General Relativity: Part II Gravity is Curved Space

1) You walk 10 km south, 10 km west and then 10 km north and you are back where you started. What colour is the bear? a) brown b) black c) white Hint: There is only one place in the world where this would happen.

We live in a 4-dimensional curved space which we cannot see or experience directly. We can get a sense of how it works by using an analogy with fewer dimensions.

Imagine that you are a smart blind ant moving about on the surface of a balloon. Draw the path of the polar explorer from the the riddle on your balloon.  

2) Suppose that there is a light at the North Pole 2) Suppose that there is a light at the North Pole. The light radiates in all directions and follows the straightest lines in this space. What will an ant at the South Pole notice? a)      Nothing. b)      A bright spot. c)      A bright ring.  

The curved arcs that you see in this photograph are coming from a distant light. Between it and the Earth there is a large mass that warps the space, so that light appears to come from many directions.

3) Try to get a planet to orbit for more We can detect how mass distorts the three dimensions of space but we can’t picture it. 3) Try to get a planet to orbit for more than a dozen times on your fabric. How do you do this? 4) How would an ant explain this motion?

When Einstein first calculated the curvature of light he got it wrong by a factor of two. Half the curvature is from the equivalence principle and the second half is from the curvature of space.

Mass curves spacetime into gravitational lenses.

Gravitational lenses are used by astronomers to measure the mass of regular matter and dark matter.

Draw a 15-cm line on your balloon Draw a 15-cm line on your balloon. At right angles to that, draw another 15-cm line. Draw two more of them. What do you get?

Planetary orbits don’t form simple ellipses either Planetary orbits don’t form simple ellipses either. They form patterns like Daisy petals - this is called the precession of the equinoxes. This was a known problem with Newtonian Gravitation that General Relativity was able to solve.

a) Jupiter because it is biggest b) Mercury because it is smallest 5) The planet with the greatest precession will be a)      Jupiter because it is biggest b)      Mercury because it is smallest c)      Mercury because it is closest to the sun d)      Neptune because it is farthest

Suppose, the balloon was expanding. What would the ant notice?

The galaxies are all moving away from us and the more distant ones are moving faster.

There is a simple relationship between velocity and distance There is a simple relationship between velocity and distance. This suggests that everything in the universe was once gathered in one point that exploded around 14 billion years ago – the Big Bang.

6) Gravity should cause this expansion to Recent evidence suggests that it speeding up! The cause of this is not understood, but it has a name - Dark Energy. 6) Gravity should cause this expansion to a) slow down b) speed up c) remain constant. Best-fit Constant velocity

7)As a star’s life ends, it collapses and gets much denser 7)As a star’s life ends, it collapses and gets much denser. What would you see if you got close to dense star whose escape velocity was almost c? a) Light rising and falling b) Faint radio waves c) Faint gamma rays Particles can rise and slow down, but not light. Light gets red-shifted.

8) What happens if the escape velocity is greater than c? a) only gamma rays escape b) only radio waves escape c) nothing escapes d) nothing escapes so it can’t be detected No light can escape. This is called a Black Hole.

You can detect one by the way it warps light.

You can detect black holes that have matter spiraling into them You can detect black holes that have matter spiraling into them. This matter will form hot disks that give off x-rays.

Black Holes often produce jets spewing matter out at speeds close to c Black Holes often produce jets spewing matter out at speeds close to c. Many of these have been found.

Black holes can also be detected by measuring the speeds of orbiting bodies. This data can be used to calculate the mass and density of the central body. M = v2 r /G

What is it like inside a Black Hole What is it like inside a Black Hole? All light and matter will be driven by the extremely curved spacetime into a singularity of infinite density.

Rapidly orbiting massive objects should generate gravitational waves, ripples in the fabric of space. These waves take energy away, so the objects should spiral into the center.

Taylor and Hulse have measured a binary pulsar doing exactly that.

Large detectors are being built around the world to detect gravitational waves directly. This is LIGO.

An even larger gravity detector called LISA, is being built An even larger gravity detector called LISA, is being built. It is made of three satellites in a huge triangle. It may be able to measure the curvature near a Black Hole.