The curvature of space and time due to matter and energy is a fundamental concept in Einstein's theory of general relativity. According to this theory, mass and energy distort the fabric of space and time, creating what is known as a gravitational field.
The exact mechanism by which matter and energy curve space and time is described mathematically by Einstein's field equations. These equations relate the distribution of matter and energy in a given region of spacetime to the curvature of spacetime itself. In simpler terms, the presence of mass and energy tells spacetime how to curve, and the curvature of spacetime tells matter and energy how to move.
To visualize this concept, imagine a flat rubber sheet representing empty space. If you place a heavy object, like a bowling ball, on the sheet, it causes the sheet to curve or deform around it. Smaller objects placed on the sheet, like marbles, will roll towards the bowling ball due to the curvature of the sheet.
Similarly, in the theory of general relativity, massive objects, like planets, stars, or even galaxies, curve the fabric of spacetime around them. This curvature determines the path that other objects, such as smaller planets or particles, will follow when moving near the massive object.
As for your second question, our current understanding of general relativity provides a mathematical framework that accurately describes how matter and energy curve spacetime. However, the underlying mechanisms that give rise to this curvature are still an active area of research and investigation in theoretical physics.
Scientists continue to explore and refine our understanding of gravity through experiments and theoretical studies. Efforts are being made to reconcile general relativity with quantum mechanics, which describes the behavior of matter and energy on very small scales. The ultimate goal is to develop a more comprehensive theory that unifies these two fundamental pillars of physics, known as a theory of quantum gravity.