Aspects of Analyticity (Lectures held at Kazan Summer School)

TL;DR

This paper explores the mathematical and physical aspects of analytic structures in spacetime models, including manifolds, black holes, and Euclidean solutions, with implications for cosmology and quantum gravity.

Contribution

It provides a comprehensive analysis of analytic continuation, maximal extensions, and global structures of various spacetime solutions in general relativity.

Findings

Maximal extensions of Walker's spacetimes are characterized.

Euclidean metrics and their physical interpretations are discussed.

Multi-black-hole solutions and their properties are analyzed.

Abstract

CONTENTS: 1 Introduction 2 Analytic Manifolds and Analytic Continuation of Metrics 3 Walker's Spacetimes and their Maximal Extension 4 Global Structure of de Sitter and Reissner-Nordstr\"om-de Sitter Cosmos 4.1 Special Cases 4.2 Collapsing Dust 5 Euclidean Metrics 6 Physical Interpretation of Euclidean Solutions, and a remark about the Gravitational Action 6.1 Thermal Interpretation 6.2 Tunneling Interpretation 7 The Multi-Black-Hole Solutions 7.1 Merging Black Holes 7.2 Continuing Beyond the Horizons 8 Naked Singularities? References