https://doi.org/10.1140/epjc/s10052-018-6478-5
Regular Article - Theoretical Physics
Quasi-normal modes of a natural AdS wormhole in Einstein–Born–Infeld Gravity
1
Department of Physics, Kunsan National University, Kunsan, 54150, Korea
2
Research Institute for Basic Science, Sogang University, Seoul, 121-742, Korea
* e-mail: muinpark@gmail.com
Received:
27
September
2018
Accepted:
26
November
2018
Published online:
3
December
2018
We study the matter perturbations of a new AdS wormhole in 
-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 
with 
, analogous to the Breitenlohner-Freedman (BF) bound in the global-AdS space, 
. It is also found that the BF-like bound 
shifts by the changes of the cosmological constant 
or angular-momentum number l, with a level crossing between the lowest complex and pure-imaginary modes for zero angular momentum 
. 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 
where the perturbations are completely frozen.
© The Author(s), 2018
