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 diff --git a/physics/gravitational waves.page b/physics/gravitational waves.pagenew file mode 100644index 0000000..5aa1744--- /dev/null+++ b/physics/gravitational waves.page@@ -0,0 +1,111 @@+=======================+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.