Einstein Field Equation
We obtain the Einstein field equation by equating the acceleration required for circular orbits with the acceleration due to gravity
- .
This is the relationship between curvature of spacetime and the stress-energy tensor.
The Ricci tensor becomes
- .
The trace of the Ricci tensor is
- .
Comparison of the Ricci tensor with the Ricci tensor calculated from the principle of least action, Theoretical motivation for general relativity#Principle of least action in general relativity identifying the stress-energy tensor with the Hilbert stress-energy, and remembering that A+B=1 removes the ambiguity in A, B, and C.
and
- .
This gives
- .
The field equation can be written
where
- .
This is the Einstein field equation that describes curvature of spacetime that results from stress-energy density. This equation, along with the geodesic equation have motivated by the kinetics and dynamics of a particle orbiting the earth in a circular orbit. They are true in general.
Read more about this topic: Theoretical Motivation For General Relativity
Famous quotes containing the words einstein, field and/or equation:
“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)
“The snow had begun in the gloaming,
And busily all the night
Had been heaping field and highway
With a silence deep and white.”
—James Russell Lowell (1819–1891)
“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)