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 diff --git a/physics/gravitational waves b/physics/gravitational wavesindex db2e667..81080c3 100644--- a/physics/gravitational waves+++ b/physics/gravitational waves@@ -2,14 +2,14 @@ Gravitational Waves ======================= -:Author: bnewbold@mit.edu+.. warning:: This is a rough work in progress!! Likely to be factual errors, poor grammer, 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 gages.+Rank 4 Riemann tensors, will cover different gauge. Waves are double integrals of curvature tensor... @@ -20,38 +20,66 @@ Invariance angles: (Spin of quantum particle) = :latex:$2 pi$ / (invariance an 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 propogation.+Also describes spin by the group of Lorentz transformations which effect propagation. -Two polarizations: cross and plus, corresponding to spin of particles aligning wiht or against propagation? (Ref: eugene vickner? reviews of modern physics)+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' multipole order :latex:$\geq$ spin of quantum = 2 for graviton ((??)) -Waves don't propogate like E, because mass monopoles don't oscillate like charges.+Waves don't propagate like E, because mass monopoles don't oscillate like charges. -:latex:$h \req \frac{G}{c^2} \frac{M_0}{r} + \frac{G}{c^3} \frac{M'_1}{r} + \frac{G}{c^4} \frac{M''_2}{r} + \frac{G}{c^4} \frac{S'_1}{r} + \frac{G}{c^5} \frac{S''_1}{r}$ +: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 qudrupole moment dominates+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 quadupole moment $M_2 \req M L^2$, h \req 1/c^2 (newtonian potential 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 $10^{-22}$ -Propogation+Propagation ----------------- -When wavelength much less than curvature of universe (background), then gravitational waves propagate like light waves: undergo red shifts, gravitational lensing, inflationary redshift, etc. +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, supernovae+ 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@@ -63,12 +91,12 @@ Extreme Low Frequency: 10^-16 Hz, Cosmic Microwave Background anisotropy Detectors ----------------- -$\Delta L = h L \lreq 4 \times 10^{-16} \text{cm}$+:m:$\Delta L = h L ~ \leq 4 \times 10^{-16} \text{cm}$ LIGO (10 Hz to 1kHz) Also GEO, VIRGO, TAMA (?), AIGO -LISA (10^-4 Hz to 0.1 Hz)+LISA (10e-4 Hz to 0.1 Hz) Resonant Bars ~~~~~~~~~~~~~~~