Take the 2-minute tour ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.

In this PDF [1], is made reference to specific energy and angular momentum of a particle. If the particle has no mass, like a photon, how should I define these terms in the equations further down for the path of the particles?

[1] Lecture XIX, Christopher M. Hirata, Caltech M/C 350-17

share|improve this question

1 Answer 1

up vote 1 down vote accepted

For complete treatement, See [this reference] (http://preposterousuniverse.com/grnotes/grnotes-seven.pdf) page 172 (formula 7.32) and following pages.

The idea is to use an affine parameter $\lambda$, such as :

$$g_{\mu\nu} \frac{dx^{\mu}}{d\lambda} \frac{dx^{\mu}}{d\lambda} = - \epsilon$$

(in a metrics $g = (-1,1,1,1))$

For massive particles, you can choose $\lambda = \tau$, which is the proper time of the particle, so $\epsilon = - 1$

For massless particles, $\lambda$ is different of $\tau$, because $d\tau=0$ , In this case, you have $\epsilon = 0 $.

So you can make all the calculus with this $\epsilon$, for instance, you Will have an effective potential as :

$$V(r) = \frac{1}{2} \epsilon - \epsilon \frac{GM}{R} + \frac{L^2}{2R^2} - \frac{GML^2}{R^3} $$(page 174 formula 7- 48 of the reference)

Page 176 of the reference, you will see the different orbits for massive and massless particles.

share|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.