MT[mu, nu] is the metric tensor in 4 dimensions.
Overview, FeynCalcExternal, FCE, FCI, MTD, MTE.
MT[\[Alpha], \[Beta]]\bar{g}^{\alpha \beta }
Contract[MT[\[Alpha], \[Beta]] MT[\[Alpha], \[Beta]]]4
MT[a, b] // StandardForm
(*MT[a, b]*)FCI[MT[a, b]] // StandardForm
(*Pair[LorentzIndex[a], LorentzIndex[b]]*)FCE[FCI[MT[a, b]]] // StandardForm
(*MT[a, b]*)