term guarantees a well-defined variation principle with the Dirichlet boundary term. The second term belongs to the joint term that is evaluated at the intersection of two non-null hypersurfaces.

In the third line, we encounter null hypersurfaces. The null boundary term gained some attention recently. The first term is the counterpart of the GHY term in the null boundary. This term can always be ignored by assuming an affine null parameter. The second term evaluates joint terms in the intersection of two hypersurfaces where at least one of the hypersurfaces is null.

We use the instruction of [@Carmi:2016wjl] to evaluate terms of . The boundary terms for null hypersurfaces were discussed in several works [@Parattu:2015gga; @Lehner:2016vdi]. The joint terms first introduced by Hayward [@Hayward:1993my] for spacelike and timelike boundaries were extended by [@Lehner:2016vdi] to the null hypersurfaces. It is notable that neither the boundary terms nor the joint terms depends on the cosmological constant. It is worth mentioning that in the context of holographic renormalization the counterterms that cancel the divergent terms in the action are related extremely to the existence of the cosmological constant[@Skenderis:2002wp; @Costa:2013vza]. As [@Costa:2013vza] observed, local counterterms in asymptotically AdS spacetimes become nonlocal in the asymptotically 