Thin-shell wormholes from the regular Hayward black hole
M. Halilsoy
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A. Ovgun
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S. Habib Mazharimousavi
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Department of Physics, Eastern Mediterranean University
, G. Magusa, North Cyprus, Mersin 10,
Turkey
We revisit the regular black hole found by Hayward in 4-dimensional static, spherically symmetric spacetime. To find a possible source for such a spacetime we resort to the nonlinear electrodynamics in general relativity. It is found that a magnetic field within this context gives rise to the regular Hayward black hole. By employing such a regular black hole we construct a thin-shell wormhole for the case of various equations of state on the shell. We abbreviate a general equation of state by p = ( ) where p is the surface pressure which is a function of the mass density ( ). In particular, linear, logarithmic, Chaplygin, etc. forms of equations of state are considered. In each case we study the stability of the thin shell against linear perturbations. We plot the stability regions by tuning the parameters of the theory. It is observed that the role of the Hayward parameter is to make the TSW more stable. Perturbations of the throat with small velocity condition are also studied. The matter of our TSWs, however, remains exotic.
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Thin-shell wormholes (TSWs) constitute one of the
wormhole classes in which the exotic matter is confined on a
hypersurface and therefore can be minimized [116] (the
d-dimensional thin-shell wormhole is considered in [17] and
the case with a cosmological constant is studied in [18]).
Finding a physical (i.e. non-exotic) source to wormholes of
any kind remains as ever a challenging problem in Einsteins
general relativity. In this regard we must add that modified
theories of gravity present more alternatives with their extra
degrees of freedom. We recall, however, that each modified
theory partly cures things, while it partly adds its own
complications. Staying within Einsteins general relativity and
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finding remedies seems to be the prominent approach,
provided the proper spacetimes are employed. An interesting
class of spacetimes that may serve the purpose is the
spacetimes of regular black holes.
Our motivation for choosing a regular black hole in the
wormhole construction can be justified by the fact that a
regular system can be established from a finite energy. In
high energy collision experiments for instance, the formation
of such regular objects is more tenable. Such a black hole
was discovered first by Bardeen and came to be known as
Bardeen black hole [1922]. Ayon-Beato and Garcia in [22]
introduced a nonlinear electric field source for the Bardeen
black hole. Bronnikov, later on, showed that the regular
electric black hole, e.g., the one considered by Ayon-Beato and
Garcia, is not a quite correct solution to the field equations,
because in these solutions the electromagnetic Lagrangian is
inevitably different in different parts of space. On the
contrary, quite correct solutions of this kind (and even with the
same metric) can be readily obtained with a magnetic field
(since in nonlinear electrodynamics (NED) there is no such
duality as in the linear Maxwell theory). All this is described
in detail in [2325]. A similar type of black hole solution
was given by Hayward [26], which provides the main
motivation and fuel to the present study. This particular black
hole solution has well-defined asymptotic limits, namely it
is Schwarzschild for r and de Sitter for r 0. In
order to make a better account of the Hayward black hole we
attempt first to explore its physical source. For this reason
we search for the NED and find that a magnetic field within
this theory accounts for such a source. Note that every NED
does not admit a linear Maxwell limit and indeed this is
precisely the case that we face in the present problem. In other
words, if our NED model did have a Maxwell limit, then
the Hayward spacetime should coincide with the Reissner
Nordstrm (RN) limit. Such a limit does not exist in the
present problem. Once we fix our bulk spacetime the next
step is to locate the thin shell which must lie outside the event
horizon of the black hole. The surface energy-momentum
tensor on the shell must satisfy the Israel junction
conditions [2731]. As the Equation of State (EoS) for the
energymomentum on the shell we choose different models, which
are abbreviated by p = ( ). Here p stands for the
surface pressure, is the mass (energy) density and ( ) is
a function of . We consider the following cases: (1) linear
gas (LG) [32,33], where ( ) is a linear function of ; (2)
Chaplygin gas (CG) [34,35], where ( ) 1 ; (3)
generalized Chaplygin gas (GCG) [3640], where ( ) 1 ( =
constant); (4) modified generalized Chaplygin gas (MGCG)
[4144], where ( ) LG+GCG; and (5) logarithmic gas
(LogG), where ( ) ln | |.
For each of the cases we plot the second derivative of the
derived potential function V (a0), where a0 stands for the
equilibrium point. The region where the second derivative
is positive (i (...truncated)