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- TL;DR Summary
- Merry Christmas - Hope you don't already have one of these.
It's yet another fun thing you can do with Black Holes !!
The Sub Photon Sphere Escape (SPSE) Game
Game Board: | Vast Empty Space |
Game Pieces: | ##\space## 1) A large perfect Schwarzschild black hole ##\space## 2) A Carrier/Trigger. This is a massless device that sets the Player Device into a selected position and velocity and then triggers it. ##\space## 3) The Player Device: This is a device of mass ##M## designed by the player. Its operation must be possible in principle. |
The Play: | ##\space## There are 2 levels. At level 1, the Player Device is triggered while it is hovering below the Photon Sphere. At level 2, the Player Device is triggered after it has dropped from infinity into the Photon Sphere. ##\space## 1) The Schwarzschild black hole is placed at the origin of the vast empty space: coordinates 0,0,0. ##\space## 2) A player designs a device of mass ##M## which can be programmed with its starting location and velocity. It can also be "triggered". When triggered, it will attempt to prevent as much of its mass as possible from falling into the Black Hole. In comparison to the mass of the black hole, mass ##M## is insignificant. ##\space## 3) That Player Device is built and programmed with the starting velocity and location (automatically). ##\space## 4) The carrier/trigger brings the Player Device to its starting conditions and triggers it: ## \space \space \space ## ##r_D##: the location 1 to 1.5 specified as the number of Schwarzschild Radii from the origin. ## \space \space \space ## ##v_D##: the starting velocity, either 0 (Level 1: hovering) or minus the vertical escape velocity (Level 2: as if dropped from infinity into the Black Hole). |
The Score: | ##\space## The total mass of all portions of the Player Device that reach the Photon Sphere and either enter a safe orbit or escape the BH entirely is ##M_e##. ##M_e## is tallied and the score is computed as ##S=M_e/M##. |
The Goal: | ##\space## The score ##S## is a function of ##r_D## and ##v_D##. The goal is to demonstrate that a Player Device will generate the highest possible score ##S(r,v)## for all ##1<r<1.5## and ##v≤c##. |
Game Levels: | ##\space## I've only described two game levels - hovering and dropping - both with a Schwarzschild BH. But at least two additional levels can be described - trajectories with horizontal components and black holes with spin. Feel free to play at those levels, but don't expect me to contribute much. I'm still working on Level 1 and 2. |
The Reward: | ##\space## This game demonstrates that, although the Event Horizon is the point of no return, it is not an abrupt boundary where all information is suddenly lost to the outer world. There are points of 20%, 50%, and 99% return. In fact, the event horizon is where the information loss ends - because there is none remaining to loose. ##\space## Also, the information is lost by way of economics. The cost of retrieving the information is more information. Ultimately, as the information approaches the Event Horizon, the cost exceeds any possible payment. |
Parameters | Symbol | Units |
Schwarzschild Radius | ##r_S## | any |
Location of event horizon | ##r_H = 1## | ##r_S## |
Location of photon sphere | ##r_S = 1.5## | ##r_S## |
Vertical escape velocity | ##v_e(r) = r^{-0.5}## | ##c## |
Starting location of Player Device | ##1 \lt r_D \le 1.5## | ##r_S## |
Starting velocity of Player Device ##\space \space## Level 1 (hovering) ##\space \space## Level 2 (dropping) | ##v_D = 0## ##v_D = -v_e(r_D)## | ##c## |
Mass of Player Device | ##M## | any |
Escaped Mass of Player Device | ##M_e## | any |
Score - a function of: ##\space \space## the player device (##P##); and ##\space \space## the starting conditions (##r,v##). | ##S(P,r,v) = M_e/M## | none |
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