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          Institute: MPI für Gravitationsphysik     Collection: Geometric Analysis and Gravitation     Display Documents



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ID: 293642.0, MPI für Gravitationsphysik / Geometric Analysis and Gravitation
How to bypass Birkhoff through extra dimensions (a simple framework for investigating the gravitational collapse in vacuum)
Authors:Bizon, Piotr; Schmidt, Bernd G.
Date of Publication (YYYY-MM-DD):2006
Title of Journal:International Journal of Modern Physics D
Volume:15
Start Page:2217
End Page:2222
Review Status:not specified
Audience:Not Specified
Abstract / Description:It is fair to say that our current mathematical understanding of the dynamics of gravitational collapse to a black hole is limited to the spherically symmetric situation and, in fact, even in this case much remains to be learned. The reason is that Einstein's equations become tractable only if they are reduced to a 1+1 dimensional system of partial differential equations. Due to this technical obstacle, very little is known about the collapse of pure gravitational waves because by Birkhoff's theorem there is no spherical collapse in vacuum. In this essay we describe a new cohomogeneity-two symmetry reduction of the vacuum Einstein equations in five and higher odd dimensions which evades Birkhoff's theorem and admits time dependent asymptotically flat solutions. We argue that this model provides an attractive 1+1 dimensional geometric setting for investigating the dynamics of gravitational collapse in vacuum.
Comment of the Author: received "honorable mention" in 2006 Gravity Research Foundation essay contest
External Publication Status:published
Document Type:Article
Communicated by:Gerhard Huisken
Affiliations:MPI für Gravitationsphysik/Geometric Analysis and Gravitation
Identifiers:URL:http://ejournals.wspc.com.sg/ijmpd/15/1512/S021827...
DOI:10.1142/S0218271806009649
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