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17 Jun 2019: Hence a 7 ax 7 S(Ka)I, so our fourth equation is. ... Level 1 k1 = K s1 = S(C(0),S0 = •) K1 = Ka S1 = Sab.

17 Jun 2019: What distinguishes a stationary metric from a“static” metric? A Killing vector field Ka of a metric gab satisfies. ... Ka;b Kb;a = 0. Show that this is equivalent to. gab,cKc gacKc,b gcbKc,a = 0.

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.

17 Jun 2019: Let. Q(k) = aR′ (a)R(a). kaj′ (ka)j(ka). Obtain the relation. tan δ =Q(k)j2(ka)ka. ... Q(k)n(ka)j(ka)ka 1. Suppose thattan δ. γ. k0 k,. for some , with all other δ small for k k0.

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

17 Jun 2019: For all N, find integers ka(N) and kb(N)such that. kb(N). k=ka(N).

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.

17 Jun 2019: If Ka are the components of a contravariant vector field and gab the componentsof a metric tensor, let. ... In a particular co-ordinate system (x1,x2,x3,x4), it is given that Ka = (0, 0, 0, 1),Qab = 0.

17 Jun 2019: cosh kx cosh ka),. where k is a constant such thatlk = 2 sinh ka.

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