28 research outputs found
Some Exact Solutions in General Relativity
No full textIn this thesis four separate problems in general relativity are considered, divided
into two separate themes: coordinate conditions and perfect fluid spheres. Regarding
coordinate conditions we present a pedagogical discussion of how the appropriate
use of coordinate conditions can lead to simplifications in the form of the spacetime
curvature — such tricks are often helpful when seeking specific exact solutions of the
Einstein equations. Regarding perfect fluid spheres we present several methods of
transforming any given perfect fluid sphere into a possibly new perfect fluid sphere.
This is done in three qualitatively distinct manners: The first set of solution generating
theorems apply in Schwarzschild curvature coordinates, and are phrased in terms
of the metric components: they show how to transform one static spherical perfect
fluid spacetime geometry into another. A second set of solution generating theorems
extends these ideas to other coordinate systems (such as isotropic, Gaussian polar,
Buchdahl, Synge, and exponential coordinates), again working directly in terms of the
metric components. Finally, the solution generating theorems are rephrased in terms
of the TOV equation and density and pressure profiles. Most of the relevant calculations
are carried out analytically, though some numerical explorations are also carried
out
Rigorous Bounds on Transmission, Reflection, and Bogoliubov Coefficients
No full textThis thesis describes the development of some basic mathematical tools of wide relevance to mathematical physics. Transmission and reflection coefficients are associated with quantum tunneling phenomena, while Bogoliubov
coefficients are associated with the mathematically related problem of excitations
of a parametric oscillator. While many approximation techniques for these quantities are known, very little is known about rigorous upper and lower bounds. In this thesis four separate problems relating to rigorous bounds on transmission, reflection and Bogoliubov coefficients are considered, divided into four separate themes: Bounding the Bogoliubov coefficients; Bounding the greybody factors for Schwarzschild black holes; Transformation probabilities and the Miller-Good transformation;
Analytic bounds on transmission probabilities
Some Exact Solutions in General Relativity
No full textIn this thesis four separate problems in general relativity are considered, dividedinto two separate themes: coordinate conditions and perfect fluid spheres. Regardingcoordinate conditions we present a pedagogical discussion of how the appropriateuse of coordinate conditions can lead to simplifications in the form of the spacetimecurvature — such tricks are often helpful when seeking specific exact solutions of theEinstein equations. Regarding perfect fluid spheres we present several methods oftransforming any given perfect fluid sphere into a possibly new perfect fluid sphere.
This is done in three qualitatively distinct manners: The first set of solution generatingtheorems apply in Schwarzschild curvature coordinates, and are phrased in termsof the metric components: they show how to transform one static spherical perfectfluid spacetime geometry into another. A second set of solution generating theoremsextends these ideas to other coordinate systems (such as isotropic, Gaussian polar,Buchdahl, Synge, and exponential coordinates), again working directly in terms of themetric components. Finally, the solution generating theorems are rephrased in termsof the TOV equation and density and pressure profiles. Most of the relevant calculationsare carried out analytically, though some numerical explorations are also carriedout.</p
Spin One Hawking Radiation from Dirty Black Holes
No full textA “clean” black hole is a black hole in vacuum such as the Schwarzschild black hole. However in real physical systems, there are matter fields around a black hole. Such a black hole is called a “dirty black hole”. In this paper, the effect of matter fields on the black hole and the greybody factor is investigated. The results show that matter fields make a black hole smaller. They can increase the potential energy to a black hole to obstruct Hawking radiation to propagate. This causes the greybody factor of a dirty black hole to be less than that of a clean black hole
Near-Horizon Geodesics for Astrophysical and Idealised Black Holes: Coordinate Velocity and Coordinate Acceleration
No full textGeodesics (by definition) have an intrinsic 4-acceleration zero. However, when expressed in terms of coordinates, the coordinate acceleration d 2 x i / d t 2 can very easily be non-zero, and the coordinate velocity d x i / d t can behave unexpectedly. The situation becomes extremely delicate in the near-horizon limit—for both astrophysical and idealised black holes—where an inappropriate choice of coordinates can quite easily lead to significant confusion. We shall carefully explore the relative merits of horizon-penetrating versus horizon-non-penetrating coordinates, arguing that in the near-horizon limit the coordinate acceleration d 2 x i / d t 2 is best interpreted in terms of horizon-penetrating coordinates
