In the theory of general relativity, the curvature of spacetime describes the way that matter and energy in the universe influence the geometry of the surrounding space and time. According to Einstein's theory, massive objects, such as stars or planets, curve the fabric of spacetime around them.
To understand this concept, imagine a flat rubber sheet representing empty space. If you place a heavy object, like a bowling ball, on the sheet, it will create a depression or indentation in the sheet. Now, if you roll a marble near the bowling ball, it will follow a curved path around the depression caused by the bowling ball. The bowling ball represents a massive object curving the two-dimensional space of the rubber sheet, and the marble's curved path represents the effect of this curvature on the motion of objects near it.
In reality, this analogy extends to three dimensions, where the massive object curves the three-dimensional space around it. However, it's important to note that the curvature of spacetime is not a physical bending or warping in the conventional sense. Instead, it describes the geometric effect of mass and energy on the fabric of the universe.
The curvature of spacetime is described mathematically by the Einstein field equations, which relate the distribution of matter and energy in the universe to the curvature of spacetime. The presence of mass and energy influences the curvature, and this curvature, in turn, affects the motion of objects and the behavior of light in the vicinity of massive objects.
So, when we say that an object curves spacetime, we mean that it creates a gravitational field that alters the geometry of the surrounding space and time. Other objects in the vicinity of this curvature then follow curved paths or experience changes in their motion due to the influence of this curved spacetime.