General Relativity vs. Special Relativity    (Einstein, 1905)
             Nothing travels faster than the speed of light
                 velocities add differently than simply adding

             If you look at something going close to the speed of light,
                  time dilates (clocks appear to be running slow)
                  lengths contract (rulers appear to be squished along the direction of motion)


Lorentz Contraction

              For v<<c the equations of special relativity predict very small corrections to 
                  Newtonian  gravity, which is why we don't notice these effects in everyday life.

Curved Space

However, in fact this is only a two dimensional depiction of what is really a 3 dimensional object.

Schwarzchild Black Hole

Karl Schwarzchild (1916) investigated the structure of a black hole, solving the equations of General Relativity.

Singularity:  The star's mass has compressed to infinite density at the singularity
Event Horizon:  Within the event horizon, no light or anything else can escape
Photon Sphere:  Photons can get trapped here, and just orbit the event horizon -- they don't fall in and they don't escape

Kerr Black Hole

 New Zealand astronomer Roy Kerr described a rotating black hole in 1963

We expect that as material accretes onto the black hole, it brings angular momentum, causing the black hole to "spin" ever faster
Here the singularity becomes a ring.
Within the ring, space may be curved like this:


Naked Singularity:
If a Kerr black hole gets spinning fast enough, the speed of rotation at the edge of the singularity approaches the speed of light.  When it reaches the speed of light, the ergosphere disappears, and what's left is a "naked singularity". 

In science fiction stories, people talk about wormholes, which are naked singularities which are connected to "parallel universes" and would allow time travel faster than the speed of light. 

Falling into a black hole:

Tidal stretching will be very severe next to a black hole.  (The force of gravity at your head is much less than the force of gravity at your toes).
Time slows down and an external observer thinks you never reach the black hole horizon.

Hawking Radiation

Stephen Hawking (author of A Brief History of Time and other popular books) postulated that the following process happens:

Particle-antiparticle pairs are sometimes created outside the event horizon of a black hole.

Three things can happen to a pair of particles just outside the event horizon:

For the third possibility, the particle that has escaped becomes real and can therefore be observed from Earth. The particle that was pulled into the black hole remains virtual and must restore its conservation of energy by giving itself a negative mass-energy. The black hole absorbs this negative mass-energy and as a result, loses mass and appears to shrink.

This may make black holes EVAPORATE, ie if you wait long enough an isolated black hole will lose enough mass and no longer exist.


There appear to be an estimated 10 million stellar black holes in the Milky Way galaxy. 

We see these black holes as X-ray sources, because of the very hot accretion disk which forms, as material "accretes" onto the black hole from a companion star.

The black hole masses are 1-10 solar masses, and the event horizons are a few kilometers across. 

X-ray Binary stars: Cygnus X-1

Why do we think Cygnus X-1 is a black hole?

Gravitational Radiation

Another prediction of General Relativity which has been confirmed by observations is the existance of GRAVITATIONAL RADIATION or GRAVITY WAVES.

Just as electromagnetic waves (light) are produced by vibrating charges (electrons), motions of masses can produce GRAVITATIONAL RADIATION, or waves in the curvature of space, which travel through space at the speed of light.

Strong gravitational radiation would be expected from, for example, two black holes orbiting each other, or coalescing.

How would you detect GRAVITY WAVES?  With a Gravity Telescope, of course:

LIGO:  The Laser Interferometry Gravitational Wave Observatory

Two sites, one in Hanford, Washington;  the other in Baton Rouge, LA

Measure motions between two mirrors, separated by 2.5 miles:

LIGO has not found anything yet.  LISA is a space version of LIGO in the planning stages.

Meanwhile, astronomers found evidence for graviational waves:
In 1975, a binary pulsar, called PSR1913+16 was discovered.  It consists of two neutron stars in orbit around each other, separated by a distance about equal to the radius of the Sun. 
The orbital period of the two neutron stars around each other is slowing down in time -- exactly as you would expect if the binary is producing gravitational radiation and therefore losing energy.  The agreement with General Relativity predictions is better than 0.5%, and is arguably the strongest evidence we have that General Relativity is correct.

In 1993,  Joseph Taylor and Russell Hulse, who discovered the binary pulsar, won the Nobel Prize in Physics.