Abstract
In general relativity, traversable wormholes are possible provided they do not represent shortcuts in the spacetime. Einstein equations, together with the achronal averaged null energy condition, demand to take longer for an observer to go through the wormhole than through the ambient space. This forbids wormholes connecting two distant regions in the space. The situation is different when higher-curvature corrections are considered. Here, we construct a traversable wormhole solution connecting two asymptotically flat regions, otherwise disconnected. This geometry is an electro-vacuum solution to Lovelock theory of gravity coupled to an Abelian gauge field. The electric flux suffices to support the wormhole throat and to stabilize the solution. In fact, we show that, in contrast to other wormhole solutions previously found in this theory, the one constructed here turns out to be stable under scalar perturbations. We also consider wormholes in AdS. We present a protection argument showing that, while stable traversable wormholes connecting two asymptotically locally AdS$_5$ spaces do exist in the higher-curvature theory, the region of the parameter space where such solutions are admitted lies outside the causality bounds coming from AdS/CFT.
Highlights
Wormholes are one of the most fascinating solutions of gravitational field equations
Conceived as a hypothesis on the structure of matter in classical physics [1], wormholes have served as illustrative examples on how abstruse the topology of spacetime can be [2], allowing us to investigate to what extent causality, locality, and energy conditions are interrelated [3]
The science fiction wormholes, are radically different from those seriously considered in theoretical physics; the main difference being their inviability at macroscopic scales
Summary
Wormholes are one of the most fascinating solutions of gravitational field equations. In such a theory, we will construct traversable wormhole geometries supported by a Maxwell field without introducing exotic matter and, as a consequence, satisfying the energy conditions. The impediments that one finds when trying to construct such a solution in Einstein theory are circumvented here due to the presence of higher-curvature terms, which suffice to support the throat. This implies, in particular, that the woprmffiffiffihole will be microscopic, i.e., with a throat of the size α. II, we will consider the spherically symmetric, static solutions to the higher-curvature theory coupled to a Maxwell field These solutions will be the building blocks of our geometry, while the blinder agent will be the junction conditions derived from the boundary term B in (1). V, we will generalize the solution to the case of asymptotically AdS5 wormholes, and we will make some comments in relation to AdS=CFT correspondence
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