ar X iv : g r - qc / 9 81 10 79 v 1 2 3 N ov 1 99 8 Instantons For Black Hole Pair Production ∗ Paul

We address the issue of constructing continuous instantons representing the pair creation of black holes in a cosmological context. The recent attempt at constructing such solutions using virtual domain walls is reviewed first. We then explore the existence of continous instantons in higher curavature gravity theories where the Lagrangian is polynomial in the Ricci scalar. Lastly, we study continous instanton solutions of ordinary gravity coupled to the Narlikar C-field. For each theory, we first consider the case of finding continuous instanton solutions which represent the “near-annihilation” of a de Sitter universe and its subsequent recreation. In situations where these solutions exist, we then ask whether solutions can be found that represent the “near-annihilation” of a de Sitter spacetime and the subsequent creation of a pair of Schwarzschild-de Sitter black holes.