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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.

12 Jul 2023: Compute PHintP and use it to derive. 〈[Hint,n. a. φa(ka)]〉 = 2 Re〈Hintn. ... a. φa(ka)〉. (ii) Then, use the in-in formalism to derive a time integral expression for 〈na φa(ka)〉to linear order in λ.

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.

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

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).

17 Jun 2019: Let N(k) = aR′(a)/R(a). Show that. tan δ(k) =N(k) j(ka) kaj′(ka)N(k) n(ka) kan′(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

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

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.

27 Jun 2024: Deduce that P and Q satisfy. PxdI1dx. QdI0dx. = 0 when x = ka.

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

7 Jul 2023: You may assume that thetransforms are well-defined.]. (c) Express the inverse transforms of cos ka and sin ka in terms of the δ-function,where a is a positive constant.

30 Aug 2019: EITHER : The Herbrand quotient and its role in norm index calculations for L/Ka cyclic extension of p-adic fields.

30 Aug 2019: ka and the final state is a fernionic particle of 4-momentum qa and a scalar with 4-.

12 Jul 2023: i) Assuming r = r+ is a Killing horizon of. ka =. (. v. )a,. determine the Hawking temperature TH of the Schwarzschild-AdS black hole.

20 Jul 2021: vector ka. END OF PAPER. Part III, Paper 309.

30 Aug 2019: spacelike) Killing vector. ka. xa=. z. and that the d-dimensional background metric is of the form.