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ブラックホール上の様々なテンソル場の安定性解析

Yoshida, Daisuke 吉田, 大祐 ヨシダ, ダイスケ 神戸大学

2020.03.25

概要

The problem of solving field equations on black holes has been a long-standing challenge in physics and mathematics. A simple example is gravitational waves which were predicted in [1]. It was detected in 2015 [2]*1. But gravitational waves are not all the fields of interest on black holes. In principle, there can be other fields on the black hole. Moreover, from the point of a unified theory, the dimension is not limited to four dimensions. Therefore, it is important to consider various fields, establish a method for analyzing them, and derive their properties. However, the behavior of differential forms on a black hole has not been studied. Differential forms are a wider class of geometric quantities that include scalar fields and vector fields. In this thesis, we focus on the dynamics of the differential form on the black hole. Then, we will do the following. (i) We explain an appropriate decomposition method for a general form field under the spherical symmetry. (ii) Using the decomposition method, we derive the master equations of the arbitrary rank form field in any dimension. (iii) We study the master equation of the form field by the S-deformation method and show that the form field on the black hole is stable. (iv) By applying the WKB method, we calculate the quasinormal mode of the form field on the black hole. We also reveal the dimension dependence and the duality of the form field. Thus, we clarify the general properties of form fields on spherically symmetric black holes.

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