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The Formation of Black Holes in General Relativity
EMS Monographs in Mathematics

Demetrios Christodoulou (ETH Zürich, Switzerland)

The Formation of Black Holes in General Relativity

ISBN print 978-3-03719-068-5, ISBN online 978-3-03719-568-0
DOI 10.4171/068
January 2009, 599 pages, hardcover, 16.5 x 23.5 cm.
98.00 Euro

In 1965 Penrose introduced the fundamental concept of a trapped surface, on the basis of which he proved a theorem which asserts that a spacetime containing such a surface must come to an end. The presence of a trapped surface implies, moreover, that there is a region of spacetime, the black hole, which is inaccessible to observation from infinity.

A major challenge since that time has been to find out how trapped surfaces actually form, by analyzing the dynamics of gravitational collapse. The present monograph achieves this aim by establishing the formation of trapped surfaces in pure general relativity through the focusing of gravitational waves.

The theorems proved in the present monograph constitute the first foray into the long-time dynamics of general relativity in the large, that is, when the initial data are no longer confined to a suitable neighborhood of trivial data. The main new method, the short pulse method, applies to general systems of Euler–Lagrange equations of hyperbolic type, and provides the means to tackle problems which have hitherto seemed unapproachable.

This monograph will be of interest to people working in general relativity, geometric analysis, and partial differential equations.

Further Information

Videos of the author's talks at Hot Topics: Black Holes in Relativity, MSRI Berkeley, September 15,2009

Review in Zentralblatt MATH 1197.83004

Review in MR 2488976

Christodoulou and Hamilton Receive 2011 Shaw Prize

EMS Review