LMS Invited Lecture Series

31 March - 4 April, 2009

Black holes in a vacuum: examples and uniqueness properties

Professor Alexandru Ionescu

The Maxwell Institute Centre for Analysis and

Nonlinear Partial Differential Equations

Local Organiser: James Wright


[Introduction] [Course Overview] [Accommodation] [Registration] [Further Information]


The 2009 LMS Invited Lectures will be given at Edinburgh University and is co-sponsered by the Maxwell Institute Centre for Analysis and Nonlinear PDEs. The series is held annually: a single speaker gives a course of 10 expository lectures, examining an important topic in depth over a five day period. In the 2009 programme there will be two lectures each morning given by Professor Ionescu from the University of Wisconsin, who will cover the following topics

  • Lorentzian geometry: basic definitions
  • The Einstein vacuum equations
  • Special solutions: Minkowski, Schwarzschild, Kerr
  • Stationary regular black holes
  • Unique continuation: examples
  • The uniqueness of the Kerr solution (3-4 lectures on this topic)
  • In addition to the lectures given by Professor Ionescu there will be more specialised one hour lectures given by

    Lars Andersson (Albert Einstein Institute) on 01 April at 3pm

    "Hidden symmetries and the wave equation on Kerr" Abstract

    Alan Rendall (Albert Einstein Institute) on 02 April at 3pm

    "Cosmic censorship: an introduction and status report"

    Juan Antonio Valiente Kroon (Queen Mary, London) on 03 April at 3pm

    "A characterisation of initial data sets for Kerr spacetime" Abstract

    Here is the timetable for the lectures Timetable

    Course Overview

    Uniqueness properties of the Kerr space-times

    A fundamental conjecture in General Relativity asserts that the domain of outer communication of a regular, stationary, four dimensional, vacuum black hole is isometrically diffeomorphic to the domain of outer communication of a Kerr black hole. One expects, due to gravitational radiation, that general, asymptotically flat solutions of the Einstein-vacuum equations1 settle down, asymptotically, into a stationary regime. Thus the conjecture, if true, would characterize all possible asymptotic states of the general evolution. So far the conjecture has been resolved, by combining results of Hawking [2] Carter [1] and Robinson [3], under the additional hypothesis of non-degenerate horizons and real analyticity of the space-time. The assumption of real analyticity is both hard to justify on physical grounds and difficult to dispense of. I will discuss some recent work, joint with S. Klainerman, aimed at understanding this conjecture in the class of smooth manifolds. We develop a new strategy to bypass analyticity based on a tensorial characterization of the Kerr space-times, and new geometric Carleman estimates.

    [1] B. Carter, An axy-symmetric black hole has only two degrees of freedom, Phys. Rev. Lett., 26, (1971) 331-333.

    [2] S.W. Hawking and G.F.R. Ellis, The large scale structure of space-time, Cambridge Univ. Press, 1973

    [3] D.C. Robinson, Uniqueness of the Kerr black hole, Phys. Rev. Lett. 34 (1975), 905-906.

    A longer course overview is available here.


    For nonlocal participants, accommodation has been arranged in single rooms with ensuite at
    Pollock Halls . In addition to accommodation, breakfast and dinner will be provided at Pollock Halls. Lunch will also be provided for course participants. Please arrive at the Reception Centre of Pollock Halls (click on "Location map" under the Pollock Halls link above) after 2pm on Monday, 30 March, 2009. There will be a registration and wine reception from 4 to 6pm in the Red Room at the Salisbury Green Hotel (see "Location map"). The lectures will finish by 2pm on Saturday, 04 April so arrange your travel back home sometime after this time.


    There is a registration fee of 30 pounds payable upon arrival. The registration fee will be waived for research students. Funds are available to support participants. Priority will be given to research students and mathematicians who would benefit from attending the lectures, but who would otherwise be prevented from attending by financial constraints.

    The number of participants will be limited so we encourage those who are interested in participating to contact James Wright (J.R.Wright@ed.ac.uk) as early as possible.

    Further Information

    For further information or to express interest in taking part in the Invited Lecture Series, contact

    Professor James Wright
    School of Mathematics
    University of Edinburgh
    Mayfield Road
    Edinburgh EH9 3JZ
    Tel. +44 (0)131 650 8570
    Fax. +44 (0)131 650 6553

    Page last modified: 20 March, 2009