Finite FLRW Spacetimes, Causal Boundaries, and the Origin of Λ

We investigate the variational boundary-value problem for a finite Friedmann--Lemaître--Robertson--Walker (FLRW) region M₋ joined across a spherical hypersurface Σ to an exterior Schwarzschild vacuum region M₊. The hypersurface Σ is treated not as an externally fixed Dirichlet boundary, but as an internal junction of a composite spacetime M=M₋∪Σ∪M₊. In the absence of a surface stress-energy layer, continuity of the induced metric and extrinsic curvature---the Darmois/Israel no-shell conditions—provides a sufficient condition for stationarity of the joined Einstein--Hilbert action. The angular junction condition admits a non-comoving causal branch in the asymptotic null limit, where the boundary radius approaches the Schwarzschild radius and the interior de Sitter scale satisfies R_Λ−=r_s, or equivalently Λ₋=3/r_s². The effective cosmological constant may then be interpreted as a quantity selected by the global causal boundary rather than as an independent local bulk parameter. This boundary is not an observable edge of the FLRW region. At finite time the observer-centred apparent horizon lies inside the global junction, so the latter is not directly visible as a wall or preferred direction. Its effect is instead encoded in the expansion history through the boundary-selected value of Λ₋. The infinite-FLRW limit is recovered for r_s→∞, for which Λ₋→0. Within this framework, a non-zero Λ₋ is associated with a finite FLRW region bounded by a causal horizon that asymptotically coincides with its Schwarzschild radius.