Synchronous gauge
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In general relativity, synchronous gauge is a gauge in which the metric takes the form
- ds2 = − dt2 + habdxadxb,
where the Latin indices a and b are summed over the spatial directions and hab is a spatial metric. Any metric can locally be put into this form by a coordinate transformation. It is called synchronous gauge because the t coordinate defines proper time for all comoving observers. However, it is not uniquely defined, as the spacelike hypersurface at t = 0 can be chosen arbitrarily. Another problem with the gauge is that caustics can occur which cause the gauge choice to break down. These problems have caused some difficulties doing cosmological perturbation theory in this gauge, however the problems are now well understood. Synchronous gauge is generally considered the most efficient gauge for doing calculations, and is used in many modern cosmology codes, such as CMBFAST. It is also useful for solving theoretical problems in which a spacelike hypersurface needs to be fixed, as with spacelike singularities.
[edit] References
- Carroll, Sean M. (2004). Spacetime and Geometry: An Introduction to General Relativity. San Francisco: Addison-Wesley. ISBN 0-8053-8732-3.. See section 7.2.
- C.-P. Ma and E. Bertshinger (1995). "Cosmological perturbation theory in the synchronous and conformal Newtonian gauges". Astrophysics J. 455: 7–25.
