 Einstein-Proca theory

ID: einstein-proca-theory

Einstein-Proca theory couples general relativity to a massive vector field governed by the Proca action. Its matter stress-energy tensor is

T_{ab} = F_{a c} F_{b}^{c} - \frac{1}{4} g_{ab} F_{c d} F^{c d} + m^{2} (A_{a} A_{b} - \frac{1}{2} g_{ab} A_{c} A^{c}) .

The contracted Bianchi identity makes the Einstein equation compatible with the covariant Proca equation.

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