Since flat space-time can be thought of in Newtonian mechanics as an absence of force or potential of gravity, the presence of such forces is ipso-facto a curvature of space and time, therefore space-time. Thats just another two lines to prove what I claimed, ideally and intuitively.
” eg when earth occupies the space-time around it, its effect, interaction or force is larger at a distance which is closer to the surface and smaller at a distance which is farther away, the force decreases radially-linearly, not linearly as such. So there are equipotential surfaces of gravity which are merely concentric spherical enclosures, one at each value of r=distance. This is tricky because its a potential energy where the reference can be chosen arbitrarily in a given situation. In other words, potential energy being negative, its the absolute or modulus of the energy we are talking about. In essence this is to say, the force without the direction specified.
Its interesting to note, thats so because force is a vector and associated with direction and energy being an integral of force, energy has to go on decreasing if energy continues to produce a force. This is again similar to a situation where like a bank account, the more time you spend in a pub the more you have to spend. “
read more Gravity warps space-time.