Eur. Phys. J. C (2014) 74:3073
DOI 10.1140/epjc/s10052-014-3073-2
Regular Article - Theoretical Physics
Counter-rotational effects on stability of 2 + 1-dimensional
thin-shell wormholes
S. Habib Mazharimousavi
a
, M. Halilsoy
b
Department of Physics, Eastern Mediterranean University, Gazimagusa, Turkey
Received: 15 July 2014 / Accepted: 10 September 2014 / Published online: 23 September 2014
© The Author(s) 2014. This article is published with open access at Springerlink.com
Abstract The role of angular momentum in a 2 + 1-
dimensional rotating thin-shell wormhole (TSW) is consid-
ered. Particular emphasis is given to stability when the shells
(rings) are counter-rotating. We find that counter-rotating
halves make the TSW supported by the equation of state
of a linear gas more s table. Under a small velocity dependent
perturbation, however, it becomes unstable.
1 Introduction
Similar to black holes, wormholes in 2 + 1 dimensions also
constitute informative objects to help us learn more about
their higher-dimensional counterparts. The same is also true
for thin-shell wormholes (TSWs) [1] which are constructed
from an energy-momentum at the throat through a cut-and-
paste technique satisfying the proper junction conditions. We
recall that the history of TSWs started with Visser’s construc-
tion in a 3 +1-dimensional flat Minkowski spacetime [1]. At
the same time he extended the idea to the Schwarzschild
spacetime [2]. In his book [3] and work with Poisson [4 ]he
introduced into physics the terminology of TSWs first. In the
latter work they considered also the stability of a TSW. Ever
since, there have been extensive attempts to understand the
various features of the new kind of wormholes. For a short list
of such attempts we refer the reader to [5–17] and references
cited therein. Among the works on TSWs we see general-
izations to higher [18–20] and lower [21–23] dimensions,
and extensions to Lovelock gravity [24–27]. The theory has
also been considered in cylindrical symmetry [28–34], dila-
ton theory [35], and so on. The common feature of all these
extensions is that the bulk spacetimes are all static. We are
well aware of the difficulties in rotating thin-shell worm-
holes (RTSWs). For this reason we restrict ourselves in this
study to the relatively simpler case of 2 +1 dimensions. The
a
e-mail: habib.mazhari@emu.edu.tr
b
e-mail: mustafa.halilsoy@emu.edu.tr
absence of gravitational degrees of freedom, namely, Weyl
curvature in the lower dimension enforces us to add new
physical parameters s uch as cosmological constant, electric /
magnetic charge, scalar charge, and rotation. Our aim in this
study is to consider RTSWs in 2 + 1 dimensions. The met-
ric function contains the square of the angular momentum
J
2
, which does not distinguish the cases of ±J for angular
momentum. We recall that rotating TSWs constructed from
a Kerr black hole in 3 + 1 dimensions have been consid-
ered in [36] and their geodesics have been analyzed in [37].
Also rotational effects for collapsing thin shells in 2 +1 and
4 + 1 dimensions have been considered in detail in [38,39],
respectively.
In our analysis of TSWs we observe that the off-diagonal
components of the extrinsic curvature tensor k
ij
and related
components of the surface energy-momentum at the throat
S
ij
vanish in the case that we assume counter-rotating com-
ponents of shells at the throat. The gas pressures from the
upper and lower shells cancel each other to modify the equa-
tion of state to the extent that it becomes equivalent to a
static case. We may draw a rough analogy with the rotat-
ing Earth. Due to the non-inertial effects curly geodesics of
winds, i.e. the Coriolis effect matching at the equator, are
counter-circular in different hemispheres. If the two hemi-
spheres of our Earth were counter-rotating instead of coro-
tating the curly motions should be identical. Counter-rotation
at the throat in the case of TSWs allows us to choose a simpler
surface energy-momentum tensor and study the stability con-
dition. We can choose, for instance, a linear gas (LG) equation
of state (EoS) at the junction in which the pressure is linearly
related to the mass density. For such a LG the counter-rotating
components make the TSW more stable. Increasing the angu-
lar momentum magnitude, i.e. the relative rotation, stabilizes
the TSW further. Our next attempt toward a s table TSW is
to assume a velocity dependent perturbation of the LG. It is
observed that our stability argument is restricted by the linear
perturbation alone in which at the equilibrium radius (R
0
)we
have the initial conditions
˙
R
0
=
¨
R
0
= 0. Once we assume
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