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<center><table cell padding=10 border=10 bgcolor=purple><tr><td><center>
<font color=gold><h1>Gravitational Radiation</center><p><h2>
At right are the results of a numerical simulation of a 
black hole/black hole collision and the gravitational radiation
which is produced (much as the manner in which water waves are 
generated by disturbances and in the manner in which EM waves are 
generated by electrical charges).</font> </td><td>
<img width=500 
src="http://pages.uoregon.edu/~imamura/122/images/bhcollision.jpg">
</td></tr></table></center>
<h2>
Reading:  Chapter 
22 (Neutron Stars and Black Holes)
<p>
<ul>
In the 1600s, Issac Newton developed his <i>Universal Theory of
Gravitation</i> and his three laws of motion.
This way of looking at the Universe works quite nicely for the motions of
the planets and most of our everyday experiences.  However, under certain
circumstances, this picture is inadequate.  To <i>fix-up</i> some problems,
Albert Einstein developed his <font color=magenta><i>Special</i></font> and 
<font color=magenta><i>General Theories of Relativity</i></font> which 
brought a new persepctive to our thinking about <i> space, time</i>, and
<i>gravitation</i>.
<p>
To get a feel for some of Einstein's ideas, we must start thinking about the
<i>space-time</i> of the Universe.  Suppose that I tell you that
Astronomy 122 
meets in 100 Willamette Hall.  Is this enough to get you to class?
Well, no, because I didn't tell you <i>when</i> the class meets, 
namely, 14:00-14:50 on MWF.
In order for you to show up for class, you must know not only 
<font color=magenta><i>where</i></font> 
it meets but also <font color=magenta><i>when</i></font> it meets.  
This is true for all events in the Universe;
you must know not only where the event occurs (its spatial position) but 
also when the event occurs (its temporal position).  
The <font color=magenta><i>space</i></font>
and <font color=magenta><i>time</i></font>
positions are equally important and we should 
think about events in the Universe in terms of their 
<font color=magenta>space-time</font> positions.<i><font color=blue><center>
An interesting property of this space-time is that it has <i>
structure</i> and is not <i>rigid</i>. </center></i></font>
<p>
</ul>
<font color="red">
<i>Question: What are some consequences of 
viewing the Universe in this manner?</i>
</font>
<p>
<ul>
The path an object rolling on a table top 
follows is determined by the shape of the surface (it rolls on the 
table top). The table top defines the <i>space-time</i> for the rolling
object. For objects <i>rolling</i> in the 
Universe, a similar idea holds in that the paths of objects
follow the shape of the shape-time.
<p><table><tr><td><h3><ul>
Locally, the space-time in this room  
is fairly flat and so, unless you push on an object, its free motion 
(unforced motion) is in a straight line.
If I were to place a large chunk of mass into the room, the mass
would distort the shape of the space-time.  In two-dimensions, this is easy
to visualize.  Imagine a rubber sheet onto which 
you place a bb.  The bb causes a depression to form in the rubber sheet.  
</ul></td><td><center>
<img width=500 
src="http://pages.uoregon.edu/~imamura/122/images/black_hole_spacetime.gif">
</center></td></tr></table>
<p>
This is analogous to what
mass does to the structure of space-time.  It causes a <i>depression</i> to 
form so that if an object <i> rolls</i> toward it, it falls into the 
pit and is captured. (This, by the way, is how Einstein envisioned  
how gravity works.  
Mass distorts the space-time causing particles to roll toward
the mass.  Note that the objects follow the shape of the 
space-time and in
this sense are following an <i>unforced</i> motion! That is, there is no
gravitational force, objects are simply following their natural motions.)
<p>
Return to the rubber sheet analogy. If I drop 
a bb on the sheet and it bounces, ripples in the sheet are produced 
which propagate 
away from the disturbance. These ripples in the space-time are referred
to as gravitational waves. 
<p><center>
<a target=_blank href="
https://www.youtube.com/watch?v=zLAmF0H-FTM&t=5s">
<img width=500 src="LIGO_ripples.png"></a> 
<a target=_blank href="https://www.youtube.com/watch?v=I_88S8DWbcU&t=17s">
<img width=500 src="LIGO_GW.png"></a> 
</center><p>
Gravitational waves</i> from compact stars and other Celestial Objects.
To the right is shown the 
<a href="https://www.ligo.caltech.edu">Laser Interferometer Gravitational-Wave
Observatory (LIGO)</a> located in Hanford, WA which announced the discovery
of gravitational waves in 2015 from GW150914, produced by the merger 
of two orbiting 
black holes (<a href="https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.116.061102">Abbott et al. 2016</a>). This important work earned the 2017 Nobel 
Prize in Physics for
Rainer Weiss, Barry C. Barish and Kip S. Thorne for "decisive 
contributions to the LIGO detector and the observation of gravitational waves."
Note that there was an earlier indirect detection of gravitational waves 
for which the Nobel Prize in Physics 1993 was aswarded to 
Russell A. Hulse and Joseph H. Taylor Jr. for "the discovery of a new type 
of pulsar, a discovery that has opened up new possibilities for the study 
of gravitation."
<p>
<center><img width=600 src="LIGO_hanford.jpeg"></center>
</td></tr></table></ul>
<p><hr><p><ul>
<font color="red">Comment: The opening of the sky to the study of grqavitational
waves was huge, but opening ot the sky to the combination of gravitational and 
the <b>Electro-magnetic (EM) spectrum</b> and the study of other forms of 
emissions from Celestial objects would be huge. 
Exampales for such GW/EM sourfes are supernovae, 
$gaqmma;-ray bursters (merging neutron stars
or black holes),  
unstable rotating neutron stars, close binary white dwarf stars... . 
<p>
The exciting discovery of gravitational
waves from merging neutron stars in the form of a &gamma;-ray burst 
has verified that indeed, gravitational waves with electromagnetic radiation
are produced by a broad range of astrophysical sources.
The recent detetion by LIGO of
a &gamma;-ray burst source has 
substantially enhanced our understanding of 
the heavy element production in the Universe.</font>
</ul>
<p><hr><p>
Possible sources for gravity waves are supernovae, merging neutron stars
or black holes,  
unstable rotating neutron stars, ... . The exciting discovery of gravitational
waves from merging neutron stars has verified that indeed, gravitational waves
are produced by a broad range of astrophysical sources, in particualr, new
sources of gravitational waves that produced large amounts of electromagnetic 
radiation.
<center>
<a target=_blank href="https://www.ligo.caltech.edu/video/ligo20171016v8">
<img width=500 src="LIGO_ns.png"></a> 
</center>
<p>
<hr><p>
</ul>
<p>
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