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author | User <bnewbold@daemon.robocracy.org> | 2009-10-13 02:52:09 +0000 |
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committer | User <bnewbold@daemon.robocracy.org> | 2009-10-13 02:52:09 +0000 |

commit | f61026119df4700f69eb73e95620bc5928ca0fcb (patch) | |

tree | f17127cff9fec40f4207d9fa449b9692644ce6db /physics/gravitational waves.page | |

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diff --git a/physics/gravitational waves.page b/physics/gravitational waves.page new file mode 100644 index 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. |