Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2006-05-21
Int.J.Mod.Phys.D15:2217-2222,2006
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
7 pages, received "honorable mention" in 2006 Gravity Research Foundation essay contest
Scientific paper
10.1142/S0218271806009649
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.
Bizoń Piotr
Schmidt Bernd G.
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