Universal Gibbons-Hawking-York term for theories with curvature, torsion and non-metricity

Motivated by establishing holographic renormalization for gravitational theories with non-metricity and torsion, we present a new efficient general method calculating Gibbons-Hawking-York (GHY) terms. Our consists of linearizing any nonlinearity in curvature, torsion or introducing suitable Lagrange multipliers. Moreover, use split formalism differential forms, writing them $(n-1)+1$ dimensions. The boundary terms the action are manifest this means Stokes' theorem, such that compensating GHY term Dirichlet problem may be read off directly. We observe only those Lagrangian contain curvature contribute to term. Terms polynomial solely do not require compensation variational well-defined. test our confirming existing results Einstein-Hilbert four-dimensional Chern-Simons modified gravity. obtain Lovelock-Chern-Simons metric-affine For all four examples, approach towards systematic hydrodynamic expansion spin hypermomentum currents within AdS/CFT.