A3 - Eval Metric

Eval Metric

evalMetric computes

1. The energy tensor

2. The Eulerian energy tensor

3. The null, weak, strong, and dominant energy conditions

4. The expansion, shear, and vorticity scalars,

All in 1 line of code.

%% Make Metric
gridSize = [1 20 20 20];
worldCenter = (gridSize+1)./2;
velocity = 0.5;
R = 5;
sigma = 0.5;
Metric = metricGet_AlcubierreComoving(gridSize,worldCenter,velocity,R,sigma);

%% Run evalMetric
[Evaluation] = evalMetric(Metric);

Get field names

fieldnames(Evaluation)

Metric

plotTensor(Evaluation.metric, 0)

Energy Tensor

plotTensor(Evaluation.energyTensor, 0)

Eulerian Energy Tensor

plotTensor(Evaluation.energyTensorEulerian, 0)

Null Energy Condition

surfq(Evaluation.null(1,3:end-2,3:end-2,round(worldCenter(4))))
title("Null")
view(2)
xlim([1 gridSize(2)-4])
ylim([1 gridSize(3)-4])

Weak Energy Condition

surfq(Evaluation.weak(1,3:end-2,3:end-2,round(worldCenter(4))))
title("Weak")
view(2)
xlim([1 gridSize(2)-4])
ylim([1 gridSize(3)-4])

Strong Energy Condition

surfq(Evaluation.strong(1,3:end-2,3:end-2,round(worldCenter(4))))
title("Strong")
view(2)
xlim([1 gridSize(2)-4])
ylim([1 gridSize(3)-4])ab

Dominant Energy Condition

surfq(Evaluation.dominant(1,3:end-2,3:end-2,round(worldCenter(4))))
title("Dominant")
view(2)
xlim([1 gridSize(2)-4])
ylim([1 gridSize(3)-4])

Expansion Scalar

surfq(Evaluation.expansion(1,:,:,round(worldCenter(4))))
title("Expansion Scalar")
view(2)
xlim([1 gridSize(2)])
ylim([1 gridSize(3)])

Shear Scalar

surfq(Evaluation.shear(1,:,:,round(worldCenter(4))))
title("Shear Scalar")
view(2)
xlim([1 gridSize(2)])
ylim([1 gridSize(3)])

Vorticity Scalar

surfq(Evaluation.vorticity(1,:,:,round(worldCenter(4))))
title("Vorticity Scalar")
view(2)
xlim([1 gridSize(2)])
ylim([1 gridSize(3)])

Vorticity should always be 0.