[[alternative]]Classical and Quantum Aspects of Black Holes and Solitons

計畫編號：NSC96-2112-M032-006-MY3研究期間：200908~201007研究經費：627,000[[abstract]]在這個計劃中，我們會進行重力理論和量子場論的研究。在重力理論 方面，重點是在黑洞的物理，其中包括高維黑洞的研究，我們會先考慮球 對稱的黑洞中，Dirac 場的準正常態、power-tail 和散射中吸收和放射的機 率。另外，我們會在有compact 的額外空間下，考慮黑弦和黑brane 的穩定 性，以及它們的相變。接下來我們會探討高維的Kerr 黑洞，即Myers-Perry 黑洞，在自旋很大時是否穩定，同時也會計算在這種情況下，各種場的準 正常態、power-tail 和散射情形。另一方面，我們希望利用stochastic 重力理 論，來探討在超越半古典的近似時，量子場的波動對於黑洞時空的影響， 以及黑洞熵的問題。最後，關於量子場論方面，我們也會考慮規範場的孤 立子解，包括尋找有compact 額外空間時，各種磁單子和instanton 的解， 並分析它們的穩定性，量子修正項，以及與超對稱的關係。 In this proposal, we plan to study the theory of gravity and that of quantum fields. On the gravity side, our concentration is on the physics of black hole. First, we shall consider the higher-dimensional black holes. In the case of the spherically symmetric black holes, we shall evaluate the corresponding quasinormal modes, the late-time power-tails and the scattering absorption and emission probabilities of the Dirac field. Then we shall examine, in the presence of compact dimensions, the stability of black strings and black branes, as well as their phase structures. We shall also consider higher-dimensional Kerr black holes, the Myers-Perry black holes. We would like to see if they are stable when the angular momentum of the black hole goes to infinity. At the same time, we shall calculate the quasinormal frequencies, the radiation power-tail and the scattering process in this situation. On the other hand, to go beyond the semi-classical approximation we shall investigate how the fluctuation of the quantum field energy-momentum tensor would affect the black hole spacetime with the theory of stochastic gravity. We shall also consider the question of black hole entropy in this formalism. Lastly, also in the study of quantum field theory, our concern is on solitons of nonabelian gauge theories. This includes the search for magnetic monopole and instanton solutions in cases with compact internal dimensions. We shall examine their stability, various quantum corrections, and their possible relation to supersymmetry.[[sponsorship]]行政院國家科學委員