Trace
The trace of the Einstein tensor can be computed by contracting the equation in the definition with the metric tensor . In dimensions (of arbitrary signature):
The special case of 4 dimensions in physics (3 space, 1 time) gives, the trace of the Einstein tensor, as the negative of, the Ricci tensor's trace. Thus another name for the Einstein tensor is the trace-reversed Ricci tensor.
Read more about this topic: Einstein Tensor
Famous quotes containing the word trace:
“Muhammad is the Messenger of God,
and those who are with him are hard
against the unbelievers, merciful
one to another. Thou seest them
bowing, prostrating, seeking bounty
from God and good pleasure. Their
mark is on their faces, the trace of
prostration....
God has promised
those of them who believe and do deeds
of righteousness forgiveness and
a mighty wage.”
—Qur’An. Victory 48:35, ed. Arthur J. Arberry (1955)
“Of moral purpose I see no trace in Nature. That is an article of exclusively human manufacture—and very much to our credit.”
—Thomas Henry Huxley (1825–95)
“A horse, a buggy and several sets of harness, valued in all at about $250, were stolen last night from the stable of Howard Quinlan, near Kingsville. The county police are at work on the case, but so far no trace of either thieves or booty has been found.”
—H.L. (Henry Lewis)