/sci/ - Science & Math

>>12566198
It's technically "antigravity" since [math]\Lambda<0[/math] is hyperbolic, so geodesics accumulate at the spatial infinity/horizon boundary. However this makes the space compact, and the strong-coupling at the boundary gives rise to a quantum theory, which is a CFT if the boundary preserves the conformal [math]PSL[/math] subgroup from the maximally-symmetric bulk.
This is all a basic, however, and perhaps she was referring to phenomenological results that I'm not aware of.

>>11474260
Ah I see, you have used the transpose but since the Lie algebra [math]\mathfrak{so}(1,2) \cong \mathfrak{sp}(1,3)[/math] it becomes the conjugate adjoint. You had picked [math]L[/math] skew-adjoint so you do indeed got [math]\{L,\neta\}=0[/math]; I was thinking of [math]L[/math] being self-adjoint so the expansion [math]\Lambda \cong I + i\epsilon L[/math] yields [math][L,\eta]=0[/math]. Just a matter of convention, you're correct.
>>11458055
Kunze-Hoffman.
>>11474583
Write [math]\begin{pmatrix}a & b \\ c & d\end{pmatrix} = ae_{11} + be_{12} + ce_{21} + d e_{22}[/math] where [math]e_{ij} = \delta_{ij} [/math] is an orthonormal basis in [math]M_2(\mathbb{R})[/math]. Then just match coefficients.
>>11463147
Indeed, near the horizon the length of your geodesic approaches [math]\infty[/math]. That analogy is fine to an extent.

I'm afraid I can't answer the other physics questions as they are nonsense.
>>11476173
0 is correct. Whatever trig limits is, you did it wrong.