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+=======================
+Gravitational Waves
+=======================
+
+.. warning:: This is a rough work in progress!! Likely to be factual errors, poor grammar, etc.
+
+.. 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 gauge.
+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 propagation.
+
+Two polarizations: cross and plus, corresponding to spin of particles aligning with or against propagation? (Ref: Eugene Vickner? reviews of modern physics)
+
+Waves' multipole order :latex:`$\geq$` spin of quantum = 2 for graviton ((??))
+
+Waves don't propagate like E, because mass monopoles don't oscillate like charges.
+
+:latex:`$ h \approx \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}$`
+First term: mass can't oscillate
+Second term: momentum can't oscillate
+Third term: mass quadrupole moment dominates
+Fourth term: angular momentum can't oscillate
+Fifth term: current quadrupole
+
+Energy
+----------------
+
+Quick calculation: for a source with mass M, size L, period P, the quadrupole
+moment :m:`$M_2 \approx M L^2$`, :m:`$h \approx 1/c^2` (Newtonian potential
+energy) ????
+
+h on the order of :m:`$10^{-22}$`
+
+Propagation
+-----------------
+
+When wavelength much less than curvature of universe (background), then gravitational waves propagate like light waves: undergo red shifts, gravitational lensing, inflationary red shift, etc.
+
+Sources
+-------------
+
+Inspirals of bodies into super-massive black holes
+ Eg, white dwarfs, neutron stars, small black holes.
+ Super-massive black holes are expected near the centers of galaxies.
+ Low frequencies (LISA); waveforms could hold data about spacetime curvature
+ local to the black hole.
+ Waveforms could be very difficult to predict.
+
+Binary black hole mergers
+ Broadband signals depending on masses.
+
+Neutron Star/Black hole mergers
+ Stellar mass objects existing in the main bodies of galaxies.
+ Higher frequencies (LIGO and AdvLIGO).
+
+Neutron Star/Neutron Star mergers
+ Have actual examples in our galaxy of these events; but final inspiral rate
+ is so low that we have must listen in other galaxies. Merger waves will
+ probably be lost in higher frequency noise, so can't probe local
+ gravitational curvature.
+ May observe "tails" of waves: scattering off of high curvature around the
+ binary.
+
+Pulsars (spinning neutron stars)
+ Known to exist in our galaxy.
+
+Spectrum
+----------------
+
+High Frequency: Above 1 Hz, LIGO (10 Hz to 1kHz), resonant bars
+ Small black holes (2 to 1k suns), neutron stars, supernovas
+
+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
+-----------------
+
+:m:`$\Delta L = h L ~ \leq 4 \times 10^{-16} \text{cm}$`
+
+LIGO (10 Hz to 1kHz)
+ Also GEO, VIRGO, TAMA (?), AIGO
+
+LISA (10e-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.