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30 Aug 2019: S = 12. (. F F kA F F). (1). where F is a four-form and A a three-form such that F = dA, and k is a constant.

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.

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

30 Aug 2019: ii) Let Ka be a solution to the Killing equation (aKb) = 0.

12 Jul 2023: iii) State Killing’s equation. Show that if Ka is a Killing vector, then Ja = TabKb.

30 Aug 2019: akb > 0 for any null vector ka. Show that, if the above metric satisfies the Einsteinequation with an energy-momentum tensor satisfying the null energy condition then.

30 Aug 2019: M =3. 32πlim. r. dk ,. where ka = (/t)a. The integral is taken over a constant t ,r surface at infinityand the orientation is dt dr dψ dθ dφ.

30 Aug 2019: MAT3, MAMA. MATHEMATICAL TRIPOS Part III. Wednesday, 5 June, 2019 1:30 pm to 3:30 pm. PAPER 335. DIRECT AND INVERSE SCATTERING OF WAVES. Attempt no more than TWO questions. There are THREE questions in total. The questions carry equal weight.

30 Aug 2019: MKomar(r) = 1. 8π. S2r. dk,. where ka = (/t)a. The integral is taken over a constant t ,r surface and theorientation is dtdrdθdϕ.

17 Jun 2019: E =12(E0 E1 4A cos ka). 12. (E0 E1)2 16A2 cos2 ka.