# Scattering theory for Dirac fields near an extreme Kerr-de Sitter black hole

@article{Borthwick2020ScatteringTF, title={Scattering theory for Dirac fields near an extreme Kerr-de Sitter black hole}, author={Jack Borthwick}, journal={arXiv: Mathematical Physics}, year={2020} }

In this paper, we construct a scattering theory for classical massive Dirac fields near the "double" horizon of an extreme Kerr-de Sitter blackhole. Our main tool is the existence of a conjugate operator in the sense of Mourre theory. Additionally, despite the fact that effects of the rotation are 'amplified' near the double horizon, we show that one can still reduce our study to a 1-dimensional problem through an appropriate decomposition of the Hilbert space.

## One Citation

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## References

SHOWING 1-10 OF 41 REFERENCES

### Time-dependent scattering theory for charged Dirac fields on a Reissner–Nordström black hole

- Mathematics
- 2010

In this paper, we prove a complete time-dependent scattering theory for charged (massive or not) Dirac fields outside a Reissner–Nordstrom black hole. We shall take the point of view of observers…

### A remark about wave equations on the extreme Reissner–Nordström black hole exterior

- Mathematics
- 2012

We consider a massless scalar field propagating on the exterior of the extreme Reissner–Nordström black hole. Using a discrete conformal symmetry of this spacetime, we draw a one-to-one relationship…

### The Dirac equation in Kerr–Newman–Ads black hole background

- Physics
- 2010

We consider the Dirac equation on the Kerr–Newman–AdS black hole background. We first perform the variable separation for the Dirac equation and define the Hamiltonian operator H. Then we show that…

### Direct and inverse scattering at fixed energy for massless charged Dirac fields by Kerr-Newman-de Sitter black holes

- Mathematics
- 2013

In this paper, we study the direct and inverse scattering theory at fixed energy for massless charged Dirac fields evolving in the exterior region of a Kerr-Newman-de Sitter black hole. In the first…

### The Unruh state for massless fermions on Kerr spacetime and its Hadamard property

- Physics
- 2020

We give a rigorous definition of the Unruh state in the setting of massless Dirac fields on slowly rotating Kerr spacetimes. In the black hole exterior region, we show that it is asymptotically…

### Maxwell field on the Reissner-Nordst∫rm-De Sitter manifold : decay and conformal scattering

- Mathematics
- 2016

We study Maxwell fields on the exterior of Reissner-Nordstrom-de Sitter black holes. We start by studying the geometry of these spacetimes: we give the condition under which the metric admits three…

### Maximal Kerr–de Sitter spacetimes

- MathematicsClassical and Quantum Gravity
- 2018

In this paper, we propose a survey of the basic geometric properties of Carter’s Kerr–de Sitter solution to Einstein’s equation with cosmological constant. In particular, we give simple…

### The absence of normalizable time-periodic solutions for the Dirac equation in the Kerr–Newman–dS black hole background

- Physics
- 2009

We consider the Dirac equation on the background of a Kerr–Newman–de Sitter black hole. By performing variable separation, we show that no time-periodic and normalizable solution of the Dirac…

### A scattering theory for the wave equation on kerr black hole exteriors

- Mathematics
- 2018

We develop a definitive physical-space scattering theory for the scalar wave equation on Kerr exterior backgrounds in the general subextremal case |a|<M. In particular, we prove results corresponding…

### 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…