In mathematics, a Killing vector field (often called a Killing field), named after Wilhelm Killing, is a vector field on a Riemannian manifold (or pseudo-Riemannian...

Einstein field equations. Mathematically a Killing horizon is a null hypersurface defined by the vanishing of the norm of a Killing vector field (both are...

conformal Killing vector field on a manifold of dimension n with (pseudo) Riemannian metric g {\displaystyle g} (also called a conformal Killing vector, CKV...

after Wilhelm Killing: Killing tensor, a generalization of a Killing vector field Killing vector field or Killing field, a vector field on a Riemannian...

Look up killing field or Killing Fields in Wiktionary, the free dictionary. Killing field may also refer to: Killing Fields, a number of sites in Cambodia...

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...

Hamiltonian Killing vector field, a vector field on a Riemannian manifold associated with a symmetry Solenoidal vector field, a vector field with zero divergence...

thus, this Killing vector field is hypersurface orthogonal. The fact that the spacetime admits an irrotational timelike Killing vector field is in fact...

In vector calculus, a complex lamellar vector field is a vector field which is orthogonal to a family of surfaces. In the broader context of differential...

A projective vector field (projective) is a smooth vector field on a semi Riemannian manifold (p.ex. spacetime) M {\displaystyle M} whose flow preserves...

thus, this Killing vector field is hypersurface orthogonal. The fact that our spacetime admits an irrotational timelike Killing vector field is in fact...

{\mathcal {L}}_{Y}]T.} A Killing vector field is one of the most important types of symmetries and is defined to be a smooth vector field X that preserves the...

In Riemannian geometry, a Jacobi field is a vector field along a geodesic γ {\displaystyle \gamma } in a Riemannian manifold describing the difference...

spacetime is static if it admits a global, non-vanishing, timelike Killing vector field K {\displaystyle K} which is irrotational, i.e., whose orthogonal...

S2CID 121548146. Killing equation Killing form Killing–Hopf theorem Killing horizon Killing spinor Killing tensor Killing vector field Levi decomposition...

I(\rho )} is the index of the representation. Casimir invariant Killing vector field Kirillov 2008, p. 102. Borel 2001, p. 5 Fulton, William; Harris,...

Cosmological horizon, a limit of observability Killing horizon, a null surface on which there is a Killing vector field Particle horizon, the maximum distance...

is the gravitational force field.[citation needed] Consequently, if ξ μ {\textstyle \xi ^{\mu }} is any Killing vector field, then the conservation law...

kind of spinor field related to Killing vector fields and Killing tensors. If M {\displaystyle {\mathcal {M}}} is a manifold with a Killing spinor, then...

In mathematics, Salomon Bochner proved in 1946 that any Killing vector field of a compact Riemannian manifold with negative Ricci curvature must be zero...

on the spacetime metric. In a stationary spacetime with timelike Killing vector field ξ {\displaystyle \xi } , the temperature T {\displaystyle T} satisfies...

electromagnetic field, a Killing vector field does not necessarily preserve the electric and magnetic fields. Affine vector field Conformal vector field Curvature...

it can be regarded as a constant vector field. In particular, the spin angular velocity is a Killing vector field belonging to an element of the Lie...

t 0 {\displaystyle t=t_{0}} admit a Bianchi III (c.f. the fourth Killing vector field). This can be rewritten as the symmetry group containing three-dimensional...

spacetime can be defined as a spacetime which possesses a timelike Killing vector field. The following discussion is an expanded and simplified version of...

change of a tensor field (including scalar functions, vector fields and one-forms), along the flow defined by another vector field. This change is coordinate...

linearly independent Killing vector fields. Indeed, in the Cartesian chart we can readily find ten linearly independent Killing vector fields, generating respectively...

spacetime, a spacetime having a global, non-vanishing, timelike Killing vector field which is irrotational Statics, a branch of physics concerned with...

relativity, specifically in the Einstein field equations, a spacetime is said to be stationary if it admits a Killing vector that is asymptotically timelike....

by similarity reduction. Affine vector field Conformal Killing vector field Curvature collineation Killing vector field Matter collineation Spacetime symmetries...