Kartik Prabhu
Some weekend reading: two new papers on blackholes
Canonical Energy and Hertz Potentials for Perturbations of Schwarzschild Spacetime http://arxiv.org/abs/1807.09883
Symmetries and charges of general relativity at null boundaries http://arxiv.org/abs/1807.11499
Kartik Prabhu
Who’s the one having fever dreams now?
Kartik Prabhu
Looks like the blackhole stability problem is getting some press https://www.quantamagazine.org/to-test-einsteins-equations-poke-a-black-hole-20180308/
Kartik Prabhu
Pretty neat way to think of the Basel problem with lighthouses and the inverse square law!
Kartik Prabhu
pretty neat game and proof!
Kartik Prabhu
Using the fact that the height bisects the apex angle you get
leg length = h sec( a/2 )
Kartik Prabhu
yes, https://en.wikipedia.org/wiki/Homogeneous_space#Homogeneous_spaces_as_coset_spaces even though I don’t know what you mean by “isometry”.
Kartik Prabhu
OK everyone, back to work. Quantum Gravity is not going to figure itself out!
Kartik Prabhu
In which signature is the “conservation of convention law” stated?
Kartik Prabhu
‘I know, I’ll use Latex macros’ Now you have two problems (also see https://xkcd.com/208/ and https://xkcd.com/927/)
Kartik Prabhu
hopefully you are using the maths convention — phi_^* for pullback since it is a “dual map”
Kartik Prabhu
there are worse convention-violations in GR; signature, Riemann tensor, extrinsic curvature… comparatively this is not a big deal!
Kartik Prabhu
because it is consistent with the index positions for objects being pulled-back, forms, vs objects being pushed-forward, vectors.
Kartik Prabhu
lot of awesome number theory here — primes, factorisation, Gaussian primes, character functions — pretty neat!
Kartik Prabhu
I never realised that you can get all Pythagorean triples from complex numbers!
Kartik Prabhu
nice demonstration of equilibrium and stability.