In the context of physics, the term space - time is a mathematical pattern that mixes space and time as two concepts that are totally inherent. In this long time space, it is where all the physical events of the universe take place; this according to the theory of relativity.
Einstein was the one who formulated this expression of space-time based on his theory of special relativity, which states that time cannot be separated from the three spatial dimensions, but that like them, time depends on the state of motion of the observer. By nature, two observers will measure different times. For the interval between two events, this difference in times will depend on the relative speed between the observers.
In the same way, if the theory is raised that the universe has three physical spatial dimensions that can be observed, it is common to consider time as the fourth dimension; leaving space-time as four-dimensional space.
It is important to highlight that space-time has geometric properties which are:
Metric: this property symbolizes spacetime as a pair (m, g), where “m” means semiriemannian differentiable manifold and “g” is a metric tensor.
Material content of space-time: this is given by the energy-impulse tensor, which is calculated directly from geometric measurements from the metric tensor.
Particle motion: particles moving through spacetime will follow a line of minimum length in a curved space.
Homogeneity, isotropy, and symmetry groups: some space-times have isometry groups of lower dimensionality. On the other hand, a space-time is homogeneous when it encompasses a homeoform subgroup that influences spatial coordinates. It will have general isotropy when there is a subgroup of isometry at one of its points.
Topology: it is related to its causal structure. For example, if there is a closed time curve in a space-time, or if there are Cauchy hypersurfaces or incomplete geodesics are present.
Finally, in the space-time used in special relativity, both can be mixed in a four-dimensional space, originating the so-called Minkowski space-time, Minkowsky, here is where three ordinary spatial dimensions and a complementary time dimension are identified.
