Cosmic Horizon

Settings

Time speed Mass per shell ΔM Your mass M₀

Old horizons Galaxies

Beacons

What am I looking at?

The spacetime

You sit on a point mass $M$ in 2+1-dimensional de Sitter space. The geometry is exact (Vaidya–de Sitter):

$$\begin{gathered} ds^2 = -f\,du^2 - 2\,du\,dr + r^2 d\phi^2,\\ f = 1 - \frac{8GM(u)}{c^2} - \frac{r^2}{\ell^2}, \end{gathered}$$

with $r$ the areal radius. In 2+1 dimensions a point mass makes a cone, not a black hole, and your horizon sits at $r_c = \ell\sqrt{1-8GM/c^2}$.

Lengths are in $\ell$, times in $\ell/c$, masses in $c^2/8G$ (the largest possible mass).

The sky

Each object is drawn where it was when it sent the light reaching you now. Its colour is the wavelength you receive, computed exactly through the changing geometry, and it fades as its light is redshifted. Galaxies look flattened along your line of sight, as light from their near and far ends implies.

Dotted circle, $r=\ell$: the horizon of empty de Sitter, reached once you have given away all your mass.
Solid circle, $r_c$: the event horizon for your present mass (if you launch nothing more). It jumps outward when you launch.
Dashed circle: the apparent horizon, as you see it now: the farthest point that the light reaching you now came from, where images freeze. It catches up with $r_c$ over a few $\ell/c$.

Launching

Each tap sends out a shell of 12 beacons at $0.999c$, carrying $\Delta M$ of your mass. The galaxies came from you too: before the game started you launched them the same way, so you begin with a horizon that is still growing.

The Penrose diagram

Light moves at 45°. Gold is your past, everything you have seen; blue is your future, everything you can still reach. The solid pink line is the event horizon (if you launch nothing more), the dashed pink line the apparent horizon, stepping out at each launch, and the pink dot the horizon as you see it now. Now keeps the present in view; Full shows the whole history.

Things to notice

Redshifts grow by a factor $e$ per $\ell/c$ of your time, $1+z \propto e^{\tau/\ell}$, whatever your mass. The mass only sets how big the horizon is.
Images pile up at the horizon and never cross it; each beacon has a last message you will ever receive.
Each launch blueshifts every galaxy a little: their light gains energy crossing your outgoing shell into the lighter region around you.
Each launch enlarges your horizon, so things beyond the old one come back into view, like modes re-entering the horizon after inflation.