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#### Seminar at the

#### Laboratoire Jacques-Louis Lions

#### Sorbonne Université, Paris

*Organizers*

#### Philippe G. LeFloch (Sorbonne, Paris)

#### Jacques Smulevici (Sorbonne, Paris)

#### Jérémie Szeftel (Sorbonne, Paris)

**Dates of the Seminar this Fall 2018**

**September 24, October 29, November 19**

#### Monday September 24, 2018

*room 15/16-309*

#### 14h Dietrich Häfner (Grenoble)

#### Scattering for Dirac and Klein-Gordon fields on the (De Sitter) Kerr metric and the Hawking effect

Abstract. We consider Dirac and Klein-Gordon fields on the (De Sitter) Kerr metric which describes rotating black holes. Whereas there exists a conserved L2 norm for the Dirac field, no positive conserved quantity exists for the Klein-Gordon field, which makes the analysis more difficult for the latter. We obtain asymptotic completeness results for the Dirac field on the Kerr and for the Klein-Gordon field on the De Sitter Kerr metric. We then present a rigorous result about the Hawking effect for fermions in the setting of a collapse of a rotating charged star. This effect predicts the creation of particles by black holes.

#### 15h30 Jean-Philippe Nicolas (Brest)

#### Peeling for scalar fields on the Kerr metric

Abstract. The peeling is an asymptotic behavior of massless fields along outgoing null geodesics in asymptotically flat spacetimes, initially observed by Sachs at the beginning of the 1960’s, then reformulated in very simple terms by Penrose in 1965 using conformal geometry. The question of its genericity, especially when talking about the peeling of the Weyl tensor of an Einstein spacetime, was controversial for several decades after Penrose’s paper. For Einstein’s equations, the question is now essentially settled, but given an Einstein spacetime, it is not clear whether there is a large class of Cauchy data giving rise to solutions with a good peeling. Lionel Mason and the speaker answered the question for fields of spin 0, 1/2 and 1 on Schwarzschild’s spacetime in 2009 and 2012. We extended recently the results to linear and non linear scalar fields on the Kerr geometry in a joint work with Pham Truong Xuan. We shall recall the history of the subject, describe the principles of the approach developed with Lionel Mason and talk about the specific features of our work for Kerr metrics.

#### Monday October 29, 2018

*room TBA*

#### 14h Joe Keir (Cambridge)

#### 15h30 Volker Schlue (Paris)

#### Scattering from infinity for semilinear wave equations

#### Monday November 19, 2018

*room 15/16-309*

#### 14h TBA

#### 15h30 TBA