  The bulk (Einstein-Hilbert) and boundary (Gibbons-Hawking) terms in the
gravitational action are generally renormalized differently when integrating
out quantum fluctuations. The former is affected by nonminimal couplings, while
the latter is affected by boundary conditions. We use the heat kernel method to
analyze this behavior for a nonminimally coupled scalar field, the Maxwell
field, and the graviton field. Allowing for Robin boundary conditions, we
examine in which cases the renormalization preserves the ratio of boundary and
bulk terms required for the effective action to possess a stationary point. The
implications for field theory and black hole entropy computations are
discussed.
