We prove this by looking at ∂ ∂ μ μ T μ μ ν ν + u α α u ν ν ∂ ∂ μ μ T μ μ α α and then multiplying each side by u ν ν . Upon doing this, and noting that u μ μ u μ μ = − − 1 , we have u ν ν ∂ ∂ μ μ T μ μ ν ν − − u α α ∂ ∂ μ μ T μ μ α α . Relabeling the indices α α as ν ν shows that the two completely cancel. This cancellation is the expected result of contracting a temporal tensor with a spatial tensor.