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Linear Perturbations of Spherically Symmetric Black Holes and Their Stability

片桐 拓弥 立教大学

2022.06.02

概要

本論文で、申請者は、一般相対論における球対称ブラックホール解の線形摂動と安定性に関して新たな知見を得た。

第四章では、遠方において特有の構造を持つ AdS 時空と呼ばれる時空中の帯電したブラックホールについて、中性スカラー場と荷電スカラー場の摂動のふるまいを解析した。その際、Robin 境界条件と呼ばれる 1 パラメータで特徴づけられる一般的な境界条件を遠方で課した。準固有振動数から安定性の情報を読み取ることで、中性スカラー場摂動に対しては境界条件に依存して不安定性が現れること、荷電スカラー場に対しては、特定の条件のもとで境界条件に依らず超放射不安定性が現れることを明らかにした。

第五章では、極限帯電ブラックホールに付随する Aretakis 定数とそれに起因する Aretakis 不安定性について、ブラックホール近傍の幾何学的構造の観点から再考した。その結果、Aretakis 定数の存在は、ブラックホール近傍の幾何学的構造が持つ対称性の帰結として理解できること、Aretakis 不安定性は、ある物理的意味のある座標系における共変微分の成分の発散に対応していることが明らかになった。

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