Volker Schlue

Volker Schlue Postdoctoral Fellow
Department of Mathematics
40 St George Street Rm 6290
Toronto, ON M5S 2E4

vschlue(at)math.utoronto.ca

I am presently a postdoctoral fellow at the University of Toronto. My research interests are in problems related to mathematical general relativity.

I received my Ph.D. in 2012 as a student of Mihalis Dafermos in Cambridge. Since then I have been a Postdoctoral Fellow at MSRI in Berkeley, where I was mentored by Hans Lindblad, and a Visiting Postdoctoral Research Associate at Princeton. Here in Toronto I work with Spyros Alexakis.

Next year I will be in Paris as a Postdoc de la Fondation Sciences Mathematiques de Paris.

Curriculum Vitae: CV.

Upcoming Talks

Recent Talks

  1. International Conference on Black Holes, Fields Institute, Toronto, June 2, 2015. [Video]
  2. Colloquium, University of Miami, February 2, 2015. [Slides]
  3. Mathematical Problems in General Relativity, Simons Center for Geometry and Physics, January 21, 2015. [Video]
  4. Analysis and PDEs Seminar, Johns Hopkins University, March 10, 2014.
  5. Analysis Seminar, Princeton University, March 3, 2014.
  6. Nonlinear Wave Equations and General Relativity Workshop, University of Oxford, January 13-14, 2014.
  7. Geometry Seminar, Stanford University, November 11, 2013.
  8. MSRI Postdoc Seminar, Evans Hall, University of California, Berkeley, October 25, 2013.
  9. MGR Programmatic Seminar, MSRI, Berkeley, October 1, 2013.
  10. more ...

Publications

  1. Decay of linear waves on higher dimensional Schwarzschild black holes,
    Analysis & PDE 6-3 (2013), 515--600.

    Published version: [pdf] (screen) [pdf] (printing)

    In this paper I prove several decay statements for solutions to the wave equation on Schwarzschild black hole spacetimes in all dimensions. While the quantitative decay rates had been established in the 3+1-dimensional case, c.f. Luk (2009), the main interest in this paper lies in its method of proof, which uses and extends the "new physical-space approach to decay" of Dafermos and Rodnianski (2009).

  2. Global results for linear waves on expanding Kerr and Schwarzschild de Sitter cosmologies,
    Communications in Mathematical Physics: Volume 334, Issue 2 (2015), 977--1023.

    Published version: Springer, arXiv: 1207.6055v2

    In this paper I develop the global study of linear waves on Kerr de Sitter spacetimes. I am particularly interested here in the so-called cosmological region that is bounded in the past by the cosmological horizons and to the future by a spacelike hypersurface at infinity. It is shown that the expansion of that region provides a stability mechanism that manifests itself in a global redshift effect; moreover this effect persists in a large class of expanding cosmologies near the Schwarzschild de Sitter geometry. Global boundedness and decay results are obtained when our estimates are combined with earlier work concerning the stationary region by Dafermos and Rodnianski (2007) and Dyatlov (2010).

  3. (with Spyros Alexakis and Arick Shao) Unique continuation from infinity for linear waves, arXiv:1312.1989, 47 pages.

    Video: Banff, Geometry and Inverse problems workshop (Spyros Alexakis).

    We explore in this paper the question if solutions to wave equations are completely determined from their radiation towards infinity. We are led to show that if the radiation fields of two solutions to a wave equation with suitably fast decaying coefficients conincide to all orders on suitable parts of null infinity, then these solutions indeed coincide in a neighborhood of infinity. The size of this neighborhood depends strongly on the geometry of the asymptotically flat background spacetime; in particular we find that a positive mass of the spacetime works strongly in our favor.

  4. (with Spyros Alexakis) Non-existence of time-periodic vacuum spacetimes, arXiv:1504.04592, 50 pages.

    Video: Simons Center for Geometry and Physics (Volker Schlue)

    In this paper we address an older question in general relativity: Is it possible for an isolated self-gravitating relativistic system to be in periodic motion? We prove that any asymptotically flat spacetime, which is assumed to be time-periodic and a solution to the Einstein vacuum equations far away from the sources, must be stationary, at least near infinity. Thus genuinely time-periodic solutions do not exist. This problem has been repeatedly studied, first by Papapetrou [Annalen der Physik, 1957], and most recently by Bicak, Scholz and Tod [arXiv:1003.3402], whose approach yields a symmetry "at infinity". Our proof relies crucially on the uniqueness results for linear waves obtained in our previous [3.] for the extension of this symmetry to the spacetime.

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