Paper66_2 - MATHEMATICAL TRIPOS Friday 30 May 2008 Part III 1.30 to 4.30 PAPER 66 BLACK HOLES Attempt no more than THREE questions There are FOUR

Paper66_2 - MATHEMATICAL TRIPOS Friday 30 May 2008 Part III...

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MATHEMATICAL TRIPOS Part III Friday 30 May 2008 1.30 to 4.30 PAPER 66 BLACK HOLES Attempt no more than THREE questions. There are FOUR questions in total. The questions carry equal weight. STATIONERY REQUIREMENTS SPECIAL REQUIREMENTS Cover sheet None Treasury Tag Script paper You may not start to read the questions printed on the subsequent pages until instructed to do so by the Invigilator.
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2 1 (a) State (without explanation) which of the space-times listed below is (i) extendible; (ii) geodesically complete; (iii) globally hyperbolic; (iv) asymptotically simple. (Present your answers in the form of a table.) The region r > 2 M of the Schwarzschild solution (with M > 0 ), Kruskal, the maximal analytic extension of extremal Reissner-Nordstrom, Rindler, the Einstein static universe. (b) The Majumdar-Papapetrou (MP) solution has metric ds 2 = - H - 2 dt 2 + H 2 ( dx 2 + dy 2 + dz 2 ) , H ( x,y,z ) = 1 + N X i =1 M i | x - x i | where M i > 0 , x = ( ), and x i are constant vectors in R 3 .
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