This quantity can be written as density times two four-velocities for dust solutions and it has only diagonal elements for perfect fluid solutions.
Conformal symmetry is anomalously broken in a curved background when this operator contracted with the metric has non-zero expectation value. In a conformal field theory, this quantity is always traceless. One trick for computing this quantity gives it as the Lagrangian times the metric minus two times the variation of the Lagrangian with respect to the metric. The ten independent components of this quantity are the (*) conserved Noether currents corresponding to spacetime translational invariance. This quantity can be written as density times two four-velocities for dust solutions and it has only diagonal elements for perfect fluid solutions. This quantity is multiplied by 8 pi G over the speed of light to the fourth power on the right side of the Einstein field equations. For 10 points, name this quantity symbolized by capital T which measures energy and momentum in spacetime.
Conformal symmetry is anomalously broken in a curved background when this operator contracted with the metric has non-zero expectation value.
stress-energy tensor [or energy-momentum tensor]