativity are often considered as possibilities in the quest for a quantum theory of gravity on one hand, or to resolve anomalies within cosmology on the other. Scalar fields, found in many areas of physics, are frequently studied in this context. This is partly due to their manifestation in the effective four dimensional theory of a number of underlying fundamental theories, most notably string theory. This thesis is concerned with the effects of scalar fields on cosmological and black hole solutions. By comparison, an analysis of an inhomogeneous cosmological model which requires no extensions to general relativity is also undertaken. In chapter three, examples of numerical solutions to black hole solutions, which have previously been shown to be linearly stable, are found. The model includes at least two scalar fields, non-minimally coupled to electromagnetism and hence possesses non-trivial contingent primary hair. We show that the extremal solutions have finite temperature for an arbitrary coupling constant. Chapter four investigates the effects of higher order curvature corrections and scalar fields on the late-time cosmological evolution. We find solutions which mimic many of the phenomenological features seen in the post-inflation Universe. The effects due to non-minimal scalar couplings to matter are also shown to be negligible in this context. Such solutions can be shown to be stable under homogeneous perturbations. Some restrictions on the value of the slope of the scalar coupling to the Gauss-Bonnet term are found to be necessary to avoid late-time superluminal behaviour and dominant energy condition violation. A number of observational tests are carried out in chapter five on a new approach to averaging the inhomogeneous Universe. In this "Fractal Bubble model" cosmic acceleration is realised as an apparent effect, due to quasilocal gravitational energy gradients. We show that a good fit can be found to three separate observations, the type Ia supernovae, the baryon acoustic oscillation scale and the angular scale of the sound horizon at last scattering. The best fit to the supernovae data is χ² ≃ 0:9 per degree of freedom, with a Hubble parameter at the present epoch of H0 = 61:7+1:4 -1:3 km sec⁻¹ Mpc⁻¹ , and a present epoch volume void fraction of 0:76 ± 0:05.

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A dissertation presented to The Faculty of Science University of the Witwatersrand Johannesburg in ful lment of the requirements for the degree of Master of Science June 2015 / At nite N, the number of restricted Schur polynomials is greater than, or equal to the number of generalized restricted Schur polynomials. In this dissertation we study this dis- crepancy and explain its origin. We conclude that, for quiver gauge theories, in general, the generalized restricted Shur polynomials correctly account for the complete set of nite N constraints and they provide a basis, while the restricted Schur polynomials only account for a subset of the nite N constraints and are thus overcomplete. We identify several situations in which the restricted Schur polynomials do in fact account for the complete set of nite N constraints. In these situations the restricted Schur polynomials and the gen- eralized restricted Schur polynomials both provide good bases for the quiver gauge theory. Further, we demonstrate situations in which the generalized restricted Schur polynomials reduce to the restricted Schur polynomials and use these results to study the anomalous dimensions for scalar operators in ABJM theory in the SU(2) sector. The operators we consider have a classical dimension that grows as N in the large N limit. Consequently, the large N limit is not captured by summing planar diagrams { non-planar contributions have to be included. We nd that the mixing matrix at two-loop order is diagonalized using a double coset ansatz, reducing it to the Hamiltonian of a set of decoupled oscilla- tors. The spectrum of anomalous dimensions, when interpreted in the dual gravity theory, shows that the energy of the uctuations of the corresponding giant graviton is dependent on the size of the giant. The rst subleading corrections to the large N limit are also considered. These subleading corrections to the dilatation operator do not commute with the leading terms, indicating that integrability probably does not survive beyond the large N limit.

