In mathematics, a Killing tensor or Killing tensor field is a generalization of a Killing vector, for symmetric tensor fields instead of just vector fields. It is a concept in Riemannian and pseudo-Riemannian geometry, and is mainly used in the theory of general relativity. Killing tensors satisfy an equation similar to Killing's equation for Killing vectors. Like Killing vectors, every Killing tensor corresponds to a quantity which is conserved along geodesics. However, unlike Killing vectors, which are associated with symmetries (isometries) of a manifold, Killing tensors generally lack such a direct geometric interpretation. Killing tensors are named after Wilhelm Killing.
\alpha }+T_{\gamma \alpha \beta }+T_{\gamma \beta \alpha })} A Killingtensor is a tensor field K {\displaystyle K} (of some order m) on a (pseudo)-Riemannian...
parameter families of conformal maps are conformal Killing fields. Killingtensor fields are symmetric tensor fields T such that the trace-free part of the...
n m {\displaystyle B_{ij}={c_{im}}^{n}{c_{jn}}^{m}} The Killing form is the simplest 2-tensor that can be formed from the structure constants. The form...
concepts named after Wilhelm Killing: Killingtensor, a generalization of a Killing vector field Killing vector field or Killing field, a vector field on...
higher order symmetry of the Kerr metric generated by a second order Killingtensor field K {\displaystyle K} (different K {\displaystyle K} than used above)...
differential geometry, the Einstein tensor (named after Albert Einstein; also known as the trace-reversed Ricci tensor) is used to express the curvature...
of tensor theory. For expositions of tensor theory from different points of view, see: TensorTensor (intrinsic definition) Application of tensor theory...
the corresponding energy–momentum tensor. When the energy–momentum tensor represents a perfect fluid, every Killing vector field preserves the energy...
field Conformal Killingtensor Curvature collineation Einstein manifold Homothetic vector field Invariant differential operator Killing vector field Matter...
spinor field related to Killing vector fields and Killingtensors. If M {\displaystyle {\mathcal {M}}} is a manifold with a Killing spinor, then M {\displaystyle...
energy–momentum tensor and the Petrov classification of the Weyl tensor. There are various methods of classifying these tensors, some of which use tensor invariants...
addition to two Killing vector fields (corresponding to time translation and axisymmetry), the Kerr geometry admits a remarkable Killingtensor. There is a...
vehicle, Tensing pulled his gun and shot Sam DuBose in the head. Sam was unarmed and sitting in his car with his seat belt on at the time of the killing. Ray...
differentiable manifold. Functions, tensor fields and forms can be differentiated with respect to a vector field. If T is a tensor field and X is a vector field...
April 2015. Retrieved 9 July 2016. "Kashmir tense after Hizbul Mujahideen militant Burhan Wani's killing". International Business Times. 10 July 2016...
store owner. Du was tried and convicted of voluntary manslaughter over the killing of Harlins, based in part on security camera footage. The judge sentenced...
time derivative of the angular displacement tensor, which is a second rank skew-symmetric tensor. This tensor Ω will have n(n−1)/2 independent components...
Indian government involvement in the killing of Hardeep Singh Nijjar. The talks between the two leaders were tense, affecting ongoing trade discussions...
following the killing, the Saudi government admitted on 25 October that he had been killed in a premeditated murder, but denied that the killing took place...
the corresponding energy-momentum tensor. When the energy-momentum tensor represents a perfect fluid, every Killing vector field preserves the energy...
Specifying a metric tensor g {\displaystyle g} is part of the definition of any Lorentzian manifold. The simplest way to define this tensor is to define it...
of point-like particles, the angular momentum tensor is expressed in terms of the stress–energy tensor of the rotating object. In special relativity alone...
The Killing of Two Lovers is an 2020 American drama film, written, directed, produced, and edited by Robert Machoian. It stars Clayne Crawford, Sepideh...
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