Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I recently read a post in physics.stackexchange that used the term "Killing vector". What is a Killing vector/Killing vector field?

share|cite|improve this question
+1, I also saw it when I was looking up the surface gravity of a black hole. Good question. – ja72 Oct 5 '12 at 12:50
please could you summarise the initial research effort you made to find out what a killing vector is? – EnergyNumbers Oct 5 '12 at 12:55
Note Killing is a name associated with the concept, as a quick look at Wikipedia will inform you. – Emilio Pisanty Oct 5 '12 at 13:17
Wikipedia is generally a trustworthy source of information for scientific concepts. If you want to know about the definition of something, we do expect you to check there before posting a question here. If there is an article that directly answers your question, as in this case, it's not really a good question for this site. – David Z Oct 5 '12 at 17:22
up vote 12 down vote accepted

I think answers your question pretty good:

"Killing fields are the infinitesimal generators of isometries; that is, flows generated by Killing fields are continuous isometries of the manifold. More simply, the flow generates a symmetry, in the sense that moving each point on an object the same distance in the direction of the Killing vector field will not distort distances on the object."

A killing vectorfield $X$ fulfills $L_X g=0$ where $L$ is the Lie derivative or more explicit $ \nabla_\mu X_\nu + \nabla_\nu X_\mu =0$.

So in a layback manner: When you move the metric $g$ a little bit by $X$ and $g$ doesn't change, X is a killing vectorfield.

For example the Schwarzschildmetric has two obvious Killing vectorfields $\partial_t$ and $\partial_\phi$ since $g$ is independent of $t$ and $\phi$.

Edit: On recommndation I add a nice link to a discussion of how to use Killing vector fields: See the answer of Willie Wong at Killing vector fields

share|cite|improve this answer
It should also be noted that one can use that fact to construct conserved quantities and sometimes make a system integrable. In the case of the Schwarzschild Metric, those killing fields relate to conservation of energy and angular momentum (respectively). – Benjamin Horowitz Feb 12 '13 at 18:36

Another definition is;

If $V$ is a vector field whose flow $\phi$ is a one parameter group of isometries, then $V$ is called a Killing vector field (or just a Killing vector).

$V$ is a killing vector if and only if $L_vg=0$ ; where Lie derivative.

Here I am giving you a good paper for reference:

share|cite|improve this answer

If any set of points is displaced by $x^i dx_i$ where all distance relationships are unchanged (i.e., there is an isometry), then the vector field is called a Killing vector.

For more,click the link below

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.