I am wondering if there are basic examples of general relativity in 2D (1+1) space time to help visualising the concept of curved space time?
I have read things like "in 1+1 and 2+1 dimensions the vacuum spacetimes are flat" so perhaps my question does not mean anything but if it does I think it would give a better and more faithful representation of what a curved space time actually is. In fact I feel like the representation traditionally displayed in vulgarisation of GR is quite erroneous.
But the reason I am asking that about 2D spacetime is because it is the only case where we can see an isometric embedding (so here a 3D representation) of a curved space time (here 2D). Basically what I would like to visualise is :
1)how the light cones are modified in presence of curvature.
2)how the coordinate transformation (similar to the Lorentz transformation in SR) applies in presence of curvature.
3)how 2 observers evolving in 2 different inertial reference frames(not sure if that makes sens in curved spacetime) would define their 1D space $x$, $\bar x$ and time $t$, $\bar t$ in a curved space time. We could then clearly see how the space $x$ of the first observer would change with $t$ and how the space of the second observer $\bar x$ would change with $\bar t$.
I thought that a paraboloid space-time could be a good example (the minimum referring to the big-bang event) and each observer would define their space from cross sections (which would be 1D objects without boundaries). What is nice is that it could also give an image of expanding universe and how particles with different world lines would envision this expansion. But I am struggling with the math and I am not sure if this example actually makes sens.
