Abstract
Massless scalar fields coupled to gravity produces two kinds of wormhole instantons, the Giddings-Strominger wormhole and the Tolman-Hawking wormhole. A new type of coupling between gravity and a massless scalar field is discussed which produces a different wormhole-like solution, [Formula: see text]. It is seen that these three solutions can be related to each other by means of suitable conformal transformations. The Wheeler DeWitt equation corresponding to a fourth-order gravity theory minimally coupled to an axionic field is obtained and some of its particular solutions are discussed.
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