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Hearing the Nature of Compact Objects

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Einstein Equations: Physical and Mathematical Aspects of General Relativity (DOMOSCHOOL 2018)

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Abstract

In this article we present results on the quasi-normal mode spectra of compact relativistic objects and discuss under what conditions they can be used to solve the inverse spectrum problem. We start from the one-dimensional wave equation for axial gravitational perturbations of spherically symmetric and non-rotating compact objects in general relativity. It is then shown how WKB methods can be used to approximate the spectrum and reconstruct the underlying perturbation potential by using different Bohr–Sommerfeld rules. The uniqueness and properties of the reconstructed relations are discussed as well.

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Notes

  1. 1.

    The approach was known before quantum mechanics, but it became popular there. We want to note that although the terminology might relate it to quantum mechanics, there is no such aspect assumed here. It is an approximate method for finding solutions of the wave equation.

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Acknowledgements

SV wants to thank the organizers and all participants of Domoschool 2018 for creating an unforgettable week of learning and cultural exchange in the beautiful town of Domodossola. The authors also want to thank Daniela D. Doneva for useful discussions. SV is indebted to the Baden-Württemberg Stiftung for the financial support of this research project by the Eliteprogramme for Postdocs and receives the PhD scholarship Landesgraduiertenförderung.

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Authors and Affiliations

  1. University of Tübingen, Theoretical Astrophysics, Tübingen, Germany

    Sebastian H. Völkel & Kostas D. Kokkotas

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  1. Sebastian H. Völkel
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  2. Kostas D. Kokkotas
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Correspondence to Sebastian H. Völkel .

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Editors and Affiliations

  1. Department of Science and High Technology, University Insubrien, Como, Italy

    Sergio Cacciatori

  2. Mathematisches Institut, Humboldt-Universität zu Berlin, Berlin, Germany

    Batu Güneysu

  3. Department of Science and High Technology, University Insubrien, Como, Italy

    Stefano Pigola

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Völkel, S.H., Kokkotas, K.D. (2019). Hearing the Nature of Compact Objects. In: Cacciatori, S., Güneysu, B., Pigola, S. (eds) Einstein Equations: Physical and Mathematical Aspects of General Relativity. DOMOSCHOOL 2018. Tutorials, Schools, and Workshops in the Mathematical Sciences . Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-18061-4_12

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