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Travel Time Tomography in Stationary Spacetimes

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Abstract

In this paper, we consider the boundary rigidity problem on a cylindrical domain in \({\mathbb {R}}^{1+n}\), \(n\ge 2\), equipped with a stationary (time-invariant) Lorentzian metric. We show that the time separation function between pairs of points on the boundary of the cylindrical domain determines the stationary spacetime, up to some time-invariant diffeomorphism, assuming that the metric satisfies some a-priori conditions.

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Acknowledgements

GU was partly supported by NSF, a Walker Family Endowed Professorship at UW and a Si-Yuan Professorship at HKUST. YY was partly supported by NSF grant DMS-1715178, DMS-2006881, and start-up fund from MSU. The authors are grateful to the referees for helpful comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, University of Washington, Seattle, WA, 98195-4350, USA

    Gunther Uhlmann

  2. Jockey Club Institute for Advanced Study, HKUST, Clear Water Bay, Hong Kong, China

    Gunther Uhlmann

  3. Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, MI, 48824, USA

    Yang Yang

  4. Department of Mathematics, University of California Santa Barbara, Santa Barbara, CA, 93106-3080, USA

    Hanming Zhou

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  1. Gunther Uhlmann
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  2. Yang Yang
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Correspondence to Hanming Zhou.

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Uhlmann, G., Yang, Y. & Zhou, H. Travel Time Tomography in Stationary Spacetimes. J Geom Anal 31, 9573–9596 (2021). https://doi.org/10.1007/s12220-021-00620-5

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  • DOI: https://doi.org/10.1007/s12220-021-00620-5

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