Einstein's theory of general relativity indeed predicts that the curvature of spacetime can be influenced by mass and energy. This curvature allows for phenomena like gravitational lensing, where light is bent by massive objects, and the slowing down of time near massive bodies.
However, it's important to note that while general relativity allows for certain "time-like" curves in spacetime, which can result in interesting temporal effects, such as time dilation, it does not provide a framework for conventional time travel as commonly depicted in science fiction. Traveling back in time, also known as retrograde time travel, would require the existence of "closed timelike curves," which are not yet proven to exist in our universe.
The existence of closed timelike curves would create a range of paradoxes and logical inconsistencies, such as the infamous "grandfather paradox." These paradoxes involve situations where traveling back in time could lead to events that contradict themselves, causing logical contradictions.
At present, there is no scientific evidence to support the existence of closed timelike curves or practical methods for time travel. While the concept is fascinating and has captured the imagination of many, it remains speculative and currently falls outside the realm of scientific possibility based on our current understanding of physics.