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Register a new userStability and instability of Ellis and phantom wormholes: Are there ghosts?
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It is concluded in the literature that Ellis wormhole is unstable under small perturbations and would decay either to the Schwarzschild black hole or expand away to infinity. While this deterministic conclusion of instability is correct, we show that the Ellis wormhole reduces to Schwarzschild black hole textit{only} when the Ellis solution parameter $gamma $ assumes a complex value $-i$. We shall then reexamine stability of Ellis and phantom wormholes from the viewpoint of local and asymptotic observers by using a completely different approach, viz., we adapt Tangherlinis nondeterministic, prequantal statistical simulation about photon motion in the real optical medium to an effective medium reformulation of motions obtained via Hamiltons optical-mechanical analogy in a gravity field. A crucial component of Tangherlinis idea is the observed increase of momentum of the photons entering a real medium. We show that this fact has a heuristic parallel in the effective medium version of the Pound-Rebka experiment in gravity. Our conclusion is that there is a non-zero probability that Ellis and phantom wormholes could appear stable or unstable depending on the location of observers and on the values of $gamma$, leading to the possibility of textit{ghost wormholes} (like ghost stars). The Schwarzschild horizon, however, would always appear certainly stable ($R=1$, $T=0$) to observers regardless of their location. Phantom wormholes of bounded mass in the extreme limit $arightarrow -1$ are also shown to be stable just as the Schwarzschild black hole is. We shall propose a thought experiment showing that our non-deterministic results could be numerically translated into observable deterministic signatures of ghost wormholes.
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We study the time evolution of the test scalar and electromagnetic fields perturbations in configurations of phantom wormholes surrounded by dark energy with state parameter $omega< -1$. We observe obvious signals of echoes reflecting wormholes properties and disclose the physical reasons behind such phenomena. In particular, we find that the dark energy equation of state has a clear imprint in echoes in wave perturbations. When $omega$ approaches the phantom divide $omega=-1$ from below, the delay time of echoes becomes longer. The echo of gravitational wave is likely to be detected in the near future, the signature of the dark energy equation of state in the echo spectrum can serve as a local measurement of the dark energy.
In this paper, we investigate the simplest wormhole solution - the Ellis-Bronnikov one - in the context of the Asymptotically Safe Gravity (ASG) at the Planck scale. We work with three models, which employ Ricci scalar, Kretschmann scalar, and squared Ricci tensor to improve the field equations by turning the Newton constant into a running coupling constant. For all the cases, we check the radial energy conditions of the wormhole solution and compare them with those valid in General Relativity (GR). We verify that asymptotic safety guarantees that the Ellis-Bronnikov wormhole can satisfy the radial energy conditions at the throat radius, $r_0$, within an interval of values of this latter. That is quite different from the result found in GR. Following, we evaluate the effective radial state parameter, $omega(r)$, at $r_0$, showing that the quantum gravitational effects modify Einsteins field equations in such a way that it is necessary a very exotic source of matter to generate the wormhole spacetime -- phantom or quintessence-like. That occurs within some ranges of throat radii, even though the energy conditions are or not violated there. Finally, we find that, although at $r_0$ we have a quintessence-like matter, on growing of $r$ we necessarily come across phantom-like regions. We speculate if such a phantom fluid must always be present in wormholes in the ASG context or even in more general quantum gravity scenarios.
A possible candidate for the late time accelerated expanding Universe is phantom energy, which possesses rather bizarre properties, such as the prediction of a Big Rip singularity and the violation of the null energy condition. The latter is a fundamental ingredient of traversable wormholes, and it has been shown that phantom energy may indeed sustain these exotic geometries. Inspired by the evolving dark energy parameter crossing the phantom divide, we consider in this work a varying equation of state parameter dependent on the radial coordinate, i.e., $omega(r)=p(r)/rho(r)$. We shall impose that phantom energy is concentrated in the neighborhood of the throat, to ensure the flaring out condition, and several models are analyzed. We shall also consider the possibility that these phantom wormholes be sustained by their own quantum fluctuations. The energy density of the graviton one loop contribution to a classical energy in a phantom wormhole background and the finite one loop energy density are considered as a self-consistent source for these wormhole geometries. The latter semi-classical approach prohibits solutions with a constant equation of state parameter, which further motivates the imposition of a radial dependent parameter, $omega(r)$, and only permits solutions with a steep positive slope proportional to the radial derivative of the equation of state parameter, evaluated at the throat. The size of the wormhole throat as a function of the relevant parameters is also explored.
We examine the linear stability of static, spherically symmetric wormhole solutions of Einsteins 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.
The stability of one type of the static Ellis-Bronnikov-Morris-Thorne wormholes is considered. These wormholes filled with radial magnetic field and phantom dust with a negative energy density.
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