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This dissertation presents a semiclassical analysis of conical topologychange in $1+1$ spacetime dimensions wherein, to lowest order, the ambientspacetime is classical and fixed while the scalar field coupled to it isquantized. The vacuum expectation value of the scalar field stress-energytensor is calculated via two different approaches. The first of these involvesthe explicit determination of the so called Sorkin-Johnston state on the coneand an original regularization scheme, while the latter employs the conformalvacuum and the more conventional point-splitting renormalization. It is foundthat conical topology change seems not to suffer from the same pathologies thattrousers-type topology change does. This provides tentative agreement withconjectures due to Sorkin and Borde, which attempt to classify topologychanging spacetimes with respect to their Morse critical points and inparticular, that the cone and yarmulke in $1+1$ dimensions lack critical pointsof unit Morse index.

Stress-Energy in the Conical Vacuum and its Implications for Topology Change