ASTRO 142 Chapter Notes - Chapter 9: Supermassive Black Hole, Gravitational Time Dilation, Gravitational Redshift
Document Summary
Death of a supermassive star results in collapse: black hole. Escape velocity: velocity required for an object to overcome the gravitational pull at the object"s surface. Karl schwarzschild comes up with a solution to einstein"s equations: Assumed perfectly spherical, stationary ball of mass surrounded by vacuum. Solved einstein"s equations to compute the spacetime curvature in the exterior of a star. Similar to flat space-time interval of special relativity, but is modified by appearance of metric coefficients. Only affect time and radial measurements (angular terms unchanged) t^2 and r^2 account for gravitational time dilation and length contraction. Valid in a vacuum outside any spherical body of mass m and radius r. Since c^2 is large, r will be extremely small unless m is also large. When mass is present, it is necessary to solve the einstein equations with the stress-energy term present. Major effect on space-time around the earth occurs through the metric coefficient of the time coordinate.
