Abstract
Here we shall show how to reconstruct the shape function of a spherically symmetric traversable Lorenzian wormhole near its throat if one knows high frequency quasinormal modes of the wormhole. The wormhole spacetime is given by the Morris–Thorne ansatz. The solution to the inverse problem via fitting of the parameters within the WKB approach is unique for arbitrary tideless wormholes and some wormholes with non-zero tidal effects, but this is not so for arbitrary wormholes. As examples, we reproduce the near throat geometries of the Bronnikov–Ellis and tideless Morris–Thorne metrics by their quasinormal modes at high multipole numbers ℓ.
Highlights
Recent observations of gravitational waves from compact objects [1] still do not single out the geometry of the sources
This occurs mainly because the mass and angular momentum of the object is known with large uncertainty, so that within the current precision of measurements a non-Kerr geometry can effectively mimic the Kerr ringdown phase, allowing for small [2], but even relatively large deviations from Kerr geometry [3]
This means the pure outgoing waves at both infinities or no waves coming from either left or right infinity. This is quite natural condition if one remembers that quasinormal modes are proper oscillations of wormholes, i.e. they represent response to the perturbation when the initial perturbation stopped acting
Summary
Recent observations of gravitational waves from compact objects [1] still do not single out the geometry of the sources (though the Kerr solution is the most celebrated and probable candidate). Neglecting the echo effects, it is reasonable to be restricted by a class of the effective potentials which have the form of the potential barrier, symmetric relatively its throat, so that the maximum of the effective potential coincides with the position of the throat This occurs for a wide class of wormholes and is guaranteed, for example for all Morris- Thorne metrics whose function gtt is monotonic in terms of the radial coordinate r. We shall consider the following inverse problem: how to reconstruct the metric of an arbitrary traversable Lorentzian wormhole near its throat if one knows the high frequency quasinormal modes of the system. VI we discuss the open questions and summarize the obtained results
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