Android : Trouble getting GoogleMap from FragmentManager

Why do I get a null pointer exception when I do GoogleMap map = ((SupportMapFragment) manager.findFragmentById(R.id.map)).getMap()? I must be missing something very obvious:

public class ReviewMap extends ActionBarActivity {

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_review_map);

        if (savedInstanceState == null) {
            FragmentManager manager = getSupportFragmentManager();
            manager.beginTransaction().add(R.id.container, new MapFragment()).commit();

            GoogleMap map = ((SupportMapFragment) manager.findFragmentById(R.id.map)).getMap();  // Null pointer exception
        }
    }

    @Override
    public boolean onCreateOptionsMenu(Menu menu) {
        getMenuInflater().inflate(R.menu.review_map, menu);
        return true;
    }

    @Override
    public boolean onOptionsItemSelected(MenuItem item) {
        return super.onOptionsItemSelected(item);
    }

    public static class MapFragment extends Fragment {

        public MapFragment() {
        }

        @Override
        public View onCreateView(LayoutInflater inflater, ViewGroup container, Bundle savedInstanceState) {
            View rootView = inflater.inflate(R.layout.fragment_review_map, container, false);
            return rootView;
        }
    }
}

My layouts:

activity_review_map.xml:

<FrameLayout xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:tools="http://schemas.android.com/tools"
    android:id="@+id/container"
    android:layout_width="match_parent"
    android:layout_height="match_parent"
    tools:context="atorch.shortestpaths.ReviewMap"
    tools:ignore="MergeRootFrame" />

fragment_review_map.xml -- this is the one I am trying to access with R.id.map:

<?xml version="1.0" encoding="utf-8"?>
<fragment xmlns:android="http://schemas.android.com/apk/res/android"
  android:id="@+id/map"
  android:name="com.google.android.gms.maps.SupportMapFragment"
  android:layout_width="match_parent"
  android:layout_height="match_parent" />

If I comment out the GoogleMap map = ((SupportMapFragment) manager.findFragmentById(R.id.map)).getMap() line in the first block of code, everything works as expected (I see a map under an ActionBar); if I leave the line in, I get a Null pointer exception in my logcat, and the app crashes before any map is displayed.