時空の熱力学的性質に対する量子効果及び非平衡効果の研究

时空热力学性质的量子效应和非平衡效应研究

• 批准号: 12J04598
• 负责人: 岡澤 晋
• 金额: $ 0.58万
• 依托单位: The Graduate University for Advanced Studies
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for JSPS Fellows
• 财政年份: 2012
• 资助国家: 日本
• 起止时间: 2012 至 2013
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12J04598/
• 关键词: ブラックホール熱力学; Hawking輻射; membrane paradigm; 時空の熱力学

・Membrane paradigmに平衡周りの揺らぎを取り入れるという研究に関して、先行研究の手法を拡張する形で定式化を行い、博士論文に成果をまとめた。元々のmembrane paradigmとは、ブラックホールホライズンから僅かに外側にstretched horizonと呼ばれる面を考え、その面に垂直な電場がmembrane上の仮想物質の電荷密度を与え、面に水平な磁場が仮想物質の電流密度を与え、面に水平な電場と仮想電流が比例し(Ohmの法則)、ブラックホールに吸収されるエネルギー量がJouleの発熱法則と解釈出来る、というものだった。本研究の狙いは、ここにHawking輻射の効果を取り入れることであり、membrane上の仮想電流にノイズ項が生じることが予想された。実際、得られた結果によると、電流と電場の比例関係であるOhmの法則はノイズ平均の意味でのみ成り立ち、Jouleの法則は発熱項だけでなくHawking輻射による放熱項も含む形に拡張されることがわかった。・Einstein方程式を時空の熱力学から導出するというJacobsonによる考え方について、異なる定式化を提案し、専門雑誌に投稿、掲載された。元々のJacobsonの考え方には、観測者の取り方の不自然さと、測地線束のexpansionが消える条件が必要になる、という困難があった。また、高階微分を含むような重力理論への拡張は、f(R)重力のような限られた理論で達成されていたものの、どこまで拡張出来るのか不明であった。そこで我々は、観測者の取り方を自然なものに変え、測地線のexpansionの値を非零とし、任意のヌル超曲面でクラウジウス関係式を仮定することを出発点として、Einstein方程式、もしくはf(R)重力の運動方程式、を導く条件を解析し、結果を与えた。

·Membrane paradigm is balanced, and research is carried out in advance. The membrane paradigm is divided into two parts: the outer stretched horizon and the outer stretched horizon. The vertical electric field is divided into two parts: the electric charge density of the desired substance on the membrane and the electric current density of the desired substance. The horizontal magnetic field is divided into two parts: the electric current density of the desired substance and the electric current density of the desired substance. The horizontal electric field is divided into two parts: the electric current density of the desired substance and the electric current density of the desired substance. The electric current density of the desired substance is divided into two parts: the electric current density of the desired substance and the electric current density of the desired substance. The electric current density of the desired substance is divided into two parts: the electric current density of the desired substance and the electric current density of the desired substance. The electric current density of the desired substance is divided into three parts: the electric current density of the desired substance and the electric current density of the desired substance. The electric current density of the desired substance is divided into three parts: the electric current density of the desired substance and the electric current density of the desired substance. The electric current density of the desired substance is divided into three parts: the electric In this study, the effects of Hawking radiation were studied. In practice, the proportional relationship between the current and the electric field is obtained. The law of Ohm means that the heat term is generated. The law of Hawking radiation contains the heat term. Einstein equation is derived from the thermodynamics of space-time. Jacobson equation is derived from Jacobson equation. The original Jacobson's test method is not natural, the surveyor's test method is not natural, the geodetic bundle's expansion is necessary, and the difficulty is difficult. The theory of gravity is not clear, and the theory of gravity is not clear. The equation of gravity, Einstein equation, equation of motion of gravity, equation of gravity, equation of gravity.