title: Geodesic Geometry of Black Holes

authors: Slezakova, Gabriela

subjects: geodesic

abstract: The study of geodesics is of intrinsic significance in the study of the geometry of space-time. In this thesis null, space-like and
time-like geodesics are studied in the case of the space-times of Schwarzschild, Reissner-Nordstrouml;m and Kerr black holes. These
space-times have been investigated with varying degrees of thoroughness in many articles and some books. However, there are some significant gaps in these treatments and the central aim of this thesis is to fill these gaps where necessary. Moreover, the following topics are covered for the first time.
1. In Chapter 4 a thorough treatment of the space-like geodesics of the Schwarzschild solutions has been given. These geodesics are the trajectories of Tachyons (faster than light particles) and are
treated in a complete manner. This has been done by obtaining exact solutions and solving them numerically.
2. In Part II all solutions for geodesics for a
Reissner-Nordstrouml;m black hole have been given in complete detail, i.e. time-like, null and space-like geodesics and orbit of a charged particle.
3. In Chapter 14 all solutions for geodesics in the equatorial plane of a Kerr black hole have been given in complete detail, i.e. time-like, null and space-like geodesics.
4. The study of special types of non-equatorial geodesics for a Kerr black hole have been given in complete detail, i.e. time-like (Chapter 17), null (Chapter 15) and space-like (Chapter 16). This has been done in order to distinguish the qualitatively different types of solutions.

Calculation of the explicit formulas, which describe these geodesics, as well as numerically computed diagrams representing the geodesics have been incorporated in these studies. The following subjects have been also treated:
5.  Solutions for the geodesics in Reissner-Nordstrouml;m black holes with |Q_*| gt;= M, which are black holes with one (|Q_*| = M) or no horizon (|Q_*|gt; M) (Chapter 8).
6. Solutions of geodesics in extreme and fast Kerr black holes, i.e. black holes with a = M (extreme) and a gt; M (fast). As in the case of |Q_*| gt; M, fast black holes have naked singularities (Chapter 14).
7. Some general observations about orbit types of the Kerr black holes regarding relationships between parameters such as angular momentum, energy, Carter constant and mass and angular momentum of black holes (Chapter 13).
8. Some corrections to errors found in the literature.

While it has not been possible to cover all different cases which occur for possible relations amongst the parameters specifying a
general black hole, interesting geodesics have, however, been studied and a more thorough  presentation of the properties of geodesics has now been given.

text: Geodesic Geometry of Black Holes The study of geodesics is of intrinsic significance in the study of the geometry of space-time. In this thesis null, space-like and
time-like geodesics are studied in the case of the space-times of Schwarzschild, Reissner-Nordstrouml;m and Kerr black holes. These
space-times have been investigated with varying degrees of thoroughness in many articles and some books. However, there are some significant gaps in these treatments and the central aim of this thesis is to fill these gaps where necessary. Moreover, the following topics are covered for the first time.
1. In Chapter 4 a thorough treatment of the space-like geodesics of the Schwarzschild solutions has been given. These geodesics are the trajectories of Tachyons (faster than light particles) and are
treated in a complete manner. This has been done by obtaining exact solutions and solving them numerically.
2. In Part II all solutions for geodesics for a
Reissner-Nordstrouml;m black hole have been given in complete detail, i.e. time-like, null and space-like geodesics and orbit of a charged particle.
3. In Chapter 14 all solutions for geodesics in the equatorial plane of a Kerr black hole have been given in complete detail, i.e. time-like, null and space-like geodesics.
4. The study of special types of non-equatorial geodesics for a Kerr black hole have been given in complete detail, i.e. time-like (Chapter 17), null (Chapter 15) and space-like (Chapter 16). This has been done in order to distinguish the qualitatively different types of solutions.

Calculation of the explicit formulas, which describe these geodesics, as well as numerically computed diagrams representing the geodesics have been incorporated in these studies. The following subjects have been also treated:
5.  Solutions for the geodesics in Reissner-Nordstrouml;m black holes with |Q_*| gt;= M, which are black holes with one (|Q_*| = M) or no horizon (|Q_*|gt; M) (Chapter 8).
6. Solutions of geodesics in extreme and fast Kerr black holes, i.e. black holes with a = M (extreme) and a gt; M (fast). As in the case of |Q_*| gt; M, fast black holes have naked singularities (Chapter 14).
7. Some general observations about orbit types of the Kerr black holes regarding relationships between parameters such as angular momentum, energy, Carter constant and mass and angular momentum of black holes (Chapter 13).
8. Some corrections to errors found in the literature.

