# Coefficient of restitution in special relativity

It seems that all books about special relativity only include discussion about perfectly elastic and perfectly inelastic collisions. The notion of the coefficient of restitution, $$e$$ in classical physics doesn't seem to appear in relativistic collisions.

My question is: how do we formulate newton's experimental law in special relativity? To be more specific, let particles $$1,2$$ collide to form particles $$3,4$$. Then (Let $$P$$ denote 4-momentum,$$m$$ denote rest mass) $${P_{1}}_r+{P_{2}}_r={P_{3}}_r+{P_{4}}_r,{P_{1}}^r+{P_{2}}^r={P_{3}}^r+{P_{4}}^r\\ {P_{i}}^r=\gamma_i m_iV_i^r,r={1,2,3,4.}$$ Here I have used tensor notation. Then the question is: how can I find $$V_3,V_4$$ in terms of $$m_i,e,V_1,V_2$$, where $$e$$ is the resititution coefficient? Or can we obtain any other meaningful relations?

• I am not a specialist on this, but maybe if SR books don't contain your answer you need to look into General Relativity books. I would imagine that modelling collisions of stars cannot be done under perfect elastic or non-elastic constraints. – Cryo Jul 11 at 21:24
• Also, don't expect to get away with a single coefficient (of restitution). I would expect it to become a full tensor, and probably even relative tensor once the real treatment begins. – Cryo Jul 11 at 21:28