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:
“You are right to demand that an artist engage his work consciously, but you confuse two different things: solving the problem and correctly posing the question.”
—Anton Pavlovich Chekhov (1860–1904)
“Certainly, young children can begin to practice making letters and numbers and solving problems, but this should be done without workbooks. Young children need to learn initiative, autonomy, industry, and competence before they learn that answers can be right or wrong.”
—David Elkind (20th century)
“If my theory of relativity is proven correct, Germany will claim me as a German and France will declare that I am a citizen of the world. Should my theory prove untrue, France will say that I am a German and Germany will declare that I am a Jew.”
—Albert Einstein (1879–1955)
“You cannot go into any field or wood, but it will seem as if every stone had been turned, and the bark on every tree ripped up. But, after all, it is much easier to discover than to see when the cover is off. It has been well said that “the attitude of inspection is prone.” Wisdom does not inspect, but behold.”
—Henry David Thoreau (1817–1862)
“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)