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 diff --git a/physics/gravitational waves b/physics/gravitational wavesnew file mode 100644index 0000000..db2e667--- /dev/null+++ b/physics/gravitational waves@@ -0,0 +1,81 @@+=======================+Gravitational Waves+=======================++:Author: bnewbold@mit.edu++.. note:: Most of this content is based on a 2002 Caltech course taught by+ Kip Thorn [PH237]_++Raw Info+-----------------+Rank 4 Riemann tensors, will cover different gages.+Waves are double integrals of curvature tensor...+ +++Gravitons as Quantum Particles+---------------------------------+Invariance angles: (Spin of quantum particle) = :latex:$2 pi$ / (invariance angle)++Graviton has :latex:$\pi$ invariance angle, so it is spin 2; photons have unique :latex:$\arrow{E}$ vector, so invariance angle is :latex:$2\pi$, spin 1++Also describes spin by the group of lorentz transformations which effect propogation.++Two polarizations: cross and plus, corresponding to spin of particles aligning wiht or against propagation? (Ref: eugene vickner? reviews of modern physics)++Waves' multipole order $\geq$ spin of quantum = 2 for graviton ((??))++Waves don't propogate like E, because mass monopoles don't oscillate like charges.++:latex:$h \req \frac{G}{c^2} \frac{M_0}{r} + \frac{G}{c^3} \frac{M'_1}{r} + \frac{G}{c^4} \frac{M''_2}{r} + \frac{G}{c^4} \frac{S'_1}{r} + \frac{G}{c^5} \frac{S''_1}{r}$ +First term: mass can't oscillate+Second term: momentum can't oscillate+Third term: mass qudrupole moment dominates+Fourth term: angular momentum can't oscillate+Fifth term: current quadrupole++Energy+----------------++Quick calculation: for a source with mass M, size L, period P, the quadupole moment $M_2 \req M L^2$, h \req 1/c^2 (newtonian potential energy) ????++h on the order of $10^{-22}$++Propogation+-----------------++When wavelength much less than curvature of universe (background), then gravitational waves propagate like light waves: undergo red shifts, gravitational lensing, inflationary redshift, etc. ++Spectrum+----------------++High Frequency: Above 1 Hz, LIGO (10 Hz to 1kHz), resonant bars+ Small black holes (2 to 1k suns), neutron stars, supernovae++Low frequency: 1Hz and lower, LISA (10^-4 Hz to 0.1 Hz), Doppler tracking of spacecraft+ Massive black holes (300 to 30 million suns), binary stars++Very Low Frequency: 10^-8 Hz, Pulsar timing (our clocks shifted by gwaves, average of distance pulsars are not over long periods)++Extreme Low Frequency: 10^-16 Hz, Cosmic Microwave Background anisotropy++Detectors+-----------------++$\Delta L = h L \lreq 4 \times 10^{-16} \text{cm}$++LIGO (10 Hz to 1kHz)+ Also GEO, VIRGO, TAMA (?), AIGO++LISA (10^-4 Hz to 0.1 Hz)++Resonant Bars+~~~~~~~~~~~~~~~+First by Webber. +Currently in Louisiana State University (Allegro), University of West Australia (Niobe), CERN (Explorer), University of Padova (Auriga), and University of Rome (Nautilus)++References+----------------++.. [PH237] Gravitational Waves:title: (aka ph237), a course taught by Kip Thorne at Caltech in 2002. See http://elmer.tapir.caltech.edu/ph237/ for notes and lecture videos.