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An index of strongly Callias operators on Lorentzian manifolds with non-compact boundary

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Abstract

We consider hyperbolic Dirac-type operator with growing potential on a spatially non-compact globally hyperbolic manifold. We show that the Atiyah-Patodi-Singer boundary value problem for such operator is Fredholm and obtain a formula for this index in terms of the local integrals and the relative eta-invariant introduced by Braverman and Shi. This extends recent results of Bär and Strohmaier, who studied the index of a hyperbolic Dirac operator on a spatially compact globally hyperbolic manifold.

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Acknowledgements

I would like to thank the Max Plank Institute for Mathematics in Bonn, where most of this work was conducted. I am also grateful to Christian Bär, Pengshuai Shi, Matthias Lesch, Werner Ballmann, and Yafet Sanchez Sanchez for valuable discussions.

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  1. Department of Mathematics, Northeastern University, Boston, MA, 02115, USA

    Maxim Braverman

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  1. Maxim Braverman
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Correspondence to Maxim Braverman.

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Maxim Braverman partially supported by the Simons Foundation collaboration grant #G00005104.

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Braverman, M. An index of strongly Callias operators on Lorentzian manifolds with non-compact boundary. Math. Z. 294, 229–250 (2020). https://doi.org/10.1007/s00209-019-02270-4

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