# Gravity and Black Holes

We are approaching the last possible phase of stellar evolution and the last step in fighting gravity wars

Before we get to that last step, need to look at gravity a little more closely.

The Newtonian view of gravity was that all masses exert an attractive force on all other masses and the strength of the force decreases with with the inverse square of the distance between objects.

Is this a good description of gravity? For relatively weak gravitational fields it is marvelously good - it explains almost every motion of the planets and moons of planets PERFECTLY and its good enough to send probes to Jupiter and beyond with extraordinary precision.

But, it does not explain everything and there are many alternative theories of gravity. To understand the mostly widely accepted one, we start with Einstein's Special Theory of Relativity.

# Special Relativity

• In the late 1800's various clever experiments were made to measure the speed of light in different reference frames. The remarkable fact began to emerge that the speed of light is independent of the velocity of the source or the observer (don't get this confused with the Doppler shift).

This is very surprising and counter-intuitive.

You can never catch up to a photon. Imagine two rocket ships, one flying toward the Sun at nearly the speed of light, one away from the Sun at nearly the speed of light. Ask them to measure the speed of the photons streaming away from the Sun and they measure the same 3 x 105 km/sec. This is not at all what happens when considering relative velocities of cars on the freeway.

• Einstein took this premise, that the speed of light is independent of reference frame, and looked to see where it led.

• This is in reality a pretty long story, but the short version is that the constancy of "c" can be explained by postulating that the lengths of Metersticks and speeds of Clocks are different in different reference frames.

• As you speed increases, your watch SLOWS DOWN! This is called time dilation.

• As you approach the speed of light, the factor v/c approaches 1 and the denominator of the equation approaches 0. When you divide anything by zero the result is - so time essentially grinds to a halt as you approach c.

• Q. Suppose you compare your watch to the watch of your friend on a rocketship moving at 98% of the speed of light. Suppose you observe a phenomenon for 1 second by your watch, how long would our friend measure for this same event?

 v = 0.98 c

So, time is stretched out by a factor of 5 for your friend in the rocketship. His/her clocks run at 1/5 the speed of yours.

• In the same way the length of measuring sticks decreases with speed - this is called Length Contraction. A ruler of length L0 at rest, when held perpendicular to the direction of motion will have a length:

So, your friend at 0.98c will have a 1-foot ruler that looks like it is only 2.4 inches long to you.

• It turns out that Mass also varies with velocity. Mass increases with velocity in the same way that time increases:

• These things conspire to make it impossible for objects with mass to ever exceed the speed of light - as you approach c, the required fuel to accelerate a little faster goes up as the mass increases toward infinity AND time slows and slows until you never reach the last instant when you reach c.

• Could any of this possibly be true? You bet!

There have been many experiments, mostly on elementary particles moving near the speed of light in accelerators that have directly measured the increases of mass, dilation of time and contraction of space. Other experiments have compared the time passage on very accurate clocks while moving in airplanes in the opposite directions. Even the discovery of cosmic rays was made possible by the fact that the half-lives of the particles was effectively extended by time dilation long enough for the particles to reach the surface of the Earth.

• The ideas Einstein got from Special Relativity - that rulers and clocks and mass could be affected by motion - he next applied to gravity.

He got away from the idea of a force and instead looked at an interpretation of gravity in terms of its effect on space and time.