Can other fundamental forces bend spacetime?

Question

I was wondering what makes gravity so special that it bends spacetime? and if it is part of the four-fundamental forces, why or why cant the other forces bend the time space continuum?

Answer 1

According to General Relativity the gravitational field is equivalent to the geometric properties of spacetime. This geometric properties are given by the curvature tensor which is determined by the Einstein's field equations (EFE)$$R_{\mu\nu} - {\textstyle 1 \over 2}R\,g_{\mu\nu} = {8 \pi G \over c^4} T_{\mu\nu}\,$$

where the left side can be interpreted as the geometric or gravitational part (as it contains the metric and the Ricci curvature tensor) and the right hand side the matter part (which is just the energy momentum tensor of the matter fields presents).

As you can see the "bending" is done by anything that contains energy or momentum which make the right hand side non-trivial.

What is surprising is that even in the absence of matter there might be some bending by the self interaction of the gravitational field. This is due to the fact that the EFE determine only certain part of the curvature tensor but not all of it.

Answer 2

A bending of space-time can be observed through the study of the metric describing it, specifically through the Riemann curvature tensor. Based on the current knowledge, space-time is assumed to be a 4-dimensional manifold which is locally modelled on flat Minkowski space-time. General relativity relates the geometry of space-time, that is the metric $g$, with the energy/matter density. It turns out that matter effectively curves space-time, but other forces, despite contributing to the stress-energy tensor, lead to some traceless contribution to the theory. That's how current theories are formulated these days and as far as I know there is a good agreement with observations.