Wormhole solutions with NUT charge in higher curvature theories

Rustam Ibadov,Sardor Murodov,Burkhard Kleihaus,Jutta Kunz

doi:10.1007/s40065-021-00350-0

Abstract

We present wormholes with a Newman–Unti–Tamburino (NUT) charge that arise in certain higher curvature theories, where a scalar field is coupled to a higher curvature invariant. For the invariants we employ (i) a Gauss–Bonnet term and (ii) a Chern–Simons term, which then act as source terms for the scalar field. We map out the domain of existence of wormhole solutions by varying the coupling parameter and the scalar charge for a set of fixed values of the NUT charge. The domain of existence for a given NUT charge is then delimited by the set of scalarized nutty black holes, a set of wormhole solutions with a degenerate throat and a set of singular solutions.

Highlights

Wormholes are intriguing solutions of numerous theories of gravity
The reason is, that the gravitational interaction itself can give rise to additional terms, that may be interpreted as contributing to an effective stress energy tensor on the right hand side of the Einstein field equations, which may lead to violation of the energy conditions
We have considered scalarized wormholes with NUT charge in two alternative gravity theories, EsGB theory and Einstein– scalar-Chern–Simons (EsCS) theory

Summary

Introduction

Wormholes are intriguing solutions of numerous theories of gravity. In General Relativity the presence of some form of exotic matter is required to construct traversable Lorentzian wormholes, since the energy conditions must be violated (see, e.g., [32,34,37]). The simplest possibility here is to employ a phantom scalar field, i.e., a field whose kinetic term has the opposite sign as compared to an ordinary scalar field Such phantom fields have been already employed decades ago by Ellis and Bronnikov, when constructing wormhole solution in General Relativity [6,14,15,31]. The reason is, that the gravitational interaction itself can give rise to additional terms, that may be interpreted as contributing to an effective stress energy tensor on the right hand side of the Einstein field equations, which may lead to violation of the energy conditions. It is the modified gravitational interaction itself which provides the necessary violation of the energy conditions (see, e.g., [7, 17,18,19,20, 22, 27, 28, 33])

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Conclusion