general relativity - Why is the gravitational force always attractive?

Why is the gravitational force always attractive? Is there another way to explain this without the curvature of space time?

PS: If the simple answer to this question is that mass makes space-time curve in a concave fashion, I can rephrase the question as why does mass make space-time always curve concavely?

Answer

Gravity is mediated by a spin two particle. Electromagnetism by spin 1.

Here is a link that answers your question:

even and odd spin do differ in that they require a product of charges with different signs to get attraction or repulsion:

spin even:

• $q_1 q_2 > 0$: attractive


• $q_1 q_2 < 0$: repulsive

spin odd:

• $q_1 q_2 < 0$: attractive


• $q_1 q_2 > 0$: repulsive

In the case of gravity, mediated by spin 2 particles, charge is mass, which is always positive. Thus, $q_1 q_2$ is always greater than zero, and gravity is always attractive. For spin 0 force mediators, however, there is no restriction on the charges and you can very well have repulsive forces. A better rephrasing of the question is: "Why do particles of odd spin generate repulsive forces between like charges, while particles of even spin generate attractive forces between like charges?"

Goes on to derive this