Rest mass of a coalescing relativistic collision ($m_3^2=m_1^2+m_2^2+2m_1{m}_2{\gamma }_1{\gamma }_2(1-u_1{u}_2/c^2)$)

When two massive particles coalesce without additional outgoing radiation, four-momentum conservation makes the final four-momentum their sum. For collinear incident velocities, its rest mass is the positive square root of the displayed invariant, and its final velocity equals the center-of-momentum frame velocity $c^2{p}_{\mathrm{total}}/E_{\mathrm{total}}$. Relative kinetic energy can become internal rest energy, so the final rest mass is generally larger than the sum of the incident rest masses.