Final answer:
Space-time is a continuum where events occur, influenced by matter and energy. In an empty universe, space-time would be flat, but the presence of mass-energy warps it, defining its geometry and the behavior of objects within it.
Step-by-step explanation:
Space-time, as described by Einstein's theory of general relativity, is the four-dimensional fabric that combines the three dimensions of space with the dimension of time. It is not a mere backdrop for the universe's events; instead, it is a dynamic and responsive component. According to general relativity, space-time would theoretically be flat in a completely empty universe, without any mass-energy to curve it. However, our universe contains mass and energy, which means that space-time is curved and warped by these constituents. The curvature of space-time affects the movement of matter and light, aligning with the principle that 'matter tells spacetime how to curve; spacetime tells matter how to move.' The geometry of space can be open, closed, or flat, depending on the total amount of matter and energy within the universe.
What is Space-Time?
Space-time is the four-dimensional continuum in which all physical events occur. Its geometry is not fixed but rather influenced by the mass-energy content within it. The general theory of relativity posits that mass-energy dictates the curvature of space-time, which in turn affects how matter and light travel within it.
The Geometry of Space
The overall shape or geometry of the universe is determined by its matter and energy content. A high density leads to a closed curvature, a critical density results in flat geometry, and a low density creates an open curvature. This curvature isn't perceptible in the human-scale region of space but affects the large-scale structure and fate of the universe.