In Chap. 22 it is shown that if \(\mathcal {K}\) is a conformal Killing vector field satisfying, on a domain \(\mathcal {U}_{\mathcal {M}}\subset \mathcal {M}\) of a 4-dimensional spacetime manifold \(\mathcal {M}\) with metric tensor field \(\mathtt {g}\) : \(\displaystyle \begin{aligned} \mathcal{L}_{\mathcal{K}}\mathtt{g} \,=\, 2\lambda\mathtt{g}, \qquad \lambda\in\mathcal{F}(\mathcal{M}), \quad \lambda>0, \end{aligned}\) \(\mathtt {T}\) is any type- \((2,0)\) symmetric tensor on \(\mathcal {M}\) with components \(\mathtt {T}_{ab}=\mathtt {T}_{ba}\) , \(\mathcal {K}\) has components \(\mathcal {K}^{a}\) and \(\displaystyle \begin{aligned} J_{\mathcal{K}}\,\equiv\, \mathtt{T}_{ab}\mathcal{K}^{a}\star e^{b} \end{aligned}\) in any cobasis \(\{e^{b}\}\) then \(\displaystyle \begin{aligned} dJ_{\mathcal{K}} \,=\, \left\{\lambda\text{Tr}^{(\mathtt{g})}(\mathtt{T}) + i_{\mathcal{K}}(\nabla\cdot \mathtt{T})\right\}\star 1. \end{aligned}\) Thus in \(\mathcal {U}_{\mathcal {M}}\) a closed 3-form can be constructed from a divergenceless and traceless symmetric tensor if it possesses a conformal Killing vector field ( \(\lambda \neq 0\) ). If \(\lambda =0\) , the vector field \(\mathcal {K}\) is a Killing vector field and, in this case, irrespective of the \(\mathtt {g}\) -trace of a divergenceless \(\mathtt {T}\) : \(\displaystyle \begin{aligned} dJ_{\mathcal{K}} \,=\, 0 \qquad (\mathcal{L}_{\mathcal{K}}\mathtt{g}=0) \end{aligned}\) (i.e. \(J_{\mathcal {K}}\) is a closed 3-form on \(\mathcal {U}_{\mathcal {M}}\) ). We then show that if \(J_{\mathcal {K}}\) has the physical dimensions of energy then: \(\displaystyle \begin{aligned} E_{\Sigma_{t_{0}}}[K] \,\equiv\, \int_{\Sigma_{t_{0}}}J_{K}, \qquad t_{0}\in [t_{1},t_{2}] \end{aligned}\) is an energy constant of the motion on the history \(\mathcal {U}_{\mathcal {M}}[t_{1},t_{2}]\) of \(\Sigma _{t_{1}}\) . It is also shown in Sect. 22.1 that if \(\mathcal {L}_{\mathcal {K}}\mathtt {g}=2\lambda \mathtt {g}\) then \(\mathcal {K}\) also satisfies \(\text{Div}(\mathcal {K})=4\lambda _{\mathcal {K}}\) . In Sect. 22.2 the general Einstein 3-form equations on 4-dimensional spacetime with a metric-compatible connection \(\nabla \) : \(\displaystyle \begin{aligned} \mathcal{G}_{a} \,=\, \kappa\,\tau_{a}^{(\text{SOURCE})} \,=\, \kappa \sum_{N}\tau_{a}^{N} \qquad (a=0,1,2,3) \end{aligned}\) are discussed in terms of the type-Nspecies matter 3-forms \(\{\tau _{a}^{N}\}\) and the constraints on \(\{\tau ^{N}_{a}\}\) imposed by the existence of spacetime Killing vectors. In Sect. 21.1 it was shown that given any set of stress-energy-momentum 3-forms \(\{\tau _{a}\}\) , one has a corresponding type- \((2,0)\) tensor: \(\displaystyle \begin{aligned} \mathtt{T} \,=\, (\star^{-1}\tau_{a}) \otimes e^{a} \,=\, (\star \tau_{a}) \otimes \tau^{a} \end{aligned}\) with \(\displaystyle \begin{aligned} \nabla \cdot \mathtt{T} \,=\, -(\star \mathfrak{D}\tau_{a})\,e^{a}. \end{aligned}\) Thus \(\nabla \cdot \mathtt {T}=0\) if and only if \(\mathfrak {D}\tau _{a}=0\) for \(a=0,1,2,3\) . If \(\mathtt {T}\) is taken to be the Maxwell