From dba922cd0c8f5ce7252f33268189259706fc9e75 Mon Sep 17 00:00:00 2001 From: bnewbold Date: Sun, 24 Jan 2010 05:23:28 -0500 Subject: partial fixes --- physics/gravitational waves.page | 117 --------------------------------------- 1 file changed, 117 deletions(-) delete mode 100644 physics/gravitational waves.page (limited to 'physics/gravitational waves.page') diff --git a/physics/gravitational waves.page b/physics/gravitational waves.page deleted file mode 100644 index 66f6c04..0000000 --- a/physics/gravitational waves.page +++ /dev/null @@ -1,117 +0,0 @@ ---- -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) = :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. -- cgit v1.2.3