# T1 - First Energy Tensor

## Calculating The Stress-Energy Tensor For a Metric

{% code overflow="wrap" lineNumbers="true" %}

```matlab
%% Alcubierre
gridSize = [1 20 20 20];
worldCenter = (gridSize+1)./2;
velocity = 0.9;
R = 5;
sigma = 0.5;
Metric = metricGet_AlcubierreComoving(gridSize,worldCenter,velocity,R,sigma);
```

{% endcode %}

## Compute Energy Tensor

The stress-energy-momentum tensor can be calculated simply by calling `getEnergyTensor(Metric)`

{% code lineNumbers="true" %}

```matlab
% Compute energy tensor
EnergyTensor = getEnergyTensor(Metric);
```

{% endcode %}

## Basic Plotting

{% code overflow="wrap" lineNumbers="true" %}

```matlab
% Plotting Metric
clf
for i = 1:4
    for j = 1:4
        h = nexttile;
        surfq(Metric.tensor{i,j}(1,:,:,round(worldCenter(4))),'EdgeColor','none')
        title(num2str(i) + "," + num2str(j))
    end
end
sgtitle(Metric.name)

% Plotting Energy Tensor
clf
for i = 1:4
    for j = 1:4
        h = nexttile;
        surfq(EnergyTensor.tensor{i,j}(1,:,:,round(worldCenter(4))),'EdgeColor','none')
        title(num2str(i) + "," + num2str(j))
    end
end
sgtitle(Metric.name + " Energy Tensor")
```

{% endcode %}

## Calculating the Eulerian Stress-Energy Tensor

{% code overflow="wrap" lineNumbers="true" %}

```matlab
% Convert to Eulerian Frame
EnergyTensorEulerian = doFrameTransfer(Metric,EnergyTensor,"Eulerian");

% Plotting Eulerian Energy Tensor
clf
for i = 1:4
    for j = 1:4
        h = nexttile;
        surfq(EnergyTensorEulerian.tensor{i,j}(1,:,:,round(worldCenter(4))),'EdgeColor','none')
        title(num2str(i) + "," + num2str(j))
    end
end
sgtitle(Metric.name + " Eulerian Energy Tensor")
```

{% endcode %}