2 Foundations

In this section, we review several of the key ideas and tools that are indispensable in our later discussions. We keep our explanations as concise as possible, and refrain from extensive proofs of any propositions. The reader will be directed to the appropriate references for the details. In large part, much of what is covered in this section should be familiar to many workers in GR.

 2.1 Asymptotic flatness and ℑ+
 2.2 Bondi coordinates and null tetrad
 2.3 The optical equations
 2.4 The Newman–Penrose formalism
 2.5 The Bondi–Metzner–Sachs group
 2.6 Algebraically-special metrics and the Goldberg–Sachs theorem

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