In the BSSN-puncture formalism, the typical variables to be evolved are

The typical basic equations are where is the Christoffel symbol associated with , and The gauges in the puncture formulation are where is an auxiliary function and is a constant chosen to be of order with being the total mass of the system.A point in the BSSN formalism is to rewrite the Ricci tensor, e.g., as

where is the Ricci tensor with respect to and Here, is the covariant derivative with respect to . Then, is written using , e.g., as With this prescription, in the weak field limit, and thus, Equations (136) and (137 essentially constitute a Klein–Gordon-type wave equations for .In the generalized harmonic GH formalism, the typical variables to be evolved are spacetime metric , and

The evolution equations in the GH formalism are written in first-order form. In contrast to the BSSN formalism, there are several options for the basic equations, in particular, in the choice of the constraint damping terms. The details of the formalism employed in the CCCW and LBPLI groups are described in [129] and [6], respectively.The GH gauge condition is explicitly written as

where is the Christoffel symbol associated with . A suitable choice for is still under development, e.g., the CCCW group employs a rather phenomenological function [58], and LBPLI employs [6].

Living Rev. Relativity 14, (2011), 6
http://www.livingreviews.org/lrr-2011-6 |
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