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+---
+format: rst
+categories: physics
+toc: no
+...
+
+=======================
+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) = $2 pi$ / (invariance angle)
+
+Graviton has $\pi$ invariance angle, so it is spin 2; photons have unique $\arrow{E}$ vector, so invariance angle is $2\pi$, 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 $\geq$ spin of quantum = 2 for graviton ((??))
+
+Waves don't propagate like E, because mass monopoles don't oscillate like charges.
+
+$ 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 $M_2 \approx M L^2$, $h \approx 1/c^2 (Newtonian potential energy) ????
+
+h on the order of $10^{-22}$
+
+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
+-----------------
+
+$\Delta L = h L ~ \leq 4 \times 10^{-16} \text{cm}$
+
+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** (aka ph237), a course taught by Kip Thorne at Caltech in 2002. See http://elmer.tapir.caltech.edu/ph237/ for notes and lecture videos.