Abstract
We study the matter perturbations of a new AdS wormhole in (3+1)-dimensional Einstein–Born–Infeld gravity, called “natural wormhole”, which does not require exotic matters. We discuss the stability of the perturbations by numerically computing the quasi-normal modes (QNMs) of a massive scalar field in the wormhole background. We investigate the dependence of quasi-normal frequencies on the mass of scalar field as well as other parameters of the wormhole. It is found that the perturbations are always stable for the wormhole geometry which has the general relativity (GR) limit when the scalar field mass m satisfies a certain, tachyonic mass bound m^2>m_*^2 with m_*^2<0, analogous to the Breitenlohner-Freedman (BF) bound in the global-AdS space, m_{mathrm{BF}}^2=3 {Lambda }/4. It is also found that the BF-like bound m_*^2 shifts by the changes of the cosmological constant {Lambda } or angular-momentum number l, with a level crossing between the lowest complex and pure-imaginary modes for zero angular momentum l=0. Furthermore, it is found that the unstable modes can also have oscillatory parts as well as non-oscillatory parts depending on whether the real and imaginary parts of frequencies are dependent on each other or not, contrary to arguments in the literature. For wormhole geometries which do not have the GR limit, the BF-like bound does not occur and the perturbations are stable for arbitrary tachyonic and non-tachyonic masses, up to a critical mass m_{c}^2>0 where the perturbations are completely frozen.
Highlights
Oscillations in closed systems with conserved energies are described by normal modes with real frequencies
In the recent detection of gravitational waves by LIGO and VIRGO, which are thought to be radiated from mergers of binary black holes or neutron stars, there is a regime, called ring-down phase, which can be described by quasi-normal modes (QNMs) [1,2]
We have studied QNMs for a massive scalar field in the background of a natural AdS wormhole in EBI gravity, which has been recently constructed without exotic matters
Summary
Oscillations in closed systems with conserved energies are described by normal modes with real frequencies. QNMs of black hole systems have been studied for a long time and much have been known in various cases (for some recent reviews, see [4,5]) There is another important system, wormhole spacetime, which corresponds to an open system so that QNMs appear too. It would be physically clear that the local deformation of a spacetime by the presence of wormholes would not change the stability properties of the whole spacetime much from the stability property at asymptotic infinity which is governed by the BF bound: It is hard to imagine a smooth spacetime where the (matter) perturbations with are partly unstable at infinity and partly stable near wormholes, by some local effects This implies that the perturbations of massive fields in the background of AdS wormholes would show both QNMs and BF bound.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
