Black Holes as Boundary Conditions: On the Mathematical Admissibility of Complementary Spacetime Continuations

Black holes are frequently described as physical objects, containers, or endpoints of gravitational collapse. In general relativity, however, an event horizon is more precisely understood as a causal boundary condition on admissible spacetime trajectories. This paper adopts a boundary-centric interpretation of black holes and examines the consequences of treating them strictly as limits on causal and temporal extensibility rather than as dynamical entities.

Because the Einstein field equations are time-reversal invariant, the same mathematics admits a complementary boundary condition corresponding to a time-reversed solution, commonly labeled a “white hole.” This work clarifies that such a white hole should be understood only as a mathematical boundary condition, not as a physical object, process, or astrophysical event. No transport of matter, information, or spacetime across a black-hole horizon is implied.

The paper further demonstrates that no universe can develop within our own across a black-hole boundary, as the horizon terminates global time and causal extensibility. At the same time, the mathematics remains consistent with the existence of separate, causally inaccessible spacetime continuations governed by distinct boundary conditions and global time orderings. These continuations are, in principle, unobservable and cannot be empirically verified.

The result is a classification and consistency analysis rather than a predictive cosmological model. By clearly distinguishing mathematical admissibility from physical instantiation and observability, this work resolves common conceptual confusions surrounding black holes, white holes, and speculative “baby universe” scenarios without invoking new physics or speculative mechanisms.