In a series of recent works the relevance of gravitational boundary degrees of freedom and their dynamics in gravity quantization and black hole information has been explored. In this work we further the progress by keenly focusing on the boundary degrees of freedom as the origin of black hole entropy. Wald's entropy formula is scrutinized, and the reason that the Wald's formula correctly captures the entropy of a black hole is examined. Afterwards, limitations of the Wald's method are discussed; a coherent view of entropy based on boundary dynamics is presented. The discrepancy observed in the literature between holographic and Wald's entropies is addressed. We generalize the entropy definition so as to handle a time-dependent black hole. Large gauge symmetry plays a pivotal role. Non-Dirichlet boundary conditions and gravitational analogues of Coleman-De Luccia bounce solutions are central in identifying the microstates and differentiating the origins of entropies associated with different classes of solutions. The result in the present work leads to a view that black hole entropy is entanglement entropy in a thermodynamic setup.
Cosmological scenarios with bounce and Genesis in Horndeski theory and beyond: An essay in honor of I.M. Khalatnikov on the occasion of his 100th birthday
Black Bounce Solutions from a Self-Interacting 3-Form Field in General Relativity
Institute of Astrophysics and Space Sciences, Faculty of Sciences, University of Lisbon（里斯本大学理学院天体物理与空间科学研究所）；Department of Physics, Faculty of Sciences, University of Lisbon（里斯本大学理学院物理学系）；Faculty of Physics, Graduate Program in Physics, Federal University of Pará（帕拉联邦大学物理学院物理研究生项目）；Faculty of Exact Sciences and Technology, Federal University of Pará（帕拉联邦大学精确科学与技术学院）
Black bounce solutions via nonminimal scalar-electrodynamic couplings
Instituto de Astrofísica e Ciências do Espaço（天体物理学与空间科学研究所）；Faculdade de Ciências da Universidade de Lisboa（里斯本大学理学院）；Universidade Federal do Pará（帕拉联邦大学）；Universidade Federal do Sul e Sudeste do Pará（帕拉南和东南联邦大学）；Faculdade de Ciências Exatas e Tecnologia（精确科学与技术学院）
Fooling the Censor: Going beyond inner horizons with the OPE
School of Mathematics and Hamilton Mathematics Institute, Trinity College（三一学院数学与汉密尔顿数学研究所）；MIT Center for Theoretical Physics—a Leinweber Institute, Massachusetts Institute of Technology（麻省理工学院莱因韦伯理论物理中心）；Faculty of Mathematics and Physics, University of Ljubljana（卢布尔雅那大学数学与物理学院）
Instability of asymptotically anti de Sitter black holes under Robin conditions at the timelike boundary
渐近反de Sitter事件视界外的静态区域有一个共形类时边界$\mathscr{I}$，在此边界上必须施加边界条件，使线性场从初始数据的演化成为适定问题.只有齐次狄利克雷、诺依曼或罗宾条件保持背景等距群对解空间的作用。我们研究的情况下，其中的线性场的模态分解导致潜在的不发散共形类时边界。我们证明了，总是有一个不稳定性，如果罗宾边界条件足够大的$γ$（商之间的导数的字段和字段的边界值）是允许的。我们解释了这种不稳定性的起源，表明，非负电位的模式有一个单一的不稳定状态，并证明了这个状态的一些属性。虽然我们的结果一般适用于半无限区域上的1+1波动方程，但我们的动机是在物理学中发起的黑洞非模态线性稳定性计划的背景下分析四维Schwarzschild anti de Sitter黑洞（SAdS ${}_4$）的引力稳定性。修订版本\ Lett. { \bf 112}，191101（2014），以及交换奇模和偶模的相关超对称类型的对偶。我们证明，这种对称性被打破，除非当一个组合的狄利克雷条件在偶数部门和一个特定的罗宾条件在奇数部门被强制执行，反之亦然，只有这两个选择的第一个导致一个稳定的动态。
Boundaries in the Instantaneous Formulation of Field Theories
Institute for Mathematics, Astrophysics and Particle Physics and Radboud Center for Natural Philosophy, Radboud University Nijmegen（拉德堡德大学数学、天体物理与粒子物理研究所及自然哲学中心）
