GENERAL RELATIVITY General relativity describes the effect of gravitational fields on space and time.

Postulates and Fundamental Concepts Einstein’s Principle of equivalence Gravity and space - time Gravitational vs. inertial mass Einstein’s principle of equivalence states that there is no fundamental difference between accelerated motion and the presence of a gravitational field. Use the rocket ship example and note the similar effects on both particles (with obvious mass) and on a light beam. Mass deforms space time causing it to become curved. Gravity is the effect on objects or light traveling through curved space time. Gravitational mass is the mass measured as a result of gravitational force between two masses. Inertial mass is an objects resistance to a change in its motion. There is no fundamental reason other than Einstein’s general theory of relativity why the quantities should be the same.

Observable Effects of General Relativity Light and gravitational fields energy matter and mass solar eclipse Gravitational redshift Since energy and matter are alternate forms of one another and display similar properties (note dual particle and wave characteristics) then energy (photons) should be affected by gravitational fields in the same way as particles. The phenomenon of gravity bending the path of light was first observed by comparing the stellar background(s) one at night, and one six months later during a solar eclipse. Gravitational redshift is a shift in frequency between two identical clocks at different heights in a gravitational field. The higher the clock in the gravitational field the more redshifted (lower) the frequency of the clock (it runs faster when compared to a clock that is lower in the field). The Pound - Rebka experiment in 1960 at the Jefferson Physical laboratory tower at Harvard University measured the shift in gamma ray photon frequencies as the photons ascended or descended the tower. The equation can be derived based on the discrepancy between two clocks on an accelerating rocket ship. First realize that there will be a relative velocity difference between a clock at the top of the ship and one at the bottom due to the acceleration during the time required for signal to travel between the two clocks. The doppler shift for the frequency from one clock to the other will be: f = f0(1 = v/c)/(1 - v2/c2)1/2 note that the relative velocity between the two clocks is gt and that the time required is approximately H/c so the relative velocity can be written gH/c. This gives the result that: f = f0(1 + gH/c2)1/2

Observable Effects of General Relativity Black holes Gravitational waves LIGO A black hole occurs when a star has expended enough of its fusion material so that the energy of it matter is not sufficient to counter its own gravitational field. The resulting gravitational field is so strong that the required escape velocity at the event horizon is equal to the speed of light at this point no matter or energy can escape from within the event horizon. The radius of the event horizon known as the Schwarzchild radius occurs when the gravitational potential energy is equal to the kinetic energy at the speed of light. Since nothing can move through space faster than the speed of light (not even information) it follows that changes in gravitational fields propagate through space at the speed of light in the form of gravitational waves.