Revisiting a family of wormholes: geometry, matter, scalar quasinormal modes and echoes
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Regular Article - Theoretical Physics
Revisiting a family of wormholes: geometry, matter, scalar quasinormal modes and echoes Poulami Dutta Roy1,a , S. Aneesh2,b , Sayan Kar1,3,c 1
Department of Physics, Indian Institute of Technology, Kharagpur 721 302, India Department of Physics, University of Florida, 2001 Museum Road, P.O. Box 118440, Gainesville, FL 32611-8440, USA 3 Centre for Theoretical Studies, Indian Institute of Technology, Kharagpur 721 302, India
2
Received: 14 July 2020 / Accepted: 23 August 2020 © The Author(s) 2020
Abstract We revisit a family of ultra-static Lorentzian wormholes which includes Ellis–Bronnikov spacetime as a special case. We first show how the required total matter stress energy (which violates the local energy conditions) may be split into a part due to a phantom scalar and another extra piece (which vanishes for Ellis–Bronnikov) satisfying the Averaged Null Energy Condition (ANEC) along radial null geodesics. Thereafter, we examine the effective potential for scalar wave propagation in a general setting. Conditions on the metric function, for which the effective potential may have double barrier features are written down and illustrated (using this class of wormholes). Subsequently, using numerous methods, we obtain the scalar quasinormal modes (QNMs). We note the behaviour of the QNMs as a function of n (the metric parameter) and b0 (the wormhole throat radius). Thus, the shapes and sizes of the wormholes, governed by the metric parameter n and the throat radius b0 are linked to the variation and the values of the QNMs. Finally, we demonstrate how, for large n, the time domain profiles exhibit, expectedly, the occurence of echoes. In summary, our results suggest that this family of wormholes may indeed be used as a template for further studies on the gravitational wave physics of exotic compact objects.
1 Introduction Much of the interest today in traversable Lorentzian wormhole spacetimes (originally proposed in [1–3]) revolve around the question: do they exist? While the existence of black holes is no longer in doubt (more so after recent observations in M87 [4]), the wormhole story is far from complete. a e-mail:
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The same may be said about naked singularities and cosmic censorship too [5,6]. The existence question on wormholes is based on a couple of issues. Firstly, classical General Relativity (GR) along with the imposed energy conditions does not allow wormholes [7–11]. In other words, the shape of the spatial slice of a wormhole is such that a converging null geodesic congruence would have to be defocused, as long as a throat and a ‘flare out to the other universe’ (second asymptotically flat region) – both necessary geometric features of wormholes – have to be admitted [12–14]. To get away with this so-called ‘defect’ or ‘problem’ one may appeal to modified theories of gravity. In such theories, the energy conditions on matter m
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