Causality, black holes, prediction, and counterfactuals in general relativity - Lesourd, M (2019)
This thesis treats foundational questions in classical general relativity. The em- phasis is towards proving new results in Lorentzian geometry which bear on these questions. For the most part, the results either improve or build upon the work of previous authors, including Geroch, Hawking, Kodama, Malament, Manchak, Newman, Penrose, Tipler, and Wald. In some cases I propose strengthened versions of known theorems, and in others I prove new results that are meant to better expose the meaning of known results. The subjects are broadly divided into three parts, II, III, and IV. Part II focuses on black hole phenomena and is composed of three independent sections treating, respectively, Hawking’s area theorem, black hole singularities in the presence of closed timelike curves, and the causal structure of evaporating black holes in view of the Kodama-Geroch-Wald theorem. Part III is focused on the epistemological status of observers in general relativis- tic spacetimes and the meaning of Penrose’s enigmatic conjecture of strong cosmic censorship. Here, the independent works of Malament and Manchak provide the crucial starting point. Part IV is more discussive and less about proving new results. The essential idea is to look for a Lewisian-inspired analysis of counterfactuals that can be formu- lated about spacetimes. The outcome is a set of perspectives along with a number of naturally arising and mathematically precise questions which could bear on the discussion.