The curvature of space-time caused by gravity is a fundamental concept in Einstein's theory of general relativity. According to this theory, massive objects, such as planets or stars, create a curvature in the fabric of space-time, and this curvature influences the motion of other objects.
While it might seem intuitive to think that moving faster than the speed of light could allow us to escape the gravitational pull of massive objects, it is not supported by the principles of general relativity. In fact, the theory predicts that the speed of light is an absolute speed limit, and nothing with mass can exceed or even reach this speed.
As an object with mass accelerates, it gains energy and its mass appears to increase according to the theory of special relativity. The more massive an object becomes, the more energy is required to accelerate it further. Approaching the speed of light would require an increasingly infinite amount of energy, making it impossible to reach or exceed the speed of light.
Moreover, the curvature of space-time caused by massive objects is not limited to their immediate vicinity. It extends throughout the surrounding space, so even if one could move faster than light, the gravitational effects would still influence their motion.
It's important to note that our current understanding of physics, particularly in the context of extreme conditions such as those near black holes or during the early moments of the universe, is an active area of research. While there may be speculative ideas and theories that explore concepts like warp drives or wormholes, they remain hypothetical and require further scientific investigation to determine their feasibility.