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)
“There are horrible people who, instead of solving a problem, tangle it up and make it harder to solve for anyone who wants to deal with it. Whoever does not know how to hit the nail on the head should be asked not to hit it at all.”
—Friedrich Nietzsche (1844–1900)
“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)
“Mine was, as it were, the connecting link between wild and cultivated fields; as some states are civilized, and others half-civilized, and others savage or barbarous, so my field was, though not in a bad sense, a half-cultivated field. They were beans cheerfully returning to their wild and primitive state that I cultivated, and my hoe played the Ranz des Vaches for them.”
—Henry David Thoreau (1817–1862)
“Jail sentences have many functions, but one is surely to send a message about what our society abhors and what it values. This week, the equation was twofold: female infidelity twice as bad as male abuse, the life of a woman half as valuable as that of a man. The killing of the woman taken in adultery has a long history and survives today in many cultures. One of those is our own.”
—Anna Quindlen (b. 1952)