Our guiding principle is that Kerr metric is diffeomorphically related to Schwarzschild, as a locally rotating Schwarzschild metric.
In "entity-component-system" ("ECS") physics simulation, it's trivial to approximate this, as like a ConformalMap layer between a Schwarzschild tangent space and the consumer of Kerr geometry methods.
As such, for GetRindlerAcceleration(), we just compose Kerr->Schwarzschild->Minkowski. For ComoveOptical(), we should fully integrate a path over time through both Kerr and Schwarzschild geometry at once, but the accuracy of an endpoint-based finite difference simulation, in either order of ConformalMap co-motion application, limits to 0 error for an infinitesimal finite difference time step.
This is surprisingly simple in "ECS" paradigm, as a step toward completing issue #50.
Our guiding principle is that Kerr metric is diffeomorphically related to Schwarzschild, as a locally rotating Schwarzschild metric.
In "entity-component-system" ("ECS") physics simulation, it's trivial to approximate this, as like a
ConformalMaplayer between a Schwarzschild tangent space and the consumer ofKerrgeometry methods.As such, for
GetRindlerAcceleration(), we just composeKerr->Schwarzschild->Minkowski. ForComoveOptical(), we should fully integrate a path over time through bothKerrandSchwarzschildgeometry at once, but the accuracy of an endpoint-based finite difference simulation, in either order ofConformalMapco-motion application, limits to 0 error for an infinitesimal finite difference time step.This is surprisingly simple in "ECS" paradigm, as a step toward completing issue #50.