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Chapter 24: Metric Tensor Fields, Surfaces and Relativity
https://doi.org/10.1142/9789813275386_0024Cited by:0 (Source: Crossref)
Abstract:
Let G be the gravitational constant and c be the speed of light in vacuum. The Einstein equation are given by
Rμν − 12 Rgμν = 8πGc4 Tμν, μ, ν = 0, 1, 2, 3
where Rμν is the Ricci tensor, R the Ricci scalar (the tensor contraction of the Ricci tensor) and T = (Tμν) is the energy momentum tensor. In local coordinates one has 3∑μ,ν =0Rμνdxμ⊗ dxν − 12 R 3∑μ,ν =0gμνdxμ⊗ dxν = 8πGc4 3∑μ,ν =0Tμνdxμ⊗ dxν .
