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31 May 2024: 6. Black Holes. Black holes are among the most enigmatic objects in the universe. They are described. by deceptively simple solutions to the Einstein equations, yet hold a host of insights. and surprises, from the meaning of causal structure, to

26 Jun 2024: The gluon exchange is now. 1N2. (6.24). but there are order N3 triplets of quarks, so again the total amplitude scales as N. ... 6N2. X. i 6=j 6=k. V3(xij, xjk). where xij = xi xj and the coecients in front of the potentials are taken from (6.23)and (6.24

26 Jun 2024: For example, we. have. m2K+. m2K0. m2. =mu mdmu md. (5.24). ... corrections, we can generalise (5.24) to. (m2K m2K0) (m2 m20). m20.

26 Jun 2024: Zrmax(t). 0. drp1 kr2/R2. = c a(t). Zt. 0. dt0. a(t0)(1.24). ... Indeed,. mathematically it could be that the integral on the left-hand side of (1.24) does not.

31 May 2024: They solvedtheir lubrication equations (24)–(32), again by an expansion in a small Deborah numberWe 1, going to the first correction. ... p/. (1. c). p 1. De. H = 21/22. 23/24. Figure 1.

26 Jun 2024: integral as. n 4. (2)3 eµ. Z 1. 0. dp p2ep2/2m =. mkBT. 22. 3/2eµ (2.24). Let’s try to interpret this. Read naively, it seems to tell ... anti-aligned to give 3 dierent spin 1 states. With these two amendments, our expression for the number density (2

31 May 2024: S T)µ1.µp1.r1.q1.s. = Sµ1.µp1.qT1.r. 1.s (2.24). Given an (r, s) tensor T , we can also construct a tensor of lower rank (r

26 Jun 2024: 0 for all S(r) and R(r) (4.24). This is clearly satisfied if R and S are finite at the origin.

26 Jun 2024: Tr T ART BR. =1. 2I(R)AB. (4.24). The Dynkin index is related to the quadratic Casimir C(R), which we previously defined.

12 Apr 2024: 1.3.1 The Landau-Ginzburg Free Energy 24. 1.3.2 The Saddle Point and Domain Walls 26.