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S. V. DHURANDHAR

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25th IAGRG meeting Kolkata. General Relativity and other disciplines ... 25th IAGRG meeting Kolkata. LISA: Space based detector for detecting low frequency GW ... – PowerPoint PPT presentation

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Title: S. V. DHURANDHAR


1
THE CHANGING FACE OF GENERAL RELATIVITY
S. V. DHURANDHAR
IUCAA PUNE
2
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

3
Effect on a ring of test particles
Metric
General Wave
4
But h is awfully small !
Quadrupole formula
Change in arm-length
d L h L
5
LIGO Louisiana 4 km armlength (US)
6
We did it !
http//www.ligocaltech.edu/lazz/distribution/LSC
_Data
7
LISA Space based detector for detecting low
frequency GW
8
Laser frequency noise
9
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10
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11
Tinto, Eastabrook, Armstrong SVD, Nayak, Vinet,
Pai
12
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13
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14
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15
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16
Open Problems
17
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


18
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
19
Example of a filter
A sinusoidal signal is embedded in noise
Data
Signal
20
Filtering the data
Best filter is the Fourier Transform
Statistic
Provides parameters of the signal eg. frequency
Generalisation Matched Filter
21
Matched filtering the inspiraling binary signal
22
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

23
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
24
International Network of GW Interferometers
1. Detection confidence 2. Source direction 3.
Polarisation info
25
Need for a (or two) detector(s) in Asia/Australia
  • AIGO Australian project
  • INDIGO Indian detector?
  • Advantages sky coverage, resolution of sources

26
Optimum location of a detector
Courtesy A. Sengupta S. Mitra
27
Optimum location
28
Network Sensitivity
AIGO/INDIGO network doubles sensitivity
29
Angular Resolution
An order of magnitude improvement
30
Summary
  • Connection of GR to several fields
  • Astrophysics, Mathematics, Statistics,
    Engineering
  • Numerical Relativity
  • Gravitation going experimental
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