Classical Scattering Theory on the Schwarzschild Metric and the Construction of Quantum Linear Fields on Black Holes

  • Bernard S. Kay
Part of the NATO ASI Series book series (NSSB, volume 144)


I would like to discuss some aspects of the theory of linear fields propagating on black holes. At the quantum level, I describe
  1. (a)

    A construction – due to Jonathan Dimock and myself – of both the Hartle-Hawking and Unruh states for linear scalar fields on the Schwarzschild metric (together with results on the asymptotic and horizon properties of these states.)

    As an essential preliminary to these quantum results, I first treat at some length

  2. (b)

    Results – due also to Jonathan Dimock and myself – on the classical scattering theory of linear scalar fields on black holes. (Included in this discussion are results on the characteristic initial value problem for data on the horizon as well as results on the classical linear stability of spherically symmetric black holes.)

    These classical results are of some interest in their own right. I also mention

  3. (c)

    An axiomatic result - due to Robert Wald and myself - on the uniqueness of the Hartle-Hawking state. This result applies to quasi-free states of linear fields only but it is of interest since it is considerably stronger than the specialization to this case of the presently known general axiomatic result.



Black Hole Minkowski Space Cauchy Surface Cauchy Data Symmetric Black Hole 
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Copyright information

© Plenum Press, New York 1986

Authors and Affiliations

  • Bernard S. Kay
    • 1
  1. 1.Institut für Theoretische PhysikUniversität ZürichZürichSwitzerland

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