Wormholes in higher dimensional space-time: Exact solutions and their linear stability analysis (original) (raw)
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Wormhole evolutions in higher-dimensional gravity
2013
We know numerically the four-dimensional Ellis wormhole solution (the so-called Morris-Thorne’s traversable wormhole) is unstable against an input of scalar-pulse from one side. We investigate this feature for higher-dimensional versions, both in ndimensional general relativity and in 5-dimensional Gauss-Bonnet gravity. We derived Ellis wormhole solutions in n-dimensional general relativity, and evolved it numerically in dual-null coordinate with/without Gauss-Bonnet corrections. Preliminary results show that those are also unstable. We also find that the throat of wormhole in Gauss-Bonnet gravity tends to expand (or shrink) after an input of ghost-scalar pulse if the coupling constant α is positive (negative).
Wormhole in higher-dimensional space-time
Journal of Physics: Conference Series, 2015
We introduce our recent studies on wormhole, especially its stability aspect in higher-dimensional space-time both in general relativity and in Gauss-Bonnet gravity. We derived the Ellis-type wormhole solution in n-dimensional general relativity, and found existence of an unstable mode in its linear perturbation analysis. We also evolved it numerically in dualnull coordinate system, and confirmed its instability. The wormhole throat will change into black hole horizons for the input of the (relatively) positive energy, while it will change into inflationary expansion for the (relatively) negative energy input. If we add Gauss-Bonnet terms (higher curvature correction terms in gravity), then wormhole tends to expand (or change to black hole) if the coupling constant α is positive (negative), and such bifurcation of the throat horizon is observed earlier in higher dimension.
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.
Journal of Physics: Conference Series, 2015
Wormholes are theoretical products in general relativity, and are popular tools in science fictions. We know numerically the four-dimensional Ellis wormhole solution (the socalled Morris-Thorne's traversable wormhole) is unstable against an input of scalar-pulse from one side. We investigate this feature for higher-dimensional versions, both in n-dimensional general relativity and in Gauss-Bonnet gravity. We derived Ellis-type wormhole solution in ndimensional general relativity, and found existence of unstable modes in its linear perturbation analysis. We also evolved it numerically in dual-null coordinate system, and confirmed its instability. The wormhole throat will change into black-hole horizon for the input of (relatively) positive energy, while it will change into inflationary expansion for (relatively) negative energy input. If we add Gauss-Bonnet terms (higher curvature correction terms in gravity), then wormhole tends to expand (or change to black-hole) if the coupling constant α is positive (negative).
Spherically symmetric wormholes can be linearly stable
2021
In this work we study the problem of linear stability of gravitational perturbations in stationary and spherically symmetric wormholes. For this purpose, we employ the Newman-Penrose formalism which is well-suited for treating gravitational radiation in General Relativity, as well as the geometrical aspect of this theory. With this method we obtain a “master equation” that describes the behavior of perturbations that are “vacuum-like” and of odd-parity in the Regge-Wheeler gauge. This equation is later applied to a specific class of Morris-Thorne wormholes and also to the metric of an asymptotically flat scalar field wormhole. The analysis of the equations that these space-times yield reveals that they are stable with respect to the type of perturbations here studied.
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.
New wormhole solutions in a viable f (R) gravity model
International Journal of Modern Physics D
Traversable wormhole solutions in General Relativity require exotic matter sources that violate the null energy condition (NEC), and such behavior may be avoided in modified gravity. In this study, we analyze the energy conditions for static, spherically symmetric traversable Morris–Thorne wormholes in a recently proposed viable [Formula: see text] gravity model. We numerically analyze solutions considering both constant and variable redshift functions, and present wormhole spacetimes respecting the NEC, supported by a phantom energy-like equation of state for the source. Moreover, we analyze the stability of the spacetimes using the generalized Tolman–Oppenheimer–Volkov equation. We demonstrate the effects of certain parameters in the [Formula: see text] model in determining energy condition violations, and establish that stable wormholes can be formulated only at the expense of violating the NEC.
Stability of Einstein-Power-Maxwell (2+1)-Dimensional Wormholes
Chinese Journal of Physics, 2019
This paper is devoted to the study of stable and unstable geometrical structures of charged thinshell wormholes constructed from Einstein-power-Maxwell black holes by using Visser cut and paste approach. We use Israel thin-shell formalism to evaluate the stress-energy tensor components of matter distribution located at the wormhole throat. The stability of thin-shell is investigated by using equations of state (phantom-like and generalized Chaplygin gas model) for exotic matter and radial perturbation about equilibrium throat radius. We conclude that stable regions increase by increasing the charge parameter. 1. Introduction Recent research trend indicates a remarkable interest to the study of black holes (BHs) configuration in (2+1)-dimensions. Such BHs have all properties that can be observed in (3+1)-dimensions or higher-dimensional BHs, i.e., event horizons, thermodynamics and Hawking temperature. It is mentioned here that the mathematical structure of higher-dimensional BHs is much complicated as compared to (2+1)-dimensional BHs. Firstly, Bañados, Teitelboim and Zanelli (BTZ) [1] introduced a (2+1)-dimensional BH, afterwards it was extended for Einstein-Maxwell-dilaton theory [2] and then Einstein-Maxwell theory [3]. Later on, Cataldo et al. [4] formulated another (2+1)-dimensional BH with a restricted class of nonlinear electrodynamics. They studied a particular power of Maxwell scalar, i.e., (F μν F μν) 3/4 by using traceless condition on the energy-momentum tensor. Hassaine and Martinez [5] considered an action for Abelian gauge field and studied the higher-dimensional BHs with a conformally invariant Maxwell source. The same authors [6] formulated charged BH solutions in arbitrary dimensions with a nonlinear electrodynamics source. They considered the matter Lagrangian with an arbitrary power (k) of the Maxwell invariant (F μν F μν) k. Gurtug et al. [7] developed a (2+1)-dimensional BH without using traceless condition in the Einstein-power-Maxwell (EPM) theory. Recently, Abbas and Ditta [8] studied the EPM BH in (2+1)-dimensions and observed the accretion process for isothermal flow of different falling fluids into the BH. In general relativity, traversable wormholes (WHs) have great interest due to their stable configuration that allow two-way observer motion from one region to another of a distant universe. The exotic matter is the main ingredient to keep the traversable WH in stable position. The presence of exotic matter at WH throat is realized through energy conditions. The surface stress-energy tensor of matter distribution can be evaluated through Israel thin-shell formalism [9]. Visser [10] observed that the violation of energy conditions can be minimized for some specific geometrical structure of WH. The stable configuration of thin-shell WH is a momentous topic in cosmology as well as astrophysics as it helps to explore the viable WH solutions. The equation of state (EoS) for matter distribution at the WH throat is the significant tool to analyze its stable
Instability of charged wormholes supported by a ghost scalar field
Physical Review D, 2009
In previous work, we analyzed the linear and nonlinear stability of static, spherically symmetric wormhole solutions to Einstein's field equations coupled to a massless ghost scalar field. Our analysis revealed that all these solutions are unstable with respect to linear and nonlinear spherically symmetric perturbations and showed that the perturbation causes the wormholes to either decay to a Schwarzschild black