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26 Nov 2019:  Gavin Ka Chun Cheung (High Energy Physics).  Antonio Girão (DPMMS).

30 Aug 2019: 2. 1 (i) If A > 0 and N is a positive integer, define KA,N : T2 R by. ... and1. (2π)2. T2. KA,N (s, t) ds dt = 1. By considering functions of the form.

30 Aug 2019: Show that a Killing covector ka satisfies. ka;bc = Rabcdkd. A spacetime is said to be static if it possesses a timelike Killing covector ka whichis hypersurface-orthogonal. ... with ρ p > 0 then the fluid 4-velocity ua is parallel to ka. [

30 Aug 2019: a) There exists a timelike Killing vector Ka such that LKgab = LKρ = LKp = 0. ... b) The velocity Ua is proportional to Ka. Express Ua in terms of Ka and hence show that.

30 Aug 2019: kaakb = κkb. evaluated on the horizon, where ka is the time translation Killing vector.

30 Aug 2019: MATHEMATICAL TRIPOS Part III. Tuesday 12 June 2001 9 to 12. PAPER 76. COMBINATORIAL NUMBER THEORY. Attempt any THREE questions. The questions carry equal weight. You may not start to read the questions. printed on the subsequent pages until.

30 Aug 2019: iii) Deduce from Plünnecke’s inequality that if A is a subset of an Abelian group,|A A| 6 C|A| and k, l are positive integers, then |kA lA| 6

30 Aug 2019: MATHEMATICAL TRIPOS Part III. Monday 9 June 2003 1.30 to 4.30. PAPER 56. BLACK HOLES. Attempt THREE questions. There are four questions in total. The questions carry equal weight. You may not start to read the questions. printed on the subsequent

30 Aug 2019: where ka is the Killing vector associated with time translations. Briefly describe why thisintegral should be proportional to the mass.

30 Aug 2019: MATHEMATICAL TRIPOS Part III. Friday 6 June 2008 9.00 to 12.00. PAPER 65. APPLICATIONS OF DIFFERENTIAL GEOMETRY TO PHYSICS. Attempt FOUR questions. There are SEVEN questions in total. The questions carry equal weight. STATIONERY REQUIREMENTSCover