Solving The Einstein Field Equation
Solving the Einstein field equation requires an iterative process. The solution is represented in the metric tensor
.
Typically there is an initial guess for the tensor. The guess is used to calculate Christoffel symbols, which are used to calculate the curvature. If the Einstein field equation is not satisfied, the process is repeated.
Solutions occur in two forms, vacuum solutions and non-vacuum solutions. A vacuum solution is one in which the stress-energy tensor is zero. The relevant vacuum solution for circular orbits is the Schwarzschild metric. There are also a number of exact solutions that are non-vacuum solutions, solutions in which the stress tensor is non-zero.
Read more about this topic: Theoretical Motivation For General Relativity
Famous quotes containing the words solving the, solving, einstein, field and/or equation:
“Will women find themselves in the same position they have always been? Or do we see liberation as solving the conditions of women in our society?... If we continue to shy away from this problem we will not be able to solve it after independence. But if we can say that our first priority is the emancipation of women, we will become free as members of an oppressed community.”
—Ruth Mompati (b. 1925)
“Will women find themselves in the same position they have always been? Or do we see liberation as solving the conditions of women in our society?... If we continue to shy away from this problem we will not be able to solve it after independence. But if we can say that our first priority is the emancipation of women, we will become free as members of an oppressed community.”
—Ruth Mompati (b. 1925)
“As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.”
—Albert Einstein (1879–1955)
“Yet, hermit and stoic as he was, he was really fond of sympathy, and threw himself heartily and childlike into the company of young people whom he loved, and whom he delighted to entertain, as he only could, with the varied and endless anecdotes of his experiences by field and river: and he was always ready to lead a huckleberry-party or a search for chestnuts and grapes.”
—Ralph Waldo Emerson (1803–1882)
“A nation fights well in proportion to the amount of men and materials it has. And the other equation is that the individual soldier in that army is a more effective soldier the poorer his standard of living has been in the past.”
—Norman Mailer (b. 1923)