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
a
, Petya Nedkova
a,b,∗
, Stoytcho Yazadjiev
a,c,d
a
Department of Theoretical Physics, Sofia University, Sofia 1164, Bulgaria
b
Institut für Physik, Universität Oldenburg, D-26111 Oldenburg, Germany
c
Theoretical Astrophysics, Eberhard-Karls University of Tübingen, Tübingen 72076, Germany
d
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
ˇ
c
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.
© 2018 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
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].
It
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].
In
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 =
1
16π
dx
4
√
−g
R +
2
g
∇
μ
ϕ
g
∇
μ
ϕ −ε e
−2ϕ
F
μν
F
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)
R
μν
=−2
g
∇
μ
ϕ
g
∇
ν
ϕ +2εe
−2ϕ
F
μβ
F
β
ν
−
g
μν
4
F
βγ
F
βγ
,
(2)
https://doi.org/10.1016/j.physletb.2018.01.059
0370-2693/
© 2018 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.
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