- #1
maverick280857
- 1,789
- 4
Hi,
I am working through Carrol's book on General Relativity. On page 206, he makes the following statement:
How does this follow from the definition of a Killing vector?
He uses this equation to determine the total energy (equation 5.61).
Thanks in advance.
EDIT: This makes sense for a timelike particle for which,
[tex]p^\mu = m \frac{dx^\mu}{d\tau}[/tex]
What about a lightlike particle?
EDIT 2: On page 207, he says that for a lightlike particle, it is convenient to normalize [itex]\lambda[/itex] in such a way that [itex]p^\mu = \frac{dx^\mu}{d\lambda}[/itex] for a lightlike particle. How does one justify this?
I am working through Carrol's book on General Relativity. On page 206, he makes the following statement:
Carroll said:If [itex]K^\mu[/itex] is a Killing vector, we know that
[tex]K_\mu \frac{dx^\mu}{d\lambda} = \mbox{ constant } [/tex]
How does this follow from the definition of a Killing vector?
He uses this equation to determine the total energy (equation 5.61).
Thanks in advance.
EDIT: This makes sense for a timelike particle for which,
[tex]p^\mu = m \frac{dx^\mu}{d\tau}[/tex]
What about a lightlike particle?
EDIT 2: On page 207, he says that for a lightlike particle, it is convenient to normalize [itex]\lambda[/itex] in such a way that [itex]p^\mu = \frac{dx^\mu}{d\lambda}[/itex] for a lightlike particle. How does one justify this?
Last edited: