In 4D nonperturbative Regge calculus a positive value of the effective cosmological constant characterizes the collapsed phase of the system. If a local term of the form $S^{\prime }={\Sigma }_{h\epsilon \{h_1,h_2,\dots \}}{\lambda }_h{V}_h$ is added to the gravitational action, where $\{h_1, h_2, \dots \}$ is a subset of the hinges and $\left\{{\lambda }_h\right\}$ are positive constants, one expects that the volumes $V_{h_1}, V_{h_2}, \dots$ tend to collapse and that the excitations of the lattice propagating through the hinges $\{h_1, h_2, \dots \}$ are damped. We study the continuum analogue of this effect. The additional term $S^{\prime }$ may represent the coupling of the gravitational field to an external Bose condensate.

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