What defines a deviation vector

[center o bass]

In the last paragraph in Wald p. 224, he states that if one considers a timelike geodesic $\gamma$ with tangent field $\xi$ and $p \in \gamma$ and now looks at the congruence of geodesics passing through $p$, then every Jacobi field which vanishes at $p$ is a deviation field for this congruence.

Questions:

1. What properties actually defines a deviation field?
2. Why is the statement above true?

 

[Ambitwistor]

1. A deviation field is a vector field that describes the deviation of nearby geodesics from a given geodesic. It can be thought of as a measure of how much the geodesics in a congruence diverge from each other.

2. The statement is true because a Jacobi field, by definition, is a vector field that satisfies the Jacobi equation along a geodesic. This means that it measures the deviation of nearby geodesics from the given geodesic. Since the tangent field of a timelike geodesic is also a Jacobi field, any other Jacobi field that vanishes at a point on the geodesic must also be a deviation field for that congruence of geodesics passing through that point.