stress-energy-momentum tensor \(\mathtt {T}^{(\text{MAX})}\) for a Maxwell field system with source electric current 3-form \(\mathcal {J}\) , it was demonstrated that: \(\displaystyle \begin{aligned} \nabla \cdot \mathtt{T}^{(\text{MAX})} \,=\, \kappa_{A}\,i_{\widetilde{\star \mathcal{J}}}F, \qquad \kappa_{a}\in \mathbb{R}\backslash\{0\}. \end{aligned}\) Thus the Maxwell stress-energy-momentum tensor is divergenceless if and only if F is a vacuum solution to Maxwell’s equation ( \(\mathcal {J}=0\) ). In Sect. 22.3, “Killing drive forms” are defined. For any field N-subsystem in a spacetime with Killing vector field K we call \(\tau _{K}^{N}\) a type-NKilling drive 3-form current. If K is a future-pointing, timelike Killing vector field that generates timelike translations, we call \(\tau _{K}^{N}\) the energy-power 3-form Killing currentEnergy-power 3-form Killing current. If K is a spacelike Killing vector field that generates spacelike translations, we call \(\tau _{K}^{N}\) a linear momentum-force 3-form Killing currentLinear momentum-force 3-form Killing current. If K is a spacelike Killing vector field that generates spacelike rotations, we call \(\tau _{K}^{N}\) an angular momentum-torque 3-form Killing currentAngular momentum-torque 3-form Killing current. For any observer field V  on spacetime ( \(\mathtt {g}(V,V)=i_{V}\widetilde {V}=-L_{0}^{2}\) ), we write any Killing drive 3-form \(\tau _{K}\) associated with any non-null spacetime Killing vector field K as: \(\displaystyle \begin{aligned} \tau_{K} &\,=\, \zeta_{K}\left(\frac{J_{K}^{(V)}}{c_{0}}\wedge \widetilde{V} + \rho_{K}^{(V)} i_{V}\star 1\right) \,=\, \zeta_{K}\left(\frac{J_{K}^{(V)}}{c_{0}}\wedge \widetilde{V} + \rho_{K}^{(V)} \star \widetilde{V}\right) \end{aligned}\) where \(\displaystyle \begin{aligned} \zeta_{K} \,=\, \left\{ \begin{array}{rl} +1, &\;\text{if}\ K\ \text{is spacelike} \\[0.2cm] -1, &\;\text{if}\ K\ \text{is timelike}. \end{array}\right. \end{aligned}\) The 2-form Killing drive current \(J_{K}^{(V)}\) observed by V  follows as: \(\displaystyle \begin{aligned} J_{K}^{(V)} \,=\, -\zeta_{K}\,\frac{c_{0}}{L_{0}^{2}}i_{V}\tau_{K} \end{aligned}\) and the 0-form Killing drive densityKilling energy density 0-form \(\rho _{K}^{(V)}\) observed by V  is: \(\displaystyle \begin{aligned} \rho_{K}^{(V)} \,=\zeta_{K}\, \frac{1}{L_{0}^{2}}i_{V}\star\tau_{K}. \end{aligned}\) The physical dimensions of \(J_{K}^{(V)}\) and \(\rho _{K}^{(V)}\) now follow from the dimension of \(\tau _{K}\) and depend upon the physical dimension of K. If K is timelike and dimensionless ( ) then \(\rho ^{(V)}_{K}\) is the Killing energy density 0-form observed by V . In Sect. 22.4 we exploit three spacelike Killing vectors in Minkowski spacetime and the “linear momentum force current Maxwell drive 3-forms” (defined in Sect. 22.3) to calculate the Killing force 2-forms \(\{J^{(V)}_{K_{j}}\}\) ( \(j=1,2,3\) ) and then verify that the global electrostatic force between two electric charges held a fixed distance \(d_{0}\) apart is proportional to the product of their charges and inversely proportional to \(d_{0}^{2}\) .