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Metrics API

Overview​

The metrics module provides implementations of various spacetime metrics used in general relativity research.

Available Metrics​

get_alcubierre_metric​

Creates an Alcubierre warp drive spacetime metric.

Parameters:

  • grid_size (Tuple[int, int, int, int]): Grid dimensions (t, x, y, z)
  • world_center (Tuple[float, float, float, float]): Center coordinates
  • v (float): Warp bubble velocity (in units of c)
  • R (float): Bubble radius
  • sigma (float): Bubble wall thickness parameter
  • device (torch.device): Target device (cuda/cpu)

Returns:

  • Metric: Object containing metric tensor and derivatives

Example:

from core.metrics.alcubierre import get_alcubierre_metric

metric = get_alcubierre_metric(
    grid_size=(1, 64, 64, 64),
    world_center=(0.0, 16.0, 16.0, 16.0),
    v=1.5,
    R=6.0,
    sigma=4.0,
    device=torch.device("cuda")
)

get_lentz_metric​

Creates a Lentz positive energy soliton metric.

Parameters:

  • grid_size (Tuple[int, int, int, int]): Grid dimensions
  • v (float): Soliton velocity
  • R (float): Soliton radius
  • device (torch.device): Target device

Returns:

  • Metric: Lentz spacetime metric object

get_schwarzschild_metric​

Creates a Schwarzschild black hole metric.

Parameters:

  • grid_size (Tuple[int, int, int, int]): Grid dimensions
  • M (float): Black hole mass
  • device (torch.device): Target device

Returns:

  • Metric: Schwarzschild metric object

get_vandenbroeck_metric​

Creates a Van Den Broeck modified micro-bubble metric.

Parameters:

  • grid_size (Tuple[int, int, int, int]): Grid dimensions
  • v (float): Bubble velocity
  • R (float): Bubble radius
  • device (torch.device): Target device

Returns:

  • Metric: Van Den Broeck metric object

Metric Object​

All metric functions return a Metric object containing:

  • g_uv (torch.Tensor): Metric tensor (4×4×grid_size)
  • derivatives: Dict of first and second derivatives
  • coordinates: Coordinate grid arrays
  • parameters: Original simulation parameters
  • device (torch.device): Computation device