Thesis (Ph. D.)--Rutgers University, 2009. / "Graduate Program in Physics and Astronomy." Includes bibliographical references (p. 75-80).

Thesis (Ph. D.)--University of Washington, 2003. / Vita. Includes bibliographical references (p. 205-211).

Thesis (Ph. D.)--University of Texas at Austin, 1999. / Vita. Includes bibliographical references (leaves 206-219). Available also in a digital version from Dissertation Abstracts.

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An investigation of Hawking radiation and a method for calculating particle creation in Schwarzschild spacetime using a quantum Langevin approach is presented in this thesis. In particular we shall show that an oscillator confined to a free-fall trajectory in Schwarzschild spacetime radiates as a result of such motions, and this radiation can be interpreted as Hawking radiation. In chapter 1 we present a literature review of the underlying concept: the Unruh effect. We also present some introductory material pertinent to the calculations. Chapter 2 is concerned with the case of a thin collapsing shell to form a black hole in Schwarzschild anti-de Sitter spacetime. We determine the temperature of the black hole to be T[subscript H] = h(r[subscript h])/4π = κ/2π where h(r[subscript h]) is the factorization of the conformal factor, r is the radial coordinate with the location of the horizon situated atr = r[subscript h], and κ the surface gravity. We also calculate the stress tensor at early and late spacetimes which allows us to calculate the renormalized stress-tensor {T[subscript μν]} which satisfies the semi-classical Einstien field equations. In chapter 3 we examine the case of a harmonic oscillator in 2D Schwarzschild spacetime and we show that the choice of trajectory is responsible for making the oscillator radiate. In chapter 4 we derive a quantum Langevin equation for the oscillator in the Heisenberg picture. By solving this equation using the Wigner-Weiskopff approximation we show that, in the case of an oscillator confined to a free fall trajectory in Schwarzschild spacetime, the oscillator radiates with respect to the Boulware vacuum. In agreement with Hawking[1] we obtain a temperature of the black hole as T = 1/8πM[subscript B]. In chapter 5 we present our conclusions and recommendations for further work.

This thesis establishes a precise mathematical connection between the Einstein equations of general relativity and the incompressible Navier-Stokes equation of fluid dynamics. We carry out a holographic analysis which relates solutions to the Einstein equations to the behaviour of a dual fluid living in one fewer dimensions. Gravitational systems are found to exhibit Navier-Stokes behaviour when we study the dynamics of the region near an event horizon. Thus, we find non-linear deformations of Einstein solutions which, after taking a suitable near horizon limit and imposing our particular choice of boundary conditions, turn out to be precisely characterised by solutions to the incompressible Navier-Stokes equation. In other words, for any solution to the Navier-Stokes equation, the set-up we present provides a solution to the Einstein equations near a horizon. We consider the cases of fluids flowing on the plane and on the sphere. Fluid dynamics on the plane is analysed foremost in the context of a flat background geometry whilst the spherical analysis is undertaken for Schwarzschild black holes and the static patch of four-dimensional de Sitter space. / Physics

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