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`http://hdl.handle.net/2381/28008`

Title: | A Quantum Langevin Approach to Hawking Radiation |

Authors: | Abel, Paul Gordon |

Supervisors: | Raine, Derek Gurman, Stephen |

Award date: | 1-May-2013 |

Presented at: | University of Leicester |

Abstract: | 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. |

Links: | http://hdl.handle.net/2381/28008 |

Type: | Thesis |

Level: | Doctoral |

Qualification: | PhD |

Rights: | Copyright © the author. All rights reserved. |

Appears in Collections: | Theses, Dept. of Physics and Astronomy Leicester Theses |

Files in This Item:

File | Description | Size | Format | |
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2013AbelPGPhD.pdf | 900.48 kB | Adobe PDF | View/Open |

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