# Why spin 2 is related with attractive force? [duplicate]

Excerpt from Introduction to Black hole physics, Valeri P. Frolov and Andrei Zelnikov.

In this textbook, there is comment about spin of gravitons as follows:

For gravitating bodies the gravitational charge i.e. their masses, always have the same sign and they attract each other. This property is directly connected with the fact that gravitons have spin 2, while the photons have spin 1.

Can anybody explain to me the reason, why spin 2 is related with attractive force in more detail?

• Not me. Gravitons remain hypothetical, whilst General Relativity is one of the best-tested theories we've got. A photon has a non-zero "active gravitational mass" and a non-zero "passive gravitational mass". But it is not surrounded by gravitons like a horse is surrounded by flies. And a black hole is not spewing out gravitons. Nothing can get out of a black hole. That's why it's black. – John Duffield Jun 26 '15 at 12:42
• Take a look at A. Zee "Quantum field theory in a nutshell". He makes this calculation explicitely. – Gabriel Cozzella Jun 26 '15 at 12:55
• @JohnDuffield,Gabriel Cozzella, thanks for comment. I will take a look at it. – phy_math Jun 26 '15 at 14:02
• Loosely speaking, the graviton propagator is $\sim\eta^2$ ($\eta$ is the Minkowski metric). The Yukawa force of gravitational attraction between two point masses $m_1$ and $m_2$ is of the form $-m_1m_2(\eta_{00})^2/r^2<0$, implying attraction. This calculation is done in Zee's book. The fact that the graviton propagator is quadratic in the metric follows directly from the spin-2 nature of gravity. – Ryan Unger Jun 26 '15 at 15:45
• Possible duplicate of A spin zero graviton? – JDługosz Dec 4 '16 at 7:18