By J. A. Peacock
Gravitation and relativity -- Classical cosmology -- fundamentals of quantum fields -- The early universe -- Observational cosmology -- Galaxy formation and clustering
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This in turn was assumed to be coupled to the trace of the energy–momentum tensor (since we need a scalar quantity to match a scalar ﬁeld), giving the joint ﬁeld equations L= 8π −1 μν φ T c4 8π φ = g μν φ;μν = T μ (matter). 92) For obvious reasons, this theory is also known as scalar–tensor gravity. One subtlety to note is that φ is coupled to the matter component of T μν only, whereas gravity responds to the total, including the contribution of φ. The coupling constant for φ is written in the peculiar form involving ω for historical reasons.
2 Weak ﬁelds 39 As in electromagnetism, this simple form of the equations is achieved only by means of a gauge condition, which is the analogue of the Lorentz gauge and takes a similar form: ∂ ¯μν h = 0. 19) The fact that general relativity contains this freedom should be immediately obvious: if a solution of Einstein’s equations for the tensor gravitational potential is known, we only need make a coordinate transformation in order to obtain a new potential. There are four degrees of freedom introduced by the transformation, which are ﬁxed by the four equations in the above gauge condition.
Sign conventions Regrettably, much of the above varies from book to book; in a situation that makes the diﬀerence between cgs and SI electromagnetism seem almost trivial, there are few universal conventions in general relativity. 78) 8πG = [S3] × 4 Tμν . c The third sign above is related to the choice of convention for the Ricci tensor: α . 79) With these deﬁnitions, Misner, Thorne & Wheeler (unsurprisingly) classify themselves as (+ + +), whereas Weinberg (1972) is (+ − −). Peebles (1980, 1993) and Efstathiou (1990) are (−++).