MTLR[p,mu,n,nb] denotes the perpendicular component in the lightcone decomposition of the metric tensor g^{\mu \nu} along the vectors n and nb. It corresponds to g^{\mu \nu}_{\perp}.
If one omits n and nb, the program will use default vectors specified via $FCDefaultLightconeVectorN and $FCDefaultLightconeVectorNB.
Overview, Pair, FVLN, FVLP, SPLP, SPLN, SPLR, MTLP, MTLN.
MTLR[\[Mu], \[Nu], n, nb]\bar{g}^{\mu \nu }{}_{\perp }
MTLR[\[Mu], \[Nu], n, nb] // FCI // StandardForm
(*Pair[LightConePerpendicularComponent[LorentzIndex[\[Mu]], Momentum[n],Momentum[nb]], LightConePerpendicularComponent[LorentzIndex[\[Nu]], Momentum[n], Momentum[nb]]]*)MTLR[\[Mu], \[Nu], n, nb] FV[p, \[Mu]] // Contract\overline{p}^{\nu }{}_{\perp }
MTLR[\[Mu], \[Nu], n, nb] FVLP[q, \[Mu], n, nb] // Contract0