Thin-shell wormholes from the regular Hayward black hole

The European Physical Journal C, Mar 2014

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 \(p=\psi (\sigma )\) where \(p\) is the surface pressure which is a function of the mass density \((\sigma )\). 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 from the regular Hayward black hole

M. Halilsoy 0 A. Ovgun 0 S. Habib Mazharimousavi 0 0 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. - 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 a e-mail: b e-mail: c e-mail: 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)


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M. Halilsoy, A. Ovgun, S. Habib Mazharimousavi. Thin-shell wormholes from the regular Hayward black hole, The European Physical Journal C, 2014, pp. 2796, Volume 74, Issue 3, DOI: 10.1140/epjc/s10052-014-2796-4