*Spacetime* is something physical which has a deep mathematical meaning.


**The General (intuitive) Idea**

Intuitively and roughly speaking, spacetime is the "place" of all *events*, or the set of all events. An *event* is something that "happens in a time $\tau$ and takes place somewhere". You can grasp the main concept with a simple example: You have a physics test, Friday 11:00 AM, at the Physics Departament building, on floor 5. Well, if you go to the right place but wrong time you will miss the test. To access the event "test" you have to be in the right place at right time. So, you necessarily must to deal with four numbers: one for time and three for space.

Because of relativity, the time are not just a parameter, but a coordinate! In Lorentz transformations you transform time as a usual coordinate. You must consider time as just another coordinate as the usual spatial ones.

**The idea of Gravity and "Deformation"**

Well, I would like to present to you an equation:

$$\textbf{G} = \frac{8\pi G}{c^{4}}\textbf{T} \tag{1}$$

This equation is called Einstein Field Equation. This equation tells us about how bodies moves in that "place of all events" (the Spacetime) due to a matter-energy distribuition. The quantity $\textbf{G}$ is called *Einstein Tensor*. This quantity encodes the curvature of this "place of all events", and because of that, other bodies have their trajectories changed due to this curved "place of all events", like Earth around the Sun. And this sounds familiar, no? Well, this is just the fingerprint of a gravitational system; gravity is a consequence of curved spacetime.

On the right hand side we have the information of which body performs the curvature; could be a planet, star, other fields... The quantity $\textbf{T}$ is called *Matter Tensor* and this quantity encondes all of the information about which type of matter are curving spacetime.

**A Very Nice Phrase**

There's a nice phrase said by a physicist called John Wheeler which is:

>"Spacetime tells matter how to move$^{*}$ and Matter tells spacetime how to curve$^{**}$"

$^{*}$ This is just the intuitive idea of what physical meaning the Einstein Tensor carries: here this quantity is just a "pure mathematical thing", which tells curvature. But this curvature modifies the trajectories of particles, and this is just gravity.

$^{**}$ And this is the intuitive idea behind the Matter Tensor: a planet (for instance) curves spacetime and then this curvature modifies trajectories of particles, and this is just gravity....and so on.


$$* * *$$

I recommend a nice book: *Relativity: The Special and General Theory* by Einstein himself.

A "self motivation" disclaimer: Special and General Relativity aren't difficult to understand when you have the basic pre-requisites, so don't be afraid.