Important thing to remember #1 - GR is a theory
The basic idea is that instead of postulating
a mysterious, invisible force between masses, GR says
In this picture, the reason the planets orbit the
Sun is not because of a central force, but rather because the
planets are tracing out straight lines in curved
- The usual analogy of tossing a shotput on a bed and
then rolling marbles along works pretty well.
- G.R. makes some predictions.
- Mercury's orbit will differ from the Netwonian predictions .
- Clocks will slow down in the presence of large gravitational fields .
- About 20 other tests .
- The deflection of starlight by large masses .
Einstein predicted that the position of
a star whose light just grazed the edge of the Sun would be deflected by
1.75 arcseconds. This is easy to measure, but the problem is the Sun is too
In 1919 astronomers made measurements
during the total eclipse of the Sun and verified the prediction.
The distortion of light when passing by large masses also causes ``gravitational
lenses'', first identified in the 1980s, and gravitational redshifts that
are routinely measured in the spectra of White Dwarfs.
- Now - this is leading towards Black Holes.
With Newtonian gravity, photon's are massless and therefore don't feel
gravitational forces. But, under GR, photons also just follow straight
lines in curved space.
- Let's think about .
Imagine tossing rocketships up in the air from the surface of the Earth.
A feeble toss and the rocketship goes up a little way then falls back
to Earth because its kinetic energy did not exceed its
gravitational potential energy.
However, toss it with a larger and larger velocity and it goes higher and
higher before falling back to Earth.
This is the escape velocity and it is calculated by setting the gravitational
potential energy equal to the kinetic energy of any object.
where M is the mass of the object from which you want to escape and R is the
radius from which you want to escape. G is the universal gravitational constant.
This is independent of the mass of the object you are tossing up, the only
mass in the formula is the mass of the Earth.
- Now, suppose you decrease the radius of the Earth by a factor off 9.
The escape velocity is proportional to .
So, for a 1/9 SMALLER Earth (that is, smaller radius, same mass, higher density) the
escape velocity goes up by a factor of 3.
- Now imagine shrinking the Earth down to about the size of a grape (1 cm).
The Escape Velocity will have increased to
With our new theory of Gravity, where photons are affected by ``gravitational
fields'', if the escape velocity of an object equals or exceeds the speed of
light, that object will no longer be observable as no information can
escape from it.
- There is a name for the critical radius for which a given
mass has an escape velocity of ``c'' -- the Schwarzschild Radius
and this is also the Event Horizon.
So, any object that is within its Schwarzschild Radius is a Black Hole.
- This is all vaguely interesting, but it turns out that
it is very, very, very difficult to shrink objects down to their
- For the Sun, you have to somehow overcome Thermal Pressure, then
degeneracy, then Neutron degeneracy and there is no known
cosmic vice that can do that for a object.
- But! if we go back to a neutron star, we are starting
to put together a pretty big vice.
Thermal pressure has already been overcome, degeneracy has been
exceeded and it is neutron degeneracy supporting the object's
mass against gravity.
- There is a limit to the mass that can be supported
by neutron degeneracy
- this is hard to calculate but it is probably between
- OK, add mass to a SNII core up to say and what
happens? The core collapses to a ZERO radius ``singularity''
For a object:
So, this core would be a Black Hole with a Schwarzchild
Radius of 8.9km. (!).
- Q. What if the Sun collapsed into a Black Hole? Would the
Earth and other planets be dragged in an disappear from the
Universe? No, the gravitational attraction of the Sun would not
change at all.
- Q. What happens when a Black Hole DOES absorb some mass?
As M increases, the radius of the event horizon increases.
- Q. Where does all that go? Good question, no
- Is the Event Horizon a physical boundary? No, it is
just the radius inside of which photons can not escape.
- Is there any reason to believe that Black Holes
- The best candidates may be observed in some X-ray binaries.
Cygnus X-1 is one of the brightest X-ray sources in the sky. It
was identified as a hot, blue main-sequence star with mass of around
. These stars are not usually x-ray sources but, it was
soon discovered that it was a Spectroscopic Binary with a
relatively short period of 5.6 days.
The companion was determined to be someplace between 5 and
10 . What is the companion? It is completely invisible
at all wavelengths (although remember the x-rays).
- If it was a Red Giant, it would be easily seen.
- If it was a main-sequence star, it would be seen with some difficulty.
- It can't be a WD because ,
- It can't be a Neutron star because .
- Not much left except Black Hole.
- The X-ray emission is also highly suggestive of a system
where mass is streaming from the companion onto a Black Hole.
For an accreting white dwarf, the temperature of the gas when it
crashes to the surface is such that these are UV radiators. For
accreting Neutron stars, the temperature is high enough for
``soft'' x-rays. In Cyg X-1 we see ``hard'' x-rays indicative of a
much depper gravitational potential well, consistent with a
- Among all the x-ray binary systems in the Galaxy and in nearby
galaxies, there are 4 good candidates for black holes and another
4 or 5 pretty good candidates.
- Q. Do Neutron stars exist? For sure.
- Q. Do Black Holes exist? Maybe, there is not yet
an airtight case.
- There are also some excellent candidates for Supermassive
black holes in the centers of some and perhaps all big galaxies.
Mon Mar 9 11:01:38 PST 1998