While it has not been possible to cover all different cases which occur for possible relations amongst the parameters specifying a
general black hole, interesting geodesics have, however, been studied and a more thorough  presentation of the properties of geodesics has now been given.

year: 2006

title: Geomorphological mapping of ice-free areas using polarimetric RADARSAT-2 data on Fildes Peninsula and Ardley Island, Antarctica

authors: Schmid, T.

subjects: periglacial

abstract: Satellite-borne Synthetic Aperture Radar (SAR) has been used for characterizing and mapping in two relevant ice-free areas in the South Shetland Islands. The objective has been to identify and characterize land surface covers that mainly include periglacial and glacial landforms, using fully polarimetric SAR C band RADARSAT-2 data, on Fildes Peninsula that forms part of King George Island, and Ardley Island. Polarimetric parameters obtained from the SAR data, a selection of field based training and validation sites and a supervised classification approach, using the support vector machine were chosen to determine the spatial distribution of the different landforms. Eight periglacial and glacial landforms were characterized according to their scattering mechanisms using a set of 48 polarimetric parameters. The mapping of the most representative surface covers included colluvial deposits, stone fields and pavements, patterned ground, glacial till and rock outcrops, lakes and glacier ice. The overall accuracy of the results was estimated at 81%, a significant value when mapping areas that are within isolated regions where access is limited. Periglacial surface covers such as stone fields and pavements occupy 25% and patterned ground over 20% of the ice-free areas. These are results that form the basis for an extensive monitoring of the ice-free areas throughout the northern Antarctic Peninsula region.

text: Geomorphological mapping of ice-free areas using polarimetric RADARSAT-2 data on Fildes Peninsula and Ardley Island, Antarctica Satellite-borne Synthetic Aperture Radar (SAR) has been used for characterizing and mapping in two relevant ice-free areas in the South Shetland Islands. The objective has been to identify and characterize land surface covers that mainly include periglacial and glacial landforms, using fully polarimetric SAR C band RADARSAT-2 data, on Fildes Peninsula that forms part of King George Island, and Ardley Island. Polarimetric parameters obtained from the SAR data, a selection of field based training and validation sites and a supervised classification approach, using the support vector machine were chosen to determine the spatial distribution of the different landforms. Eight periglacial and glacial landforms were characterized according to their scattering mechanisms using a set of 48 polarimetric parameters. The mapping of the most representative surface covers included colluvial deposits, stone fields and pavements, patterned ground, glacial till and rock outcrops, lakes and glacier ice. The overall accuracy of the results was estimated at 81%, a significant value when mapping areas that are within isolated regions where access is limited. Periglacial surface covers such as stone fields and pavements occupy 25% and patterned ground over 20% of the ice-free areas. These are results that form the basis for an extensive monitoring of the ice-free areas throughout the northern Antarctic Peninsula region.

year: 2016

title: Implications and opportunities for Maori land in the Rotorua catchment

authors: Tahana, Arapeta

abstract: Arapeta is the Portfolio Manager, Waiariki Region, at Te Tumu Paeroa. He works with Maori land owners to enable them to achieve higher aspirations for their land and assets. He also collaborates with a wide range of other people and organisations, from owners in Māori land blocks, to government agencies, private sector companies and experts in many fields to find innovative and pragmatic solutions to the challenges of growing Māori. He is an elected member on the Māori Advisory Committee to RDC working to develop a meaningful partnership between Te Arawa and the Council.

text: Implications and opportunities for Maori land in the Rotorua catchment Arapeta is the Portfolio Manager, Waiariki Region, at Te Tumu Paeroa. He works with Maori land owners to enable them to achieve higher aspirations for their land and assets. He also collaborates with a wide range of other people and organisations, from owners in Māori land blocks, to government agencies, private sector companies and experts in many fields to find innovative and pragmatic solutions to the challenges of growing Māori. He is an elected member on the Māori Advisory Committee to RDC working to develop a meaningful partnership between Te Arawa and the Council.

year: 2013