Notes

tagged math

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
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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
replied to a post on Twitter with
Using the fact that the height bisects the apex angle you get leg length = h sec( a/2 )
Kartik Prabhu
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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
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OK everyone, back to work. Quantum Gravity is not going to figure itself out!
Kartik Prabhu
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In which signature is the “conservation of convention law” stated?
Kartik Prabhu
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‘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
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hopefully you are using the maths convention — phi_^* for pullback since it is a “dual map”
Kartik Prabhu
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there are worse convention-violations in GR; signature, Riemann tensor, extrinsic curvature… comparatively this is not a big deal!
Kartik Prabhu
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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.