by Tsang Yue Kin. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 120-122). / by Tsang Yue Kin. / Contents --- p.ii / List of Figures --- p.iv / List of Tables --- p.vi / Abstract --- p.vii / Acknowledgement --- p.viii / Chapter Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- Probability Density Function in Turbulence --- p.2 / Chapter 1.2 --- Scaling Laws in Turbulence --- p.6 / Chapter Chapter 2. --- The Problem --- p.12 / Chapter 2.1 --- Random Advection of a Passive Scalar --- p.12 / Chapter 2.2 --- Numerical Implementation --- p.14 / Chapter Chapter 3. --- Statistics of Scalar Fluctuation --- p.19 / Chapter 3.1 --- Results --- p.19 / Chapter 3.1.1 --- Probability Density Function of Scalar Fluctuation --- p.20 / Chapter 3.1.2 --- Exact Formula for PDF --- p.20 / Chapter 3.1.3 --- Other Velocity Statistics --- p.24 / Chapter 3.2 --- Conditional Averages q(x) and r(x) --- p.25 / Chapter 3.2.1 --- q(x) --- p.25 / Chapter 3.2.2 --- r(x) --- p.39 / Chapter 3.2.3 --- PDF calculated from various forms of q(x) and r(x) --- p.46 / Chapter 3.3 --- Other Velocity Statistics --- p.55 / Chapter Chapter 4. --- Statistics of Scalar Difference --- p.75 / Chapter 4.1 --- PDF of Scalar Difference --- p.75 / Chapter 4.1.1 --- Results --- p.76 / Chapter 4.1.2 --- Relation between PT{x) and 5S2n(T) --- p.80 / Chapter 4.2 --- Scaling of S2n(T) --- p.82 / Chapter 4.3 --- Other Velocity Statistics --- p.90 / Chapter 4.4 --- Discussions --- p.103 / Chapter Chapter 5. --- Conclusion --- p.105 / Appendix A. PDF of Stream Functions --- p.107 / Chapter A.1 --- General Formalism --- p.107 / Chapter A.2 --- Applications --- p.108 / Appendix B. Generation of Random Deviates --- p.112 / Appendix C. Check of Stationarity --- p.114 / Appendix D. Calculations of the coefficients of q(x) and r(x) --- p.117 / Bibliography --- p.120

Extensions to general relativity are often considered as possibilities in the quest for a quantum theory of gravity on one hand, or to resolve anomalies within cosmology on the other. Scalar fields, found in many areas of physics, are frequently studied in this context. This is partly due to their manifestation in the effective four dimensional theory of a number of underlying fundamental theories, most notably string theory. This thesis is concerned with the effects of scalar fields on cosmological and black hole solutions. By comparison, an analysis of an inhomogeneous cosmological model which requires no extensions to general relativity is also undertaken. In chapter three, examples of numerical solutions to black hole solutions, which have previously been shown to be linearly stable, are found. The model includes at least two scalar fields, non-minimally coupled to electromagnetism and hence possesses non-trivial contingent primary hair. We show that the extremal solutions have finite temperature for an arbitrary coupling constant. Chapter four investigates the effects of higher order curvature corrections and scalar fields on the late-time cosmological evolution. We find solutions which mimic many of the phenomenological features seen in the post-inflation Universe. The effects due to non-minimal scalar couplings to matter are also shown to be negligible in this context. Such solutions can be shown to be stable under homogeneous perturbations. Some restrictions on the value of the slope of the scalar coupling to the Gauss-Bonnet term are found to be necessary to avoid late-time superluminal behaviour and dominant energy condition violation. A number of observational tests are carried out in chapter five on a new approach to averaging the inhomogeneous Universe. In this "Fractal Bubble model" cosmic acceleration is realised as an apparent effect, due to quasilocal gravitational energy gradients. We show that a good fit can be found to three separate observations, the type Ia supernovae, the baryon acoustic oscillation scale and the angular scale of the sound horizon at last scattering. The best fit to the supernovae data is χ² ≃ 0:9 per degree of freedom, with a Hubble parameter at the present epoch of H0 = 61:7+1:4 -1:3 km sec⁻¹ Mpc⁻¹ , and a present epoch volume void fraction of 0:76 ± 0:05.

Thesis (Ph. D.)--University of Canterbury, 2007. / Typescript (photocopy). Includes bibliographical references (p. 117-140). Also available via the World Wide Web.

Thesis (M.S.)--Rutgers University, 2008. / "Graduate Program in Electrical and Computer Engineering." Includes bibliographical references (p. 60-61).

As equações de movimento de uma partícula (nucleon) interagindo com um campo escalar (mesônico) são obtidas pelo método dos momentos do tensor energia-momentum, de Papapetrou. Depois de um estudo detalhado do campo de radiação mesônico estabelecemos a expressão da força de reação de radiação do campo sobre a partícula. / The equations of motion of a particle (nucleon) interacting with a scalar (mesonic) field are derived by the energy-momentum tensor moments method of Papapetrou. After a detailed study of the mesonic radiation field we establish an expression of the reactive radiation force on the field upon the particle.

by Chi-chung Lee. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1993. / Includes bibliographical references (leaves 45-47). / INTRODUCTION --- p.1 / Chapter CHAPTER 1 --- RADIAL SYMMETRY OF GROUND STATES --- p.7 / Chapter CHAPTER 2 --- EXISTENCE OF A GROUND STATE --- p.14 / Chapter CHAPTER 3 --- UNIQUENESS OF GROUND STATE I --- p.23 / Chapter CHAPTER 4 --- UNIQUENESS OF GROUND STATE II --- p.35 / REFERENCES --- p.45