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:
“And in these dark cells,
packed street after street,
souls live, hideous yet
O disfigured, defaced,
with no trace of the beauty
men once held so light.”
—Hilda Doolittle (1886–1961)
“What terrible questions we are learning to ask! The former men believed in magic, by which temples, cities, and men were swallowed up, and all trace of them gone. We are coming on the secret of a magic which sweeps out of men’s minds all vestige of theism and beliefs which they and their fathers held and were framed upon.”
—Ralph Waldo Emerson (1803–1882)
“The land of shadows wilt thou trace
And look nor know each other’s face
The present mixed with reasons gone
And past and present all as one
Say maiden can thy life be led
To join the living with the dead
Then trace thy footsteps on with me
We’re wed to one eternity”
—John Clare (1793–1864)