Thesis (M. Sc.)--University of Hong Kong, 2003. / Also available in print.

Thesis (M. Sc.)--University of Hong Kong, 2003.

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No description available.

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of requirements for the degree of Master of Science. 01 September 2014. / In this thesis I explore the evidence for whether gravity is an emergent phenomenon. I provide a review of black hole thermodynamics and demonstrate how it provides evidence that gravity is an emergent phe- nomenon. In addition I provide a review of Jacobson's calculation which shows how the Einstein eld equations can be interpreted as a thermo- dynamic equation of state. I then use Jacobson's work and the Seiberg- Witten map to derive a new gravitational equation of state which shows what gravity on a non-commutative manifold would look like.

The definition of the shape of the geoid is a fundamental objective of geodesy, since it allows for the conversion between orthometric and ellipsoidal height systems. The geoid can be computed from gravity values measured over the surface of the earth, and considerable effort continues to achieve a global coverage of gravity values. One technique that has been very successful in recent years in providing gravity coverage in areas which previously have been too difficult to access is airborne gravimetry. This technique has proved very useful in covering near offshore regions, for example. The coastal regions of Australia are recognised as locations where airborne gravimetry has the potential to fill in missing gravity data. A pilot survey using an airborne gravity meter was undertaken off the north east coast of Australia. In areas that remain unsurveyed it is sometimes useful to fill in the missing gravity data values with predicted gravity values. Previous research has examined the possibility of predicting gravity values from other observed quantities. The best success has been achieved by using the gravity effect calculated from bathymetric information. Often the corresponding isostatic compensation is computed, and the combined bathymetric-isostatic gravity effect is used. However, the type and extent of compensation that exists in any particular region mostly remains unknown. Theoretical considerations indicate that the short wavelength part of the gravity field may be adequately modelled by the gravity effect of the bathymetry alone, without reference to an assumed compensation mechanism. With this in mind, a prediction scheme has been developed which utilises the short wavelength gravity field information implied by the bathymetry, combined with the long wavelength gravity field information from existing observed gravity. This scheme allows the prediction of ???fill-in??? gravity values in areas with limited observed gravity. The prediction technique was used on a test set of data off the east coast of Greenland. The prediction technique was seen to outperform a simple interpolation of gravity values by approximately ten percent. Geoid computations performed with the predicted gravity values indicate that the prediction technique can provide significant improvements in computed geoids.

Techniques for computing gravity anomalies by multipole expansions obtained from surface integrals and volume integrals are derived together with a vertical line element method. The results are compared with exact calculation for right rectangular prisms and right circular cylinders and the effects of block size and separation between the field point and source body are evaluated. For sources near field points, the multipole expansion of volume integrals consistantly yielded more accurate approximations of the gravity field than either vertical line element or surface integrals. For a given source, the surface integral method compared to vertical line elements gives a better approximation of the field. As distance increases, all three techniques yield accurate gravity values. Improved estimates of the gravity field can be obtained by subdividing the source body into small elements and summing the effect of the elements. The 2nd-order or quadrupole term of the expansions is dominant for near sources while the 0th-order or monopole term becomes increasingly important with increasing separation of the source and field point. / Graduation date: 1971

Graduation date: 1979

Graduation date: 1968

The cosmology in the Hubble expansion era of the Horava-Witten M-theory compactified on a Calabi-Yau threefold is studied in the reduction to five-dimensions where the effects of the Calabi-Yau manifold are summarized by the volume modulus, and all perturbative potentials are included. Matter on the branes are treated as first order perturbations of the static vacuum solution, and all equations in the bulk and all boundary conditions on both end branes are imposed. It is found that for a static volume modulus and a static fifth dimension, y, one can recover the four dimensional Robertson-Friedmann-Walker cosmology for relativistic matter on the branes, but not for non-relativistic matter. For relativistic matter, the Hubble parameter H becomes independent of y to first order in matter density, and if a consistent solution for nonrelativistic matter exists it would require H to be y dependent. These results hold also when an arbitrary number of 5-branes are included in the bulk. The five dimensional Horava-Witten model is compared with the Randall Sundrum phenomenology with a scalar field in the bulk where a bulk and brane potential are used so that the vacuum solutions can be rigorously obtained.(In the Appendix, the difficulty of obtaining approximate vacuum solutions for other potentials is discussed.) In this case nonrelativistic matter is accommodated by allowing the distance between the branes to vary. It is suggested that non-perturbative potentials for the vacuum solution of Horava-Witten theory are needed to remove the inconsistency that non-relativistic matter creates. Also considered is the problem of gravitational forces between point particles on the branes in a Randall-Sundrum (R-S) two brane model with S1/Z2 symmetry. Matter is assumed to produce a perturbation to the R-S vacuum metric and all the 5D Einstein equations are solved to linearized order (for arbitrary matter on both branes). We show that while the gauge condition hi5 = 0, i = 0, 1, 2, 3 can always be achieved without brane bending, the condition h55 = 0 leads to large brane bending. The static potential arising from the zero modes and the corrections due to the Kaluza-Klein (KK) modes are calculated. Gravitational forces on the Planck (y1 = 0) brane recover Newtonian physics with small KK corrections (in accord with other work). However, forces on the TeV (y2) brane due to particles on that brane are strongly distorted by large R-S exponentials, making the model in disagreement with experiment if the TeV brane is the physical brane.