To avoid confusion, the covariant derivative and Ricci tensor associated with will be written with over-bars – and . I will also frequently deal with an auxiliary 3-dimensional space with a metric that is conformally related to the metric of the physical space. The metric for this space will be denoted . The covariant derivative and Ricci tensor associated with this metric will be written with tildes – and . Other quantities that have a conformal relationship to quantities in the physical space will also be written with a tilde over them.
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