# The Formation of Black Holes in General Relativity

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*Demetrios Christodoulou*

A publication of the European Mathematical Society

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.

Since that time a major challenge 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 this 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.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

#### Readership

Graduate students and research mathematicians interested in mathematical physics.