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Quasi-Normal Modes of a Natural AdS Wormhole in Einstein-Born-Infeld Gravity
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^2_BF = 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^2_c > 0 where the perturbations are completely frozen.Comment: Added comments and references, Accepted in EPJ
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