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Physics Letters B 778 (2018) 408–413

Contents lists available at ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Uniqueness theorem for static phantom wormholes

in Einstein–Maxwell-dilaton theory

Boian Lazov

, Petya Nedkova

a,b,∗

, Stoytcho Yazadjiev

a,c,d

Department of Theoretical Physics, Soﬁa University, Soﬁa 1164, Bulgaria

Institut für Physik, Universität Oldenburg, D-26111 Oldenburg, Germany

Theoretical Astrophysics, Eberhard-Karls University of Tübingen, Tübingen 72076, Germany

Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Soﬁa 1164, Bulgaria

a r t i c l e i n f o a b s t r a c t

Article history:

Received

8 November 2017

Received

in revised form 14 January 2018

Accepted

22 January 2018

Available

online xxxx

Editor:

M. Cveti

We prove a uniqueness theorem for completely regular traversable electrically charged wormhole

solutions in the Einstein–Maxwell-dilaton gravity with a phantom scalar ﬁeld and a possible phantom

electromagnetic ﬁeld. In a certain region of the parameter space, determined by the asymptotic values

of the scalar ﬁeld and the lapse function, the regular wormholes are completely speciﬁed by their mass,

scalar charge and electric charge. The argument is based on the positive energy theorem applied on an

appropriate conformally transformed Riemannian space.

(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP

1. Introduction

Wormholes arise naturally in general relativity and alternative

theories of gravity as solutions which form bridges between differ-

ent

universes, or different regions of the same universe [1]. Phys-

ically

most interesting are the traversable wormholes, which are

free of conical or curvature singularities, and can be considered

in context of future spacetime travel [2]. Solutions with conical

singularity localized in the equatorial plane (ring wormholes) also

attract attention as models of elementary particles sourced by a

cosmic string [3].

is well known that in general relativity traversable worm-

holes

cannot be supported by matter obeying the null energy con-

dition [4].

Its violation requires the existence of some exotic matter

with negative energy density. Such scenarios are widely investi-

gated

also in cosmological context in view of dark energy models.

One of the most simple models proposes the introduction of phan-

tom

matter ﬁelds, which possess kinetic terms coupled repulsively

to gravity, such as phantom scalar or electromagnetic ﬁelds. Their

presence agrees with current cosmological observations, and en-

ables

a variety of wormhole solutions [5], arising also as ﬁnal

states in dynamical collapse [6]. We should note, however, that

Corresponding author.

E-mail

addresses: boian_lazov@phys.uni-soﬁa.bg (B. Lazov),

pnedkova@phys.uni-soﬁa.bg (P. Nedkova), yazad@phys.uni-soﬁa.bg (S. Yazadjiev).

regular wormholes can exist in certain alternative theories of grav-

ity

without introducing any exotic matter [7].

contrast to black holes, wormhole solutions, although avail-

able

in many cases, are not classiﬁed systematically. A recent work

proved that the Ellis–Bronnikov wormhole is the unique static

traversable wormhole in Einstein-scalar ﬁeld theory, which is free

of any singularities [8]. The goal of the present paper is to pro-

vide

a uniqueness theorem for completely regular traversable elec-

trically

charged wormholes in the static sector of the Einstein–

Maxwell-dilaton

theory with a phantom dilaton ﬁeld and a pos-

sible

phantom electromagnetic ﬁeld. We consider the case of

dilaton-Maxwell coupling constant equal to unity.

2. Field equations and general deﬁnitions

We consider Einstein–Maxwell-dilaton theory with a phantom

dilaton ﬁeld deﬁned by the following action

S =

16π



√

−g



R +

∇

ϕ −ε e

−2ϕ

μν



(1)

We further allow that the Maxwell-gravity coupling constant ε can

take either positive, or negative values ε =±1. Thus, we include in

our analysis also phantom Maxwell ﬁelds. The action leads to the

following ﬁeld equations on the spacetime manifold M

(4)

μν

=−2

∇

ϕ +2εe

−2ϕ



μβ

−

μν

βγ



(2)

https://doi.org/10.1016/j.physletb.2018.01.059

0370-2693/

SCOAP

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