On the stability of spherically symmetric and wormhole solutions supported by the sine-Gordon ghost scalar field (original) (raw)
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Physical Review D, 2010
In this paper we investigate wormhole and spherically symmetric solutions in 4D gravity plus a matter source consisting of a ghost scalar field with a sine-Gordon potential. For the wormhole solutions we also include the possibility of electric and/or magnetic charges. For both types of solutions we perform a linear stability analysis and show that the wormhole solutions are stable and that when one turns on the electric and/or magnetic field the solution remains stable. The linear stability analysis of the spherically symmetric solutions indicates that they can be stable or unstable depending on one of the parameters of the system. This result for the spherically symmetric solution is nontrivial since a previous investigation of 4D gravity plus a ghost scalar field with a lambdaphi4\lambda \phi ^4lambdaphi4 interaction found only unstable spherically symmetric solutions. Both the wormhole and spherically symmetric solutions presented here asymptotically go to anti-de-Sitter space-time.
Instability of wormholes supported by a ghost scalar field: I. Linear stability analysis
Classical and Quantum Gravity, 2009
We examine the linear stability of static, spherically symmetric wormhole solutions of Einstein's field equations coupled to a massless ghost scalar field. These solutions are parametrized by the areal radius of their throat and the product of the masses at their asymptotically flat ends. We prove that all these solutions are unstable with respect to linear fluctuations and possess precisely one unstable, exponentially in time growing mode. The associated time scale is shown to be of the order of the wormhole throat divided by the speed of light. The nonlinear evolution is analyzed in a subsequent article.
Wormhole solutions with a complex ghost scalar field and their instability
Physical Review D
We study compact configurations with a nontrivial wormholelike spacetime topology supported by a complex ghost scalar field with a quartic self-interaction. For this case, we obtain regular asymptotically flat equilibrium solutions possessing reflection symmetry. We then show their instability with respect to linear radial perturbations.
Instability of wormholes supported by a ghost scalar field: II. Nonlinear evolution
Classical and Quantum Gravity, 2009
We analyze the nonlinear evolution of spherically symmetric wormhole solutions coupled to a massless ghost scalar field using numerical methods. In a previous article we have shown that static wormholes with these properties are unstable with respect to linear perturbations. Here we show that depending on the initial perturbation the wormholes either expand or decay to a Schwarzschild black hole. We estimate the time scale of the expanding solutions and the ones collapsing to a black hole and show that they are consistent in the regime of small perturbations with those predicted from perturbation theory. In the collapsing case, we also present a systematic study of the final black hole horizon and discuss the possibility for a luminous signal to travel from one universe to the other and back before the black hole forms. In the expanding case, the wormholes seem to undergo an exponential expansion, at least during the run time of our simulations.
Scalar Fields as Sources for Wormholes and Regular Black Holes
Particles, 2018
We review nonsingular static, spherically symmetric solutions of general relativity with minimally coupled scalar fields. Considered are wormholes and regular black holes (BHs) without a center, including black universes (BHs with expanding cosmology beyond the horizon). Such configurations require a "ghost" field with negative kinetic energy K. Ghosts can be invisible under usual conditions if K < 0 only in strong-field region ("trapped ghost"), or they rapidly decay at large radii. Before discussing particular examples, some general results are presented, such as the necessity of anisotropic matter for asymptotically flat or AdS wormholes, no-hair and global structure theorems for BHs with scalar fields. The stability properties of scalar wormholes and regular BHs under spherical perturbations are discussed. It is stressed that the effective potential V eff for perturbations has universal shapes near generic wormhole throats (a positive pole regularizable by a Darboux transformation) and near transition surfaces from canonical to ghost scalar field behavior (a negative pole at which the perturbation finiteness requirement plays a stabilizing role). Positive poles of V eff emerging at "long throats" (with the radius r ≈ r 0 + const • x 2n , n > 1, x = 0 is the throat) may be regularized by repeated Darboux transformations for some values of n.
Instabilities of wormholes and regular black holes supported by a phantom scalar field
Physical Review D, 2012
We test the stability of various wormholes and black holes supported by a scalar field with a negative kinetic term. The general axial perturbations and the monopole type of polar perturbations are considered in the linear approximation. Two classes of objects are considered: (i) wormholes with flat asymptotic behavior at one end and AdS on the other (M-AdS wormholes) and (ii) regular black holes with asymptotically de Sitter expansion far beyond the horizon (the so-called black universes). A difficulty in such stability studies is that the effective potential for perturbations forms an infinite wall at throats, if any. Its regularization is in general possible only by numerical methods, and such a method is suggested in a general form and used in the present paper. As a result, we have shown that all configurations under study are unstable under spherically symmetric perturbations, except for a special class of black universes where the event horizon coincides with the minimum of the area function. For this stable family, the frequencies of quasinormal modes of axial perturbations are calculated.
Stable Wormholes in the Background of an Exponential f(R) Gravity
Universe, 2020
The current paper is devoted to investigating wormhole solutions with an exponential gravity model in the background of f ( R ) theory. Spherically symmetric static spacetime geometry is chosen to explore wormhole solutions with anisotropic fluid source. The behavior of the traceless matter is studied by employing a particular equation of state to describe the important properties of the shape-function of the wormhole geometry. Furthermore, the energy conditions and stability analysis are done for two specific shape-functions. It is seen that the energy condition are to be violated for both of the shape-functions chosen here. It is concluded that our results are stable and realistic.
Notes on wormhole existence in scalar-tensor and F(R) gravity
2010
Some recent papers have claimed the existence of static, spherically symmetric wormhole solutions to gravitational field equations in the absence of ghost (or phantom) degrees of freedom. We show that in some such cases the solutions in question are actually not of wormhole nature while in cases where a wormhole is obtained, the effective gravitational constant G eff is negative in some region of space, i.e., the graviton becomes a ghost. In particular, it is confirmed that there are no vacuum wormhole solutions of the Brans-Dicke theory with zero potential and the coupling constant ω > −3/2 , except for the case ω = 0 ; in the latter case, G eff < 0 in the region beyond the throat. The same is true for wormhole solutions of F (R) gravity: special wormhole solutions are only possible if F (R) contains an extremum at which G eff changes its sign.
Wormholes in higher dimensional space-time: Exact solutions and their linear stability analysis
Physical Review D, 2013
We derive the simplest traversable wormhole solutions in n-dimensional general relativity, assuming static and spherically symmetric spacetime with a ghost scalar field. This is the generalization of the Ellis solution (or the so-called Morris-Thorne's traversable wormhole) into a higher-dimension. We also study their stability using linear perturbation analysis. We obtain the master equation for the perturbed gauge-invariant variable and search their eigenvalues. Our analysis shows that all higher-dimensional wormholes have an unstable mode against the perturbations with which the throat radius is changed. The instability is consistent with the earlier numerical analysis in fourdimensional solution.
Study of static wormhole solutions in F(T,TG) gravity
Annals of Physics
In this paper, we investigate static spherically symmetric wormhole solutions in the background of F (T, T G) gravity (T is the torsion scalar and T G represents teleparallel equivalent of the Gauss-Bonnet term). We study the wormhole solutions by assuming four different matter contents, a specific redshift function and a particular F (T, T G) model. The behavior of null/weak energy conditions for these fluids is analyzed graphically. It turns out that wormhole solutions can be obtained in the absence of exotic matter for some particular regions of spacetime. We also explore stability of wormhole solutions through equilibrium condition. It is concluded that there exist physically acceptable wormhole solutions for anisotropic, isotropic and traceless fluids.