Manuscript Em01-G@5 · Em01-G-v5.tex · section · 3fbfe951

Non-tip derivative placement and cubic cancellation

Non-tip derivative placement and cubic cancellation · lines 1469–1492

Em01-G@5#eq:Bkin, Em01-G@5#eq:Bkin-null, Em01-G@5#eq:Bkin-box

Define the constant kinetic completeness tensor

B_{kin}^{α β κ ν} = I \sum A^{α β, I} (e^{I})^{κ ν} = \frac{1}{2} η^{α β} η^{κ ν} - \frac{1}{2} (η^{α κ} η^{β ν} + η^{α ν} η^{β κ}) .

Directly,

B_{kin}^{α β κ ν} ℓ_{α} ℓ_{κ} B_{kin}^{α β κ ν} \partial_{2, α} \partial_{2, κ} = 0, = - \frac{1}{2} η^{β ν} □_{η, 2} .

Displayed formulas in this passage

Em01-G@5#eq:Bkin · line 1472
$B_{kin}^{α β κ ν} = I \sum A^{α β, I} (e^{I})^{κ ν} = \frac{1}{2} η^{α β} η^{κ ν} - \frac{1}{2} (η^{α κ} η^{β ν} + η^{α ν} η^{β κ}) .$
Em01-G@5#eq:Bkin-null · line 1484
$B_{kin}^{α β κ ν} ℓ_{α} ℓ_{κ} B_{kin}^{α β κ ν} \partial_{2, α} \partial_{2, κ} = 0, = - \frac{1}{2} η^{β ν} □_{η, 2} .$
Em01-G@5#eq:Bkin-box · line 1484
$B_{kin}^{α β κ ν} ℓ_{α} ℓ_{κ} B_{kin}^{α β κ ν} \partial_{2, α} \partial_{2, κ} = 0, = - \frac{1}{2} η^{β ν} □_{η, 2} .$