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As a research seminar, this course doesn't really so much have a
syllabus as a list of topics. In the interest of the historical
record, I'm going to make a "post-facto" syllabus showing what each
day actually covered. Beyond that, my plan is to give a list of
topics for future classes. Note, towards the end, most of the
lectures will be used for student project presentations.
Past classes
Lec 1, Sep 6 2007: Overview; semi-quantitative comparison of
interaction of GW with matter vs EM wave with matter.
Lec 2, Sep 11 2007: History of the field; radiative moments and
conservation principles. Geometrized units and useful conversion
factors.
Lec 3, Sep 13 2007: Radiative moments continued; overview of
astrophysically interesting bands of gravitational radiation.
Lec 4, Sep 18 2007: Review of general relativity I.
Lec 5, Sep 20 2007: Review of general relativity II;
linear limit of GR.
Lec 6, Sep 25 2007: Solution of linearized field equation.
Introduction to symmetric trace-free tensors.
Lec 7, Sep 27 2007: Continuation of linearized field equation
analysis. Using STF tensors to connect near zone solution to source
dynamics; selecting gauge to reduce solution to gauge invariant,
radiative degrees of freedom. Most general solution for GWs in
linearized theory in terms of mass and current moments of a source.
Lec 8, Oct 2 2007: Propagation of waves across spacetime.
Multiple lengthscale expansion.
Lec 9, Oct 4 2007: Propagation of waves across spacetime;
derivation of geometric optics limit; how (in principle) to go beyond
this limit.
Lec 10, Oct 11 2007: Interaction of waves with matter. General
formalism; use of of "exact" Einstein equation with "background"
Einstein equation to find "difference" equation which provides
equation of motion of interaction. No interaction between GW and
homogeneous perfect fluid.
Lec 11, Oct 16 2007: Continuation of interaction of GWs with
matter. Coupling of waves to dissipative fluids, and to inhomogeneous
elastic media. Foundations for detectors. Interferometric detectors:
response to a GW in local reference frame and in TT coordinates.
Lec 12, Oct 18 2007: Continuation of interaction of detectors
with GWs. Why a laser isn't stretched and squeezed as the detector's
arms are stretched and squeezed. Real detectors: Introduction to the
theory of random processes.
Lec 13, Oct 23 2007: Theory of random processes;
fluctuation-dissipation theorem. Thermal noise in GW detectors. Shot
noise, standard quantum limit (highly simplified version).
Lec 14, Oct 25 2007: Concepts in GW signal analysis. Pulling a
weak signal from noisy data. Derivation of the "optimal" filter; gain
from optimal filter vs cruder filtering methods.
Lec 15, Oct 30 2007: Waves in inflationary cosmology. Quick
review of concepts from cosmology. Wave equation for primordial GW
modes; their evolution in an expanding universe.
Lec 16, Nov 1 2007: Waves in inflationary cosmology, continued.
Derivation of two regimes for mode behavior: Frozen if mode is outside
Hubble volume, dying away if mode is inside Hubble volume.
Translation to frequency power law behavior (in energy density) for
different cosmological equations of state. Comparison to detector
sensitivity.
Lec 17, Nov 6 2007: Characteristics of binaries. Division into
inspiral, merger, and ringdown. Predictable evolution of inspiral
waveform; need for numerical modeling in merger.
Lec 18, Nov 8 2007: Binaries in the high frequency (LIGO etc)
band. Observations of NS-NS systems; how to extrapolate from observed
population to the likely population in the universe. Various "Drake
Factors" associated with the extrapolation; uncertainties in those
extrapolations.
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