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Radiation Fields on Schwarzschild Spacetime

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Abstract

In this paper we define the radiation field for the wave equation on the Schwarzschild black hole spacetime. In this context it has two components: the rescaled restriction of the time derivative of a solution to null infinity and to the event horizon. In the process, we establish some regularity properties of solutions of the wave equation on the spacetime. In particular, we prove that the regularity of the solution across the event horizon and across null infinity is determined by the regularity and decay rate of the initial data at the event horizon and at infinity. We also show that the radiation field is unitary with respect to the conserved energy and prove support theorems for each piece of the radiation field.

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Authors and Affiliations

  1. Northwestern University, Evanston, USA

    Dean Baskin

  2. Shanghai Jiao Tong University, Shanghai, China

    Fang Wang

Authors
  1. Dean Baskin
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  2. Fang Wang
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Correspondence to Dean Baskin.

Additional information

Communicated by P. T. Chruściel

The authors are grateful to Antônio Sá Barreto for pointing out the simple proof of the 1 + 1-dimensional support theorem. D.B. was supported by NSF postdoctoral fellowship DMS-1103436.

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Baskin, D., Wang, F. Radiation Fields on Schwarzschild Spacetime. Commun. Math. Phys. 331, 477–506 (2014). https://doi.org/10.1007/s00220-014-2047-4

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  • DOI: https://doi.org/10.1007/s00220-014-2047-4

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