Traversable wormholes and energy conditions in Lovelock-Brans-Dicke gravity

Understand

Following the recent theory of Lovelock-Brans-Dicke gravity, we continue to investigate the conditions to support traversable wormholes by the gravitational effects of spacetime parity and topology, which arise from the nonminimal couplings of a background scalar field to the Chern-Pontryagin density and the Gauss-Bonnet invariant.

• The flaring-out condition indicates that a Morris-Thorne-type wormhole can be maintained by violating the generalized null energy condition, and thus also breaking down the generalized weak, strong, and dominant energy conditions; meanwhile, analyses of the zero-tidal-force solution show that the standard null energy condition in general relativity can still be respected by the physical matter threading the wormhole.
• This way, the two topological effects have to dominate over the ordinary-matter source of gravity, and the scalar field is preferred to be noncanonical.
• By treating Brans-Dicke gravity as a reduced situation of Lovelock-Brans-Dicke gravity, we also examine the Brans-Dicke wormholes and energy conditions.