# M1 - First Metric

## Welcome to Warp Factory!

In this example, we'll learn the basics of metrics.

## First metric 

<pre class="language-matlab" data-line-numbers><code class="lang-matlab">gridSize = [1 10 10 10];
gridScaling = [1 1 1 1];
<a data-footnote-ref href="#user-content-fn-1">MyFirstMetric = metricGet_Minkowski(gridSize, gridScaling);</a>
</code></pre>

Check out the properties of the metric struct&#x20;

{% code lineNumbers="true" %}

```matlab
fieldnames(MyFirstMetric)
```

{% endcode %}

## MyFirstMetric.type

This one is simple. The `.type` property of this tensor is "metric". This identifies this tensor object as a metric.

{% code lineNumbers="true" %}

```matlab
MyFirstMetric.type
```

{% endcode %}

## MyFirstMetric.index

This property specifies what form the tensor is in. A metric tensor index can either be "covariant" ( $$g\_{\mu\nu}$$ ) or "contravariant" ( $$g^{\mu\nu}$$ ).

<pre data-line-numbers><code><strong>MyFirstMetric.index
</strong></code></pre>

## MyFirstMetric.tensor

The tensor contains the values for metric at each point in space and time for each tensor component. The tensor object is a 4x4 cell array. Each cell contains an array of values for each point in spacetime. The size of this array is equal to the `gridSize` of your spacetime.

{% code lineNumbers="true" %}

```matlab
MyFirstMetric.tensor
```

{% endcode %}

Let's take a look at the tensor values for a slice of the space.

{% code lineNumbers="true" %}

```matlab
for i = 1:4
    for j = 1:4
        nexttile
        surfq(MyFirstMetric.tensor{i,j}(1,:,:,1))
    end
end
```

{% endcode %}

Just as expected for Minkowski space! ( $$g\_{\mu\nu} = \eta\_{\mu\nu}$$ for all points in the slice)

## Other Properties

`.name` - Your metric has a name!&#x20;

`.date` - Your metric stores a date when it is made.&#x20;

`.scaling` - Your metric has scaling information about the coordinate grid step size in time and space. We'll get into this more in later examples.&#x20;

`.coords` - The coordinate system associated with the metric. 'cartesian'.

{% code lineNumbers="true" %}

```
MyFirstMetric.name
MyFirstMetric.date
MyFirstMetric.scaling
MyFirstMetric.coords
```

{% endcode %}

[^1]:


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