General Relativity

Contents

(1, 1)-tensor t = tⁱ_j ∂_i ⊗ dx^j, t(-, v) = tⁱ_j ∂_i ⊗ dx^j (v^k ∂_k) = tⁱ_j v^k ∂_i ⊗ dx^j (∂_k) = tⁱ_j v^k δ_k^j ∂_i = tⁱ_j v^j ∂_i. g(v, v) = g_{i, j} vⁱ v^j = -1. Metric tensor g = g_{i, j} dxⁱ ⊗ dx^j. g(-, v) = g_{i, j} dxⁱ ⊗ dx^j (v^k ∂_k) = (g_{i, j} v^j) dxⁱ.

Gravity

References

• Jacob Lurie. Lie Algebras and Homotopy Theory. 2019.