S. V. DHURANDHAR

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THE CHANGING FACE OF GENERAL RELATIVITY
S. V. DHURANDHAR
IUCAA PUNE
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General Relativity and other disciplines

• GR finds its home in astronomy astrophysics
• The binary blackhole problem
• No exact two body solution PN Numerical
  Relativity
• Cosmology observational data, COBE, WMAP, PLANCK

• Mathematics Commutative algebra, differential
  
• geometry in statistics
• Statistics Hypothesis testing, statistical
  tests, maximum likelihood, etc. - Signal
  processing
• Gravitation has gone experimental Gravitational
  waves

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Effect on a ring of test particles
Metric
General Wave
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But h is awfully small !
Quadrupole formula
Change in arm-length
d L h L
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LIGO Louisiana 4 km armlength (US)
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We did it !
http//www.ligocaltech.edu/lazz/distribution/LSC
_Data
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LISA Space based detector for detecting low
frequency GW
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Laser frequency noise
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Tinto, Eastabrook, Armstrong SVD, Nayak, Vinet,
Pai
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Open Problems
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Inspiraling compact binaries
GW

• Broadband source best for interferometric
  detectors
• Waveform is well modeled by PN approximations
  waveform obtained to 3.5 PN
• Numerical Relativity great advances
  merger
• Signal is way below the noise data analysis
  filtering

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Breakthrough in Numerical Relativity

• Numerical Relativity
• solves
• merger waveform
• 3.5 of total restmass energy as compared to
  1.5 in inspiral waveform!

Work in progress on stitching together
waveforms India has the right talent/aptitude for
NR
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Example of a filter
A sinusoidal signal is embedded in noise
Data
Signal
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Filtering the data
Best filter is the Fourier Transform
Statistic
Provides parameters of the signal eg. frequency
Generalisation Matched Filter
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Matched filtering the inspiraling binary signal
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Statistics and geometry

• Statistic c(t)
• Where does one set the threshold? False alarm
  probability choose threshold such that this is
  small
• Detection probability choose this high
• Signal depends on many parameters masses,
  kinematical parameters initial phase, time of
  arrival
• Parameter space
• Parameter space can be viewed as a manifold with
  the
• parameters as coordinates
• Metric mismatch between signal and template

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Parameter space metric
Coordinates li
gik Dli Dlk e
Choose coordinates so that metric is simplest
Cartesian coordinates For inspiral choose chirp
times instead of masses t0 , t3 Metric const
Uniform placement of templates Number of
templates volume of parameter space / template
size
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International Network of GW Interferometers
1. Detection confidence 2. Source direction 3.
Polarisation info
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Need for a (or two) detector(s) in Asia/Australia

• AIGO Australian project
• INDIGO Indian detector?
• Advantages sky coverage, resolution of sources

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Optimum location of a detector
Courtesy A. Sengupta S. Mitra
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Optimum location
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Network Sensitivity
AIGO/INDIGO network doubles sensitivity
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Angular Resolution
An order of magnitude improvement
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Summary

• Connection of GR to several fields
• Astrophysics, Mathematics, Statistics,
  Engineering
• Numerical Relativity
• Gravitation going experimental