# Hadamard Property of the in and out States for Klein–Gordon Fields on Asymptotically Static Spacetimes

@article{Grard2016HadamardPO, title={Hadamard Property of the in and out States for Klein–Gordon Fields on Asymptotically Static Spacetimes}, author={Christian G{\'e}rard and Michał Wrochna}, journal={Annales Henri Poincar{\'e}}, year={2016}, volume={18}, pages={2715-2756} }

We consider the massive Klein–Gordon equation on a class of asymptotically static spacetimes (in the long-range sense) with Cauchy surface of bounded geometry. We prove the existence and Hadamard property of the in and out states constructed by scattering theory methods.

## 21 Citations

An evolution equation approach to the
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- Mathematics, PhysicsCommunications in Mathematical Physics
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- MathematicsAmerican Journal of Mathematics
- 2019

We consider the massive Klein-Gordon equation on asymptoti-cally Minkowski spacetimes, in the sense that the manifold is R 1+d and the metric approaches that of Minkowski space at infinity in a…

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- Mathematics, PhysicsInternational Mathematics Research Notices
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- Mathematics, Physics
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## References

SHOWING 1-10 OF 73 REFERENCES

Scattering theory for the Dirac equation on the Schwarzschild-Anti-de Sitter spacetime

- Physics, Mathematics
- 2014

We show asymptotic completeness for linear massive Dirac fields on the Schwarzschild-Anti-de Sitter spacetime. The proof is based on a Mourre estimate. We also construct an asymptotic velocity for…

Adiabatic Vacua and Hadamard States for Scalar Quantum Fields on Curved Spacetime

- Physics
- 1995

Quasifree states of a linear Klein-Gordon quantum field on globally hyperbolic spacetime manifolds are considered. Using techniques from the theory of pseudodifferential operators and wavefront sets…

Asymptotic completeness for superradiant Klein-Gordon equations and applications to the De Sitter Kerr metric

- Mathematics, Physics
- 2014

We show asymptotic completeness for a class of superradiant Klein-Gordon equations. Our results are applied to the Klein-Gordon equation on the De Sitter Kerr metric with small angular momentum of…

Classical and quantum scattering theory for linear scalar fields on the Schwarzschild metric. II

- Physics
- 1986

An alternate treatment of the results of paper I is given. As in that paper, the Unruh boundary condition is formulated, the Unruh vacuum is defined as a state satisfying this boundary condition and…

Existence of the S-matrix in quantum field theory in curved space-time☆

- Physics
- 1979

The existence of the S-matrix is proven for particle creation by an external gravitational field of compact support. No infrared divergences occur even for massless quantum fields; in particular, a…

Hadamard States for the Klein–Gordon Equation on Lorentzian Manifolds of Bounded Geometry

- Mathematics, Physics
- 2016

We consider the Klein–Gordon equation on a class of Lorentzian manifolds with Cauchy surface of bounded geometry, which is shown to include examples such as exterior Kerr, Kerr-de Sitter spacetime…

Conformal scattering on the Schwarzschild metric

- Physics, Mathematics
- 2013

We show that existing decay results for scalar fields on the Schwarzschild metric are sufficient to obtain a conformal scattering theory. Then we re-interpret this as an analytic scattering theory…

Hadamard state in Schwarzschild-de Sitter spacetime

- Physics, Mathematics
- 2014

We construct a state in the Schwarzschild-de Sitter spacetime which is invariant under the action of its group of symmetries. Our state is not defined in the whole Kruskal extension of this…

A Quantitative Version of Hawking Radiation

- Physics, Mathematics
- 2015

AbstractWe present a proof of the existence of the Hawking radiation for massive bosons in the Schwarzschild--de Sitter metric. It provides estimates for the rates of decay of the initial quantum…

Hadamard States for the Linearized Yang–Mills Equation on Curved Spacetime

- Mathematics, Physics
- 2014

We construct Hadamard states for the Yang–Mills equation linearized around a smooth, space-compact background solution. We assume the spacetime is globally hyperbolic and its Cauchy surface is…