Specification — Wormhole Multi-Scene System¶

Charter section: §15 Wormhole System Status: Planned (Phase 3) Target location: RendererCore/Wormhole/

1) Purpose¶

Defines how the renderer handles wormhole throat geometry: coordinate chart transitions, multi-scene dispatch, and throat-region rendering. This is the most speculative tier of the transport roadmap and depends on Tier 2 (full GR geodesic integration) being operational.

2) Physics Basis¶

The Morris–Thorne wormhole metric (Morris & Thorne 1988):

ds² = -e^(2Φ) dt² + dr²/(1 - b(r)/r) + r² dΩ²

Where b(r) is the shape function and Φ(r) is the redshift function. For a traversable wormhole with zero tidal forces, Φ = 0 and b(r) = b₀²/r.

The key rendering challenge: a single ray may cross the throat and emerge in a different coordinate patch (and potentially a different scene).

3) Coordinate Atlas¶

IChartMap¶

public interface IChartMap
{
    ChartTransitionResult TryTransition(
        in RayState4 state,
        int currentChartId);
}

public struct ChartTransitionResult
{
    public bool Transitioned;
    public int NewChartId;
    public RayState4 NewState;    // transformed to new chart
}

The atlas is a collection of overlapping charts. When a ray exits one chart's validity domain (e.g., crosses the throat coordinate singularity), the atlas provides the transition to the next chart.

Chart Types (Planned)¶

Chart	Domain	Use
Exterior A	r > b₀ (universe A)	Standard far-field
Throat	r ≈ b₀	Transition zone
Exterior B	r > b₀ (universe B)	Destination scene

4) Multi-Scene Dispatch¶

Scene Hierarchy¶

RootScene (Universe A)
  ├─ WormholeMouth (position, orientation, throat radius)
  │     └─ chart transition → ChildScene (Universe B)
  └─ normal geometry

When a ray transitions through the throat chart, the integrator switches to the child scene's SceneSnapshot and continues evaluation.

IRaySampler¶

public interface IRaySampler
{
    RaySeg[] ContinueInScene(
        in RayState4 entryState,
        int targetSceneId,
        in SceneSnapshot targetSnapshot);
}

5) Throat Rendering¶

Near the throat, several effects require special handling:

Metric divergence: g_rr → ∞ at r = b(r) requires regularised coordinates or proper chart overlap
Light ring: Photon orbits at the effective potential peak need sub-step precision
Lensing ring: Multiple images from rays that orbit before escaping
Redshift: e^(Φ) factor applied to colour/intensity at film write

6) Data Structures¶

WormholeSOA (Planned addition to SceneSnapshot)¶

public sealed class WormholeSOA
{
    public int Count { get; init; }
    public Vector3[] MouthCenterWorld { get; init; }
    public float[] ThroatRadius { get; init; }     // b₀
    public int[] ChartTypeEnum { get; init; }
    public int[] ChildSceneId { get; init; }
}

SceneId¶

SceneSnapshot gains a SceneId field. The integrator maintains a stack of scene contexts to handle nested wormhole traversal (bounded depth).

7) Integration with Transport Tiers¶

Wormhole integration is Tier 3: it extends Tier 2 geodesic integration with chart awareness. The transport interface remains unchanged — IRayTransport returns RaySeg[] regardless of how many chart transitions occurred.

The chart transition logic lives inside the Tier 3 IRayTransport implementation, not in the scheduler or backend.

8) Scope and Deferral¶

This spec intentionally omits: - Rotating (Kerr-like) wormholes - Time-dependent throats - Traversability physics (stress-energy constraints) - Multi-wormhole nesting beyond depth 2

These are deferred to a separate research note if the project reaches Phase 3. The architecture (interface-based chart dispatch) does not preclude them.

9) References¶

Morris, M.S. & Thorne, K.S. (1988). "Wormholes in spacetime and their use for interstellar travel." American Journal of Physics 56(5).
James, O. et al. (2015). "Gravitational lensing by spinning black holes in astrophysics, and in the movie Interstellar." Classical and Quantum Gravity 32(6).