The way you should be doing it in React Native (as I understand it), is by saving your 'global' variable in your index.js, for example. From there you can then pass it down using props.
Example:
class MainComponent extends Component {
componentDidMount() {
//Define some variable in your component
this.variable = "What's up, I'm a variable";
}
...
render () {
<Navigator
renderScene={(() => {
return(
<SceneComponent
//Pass the variable you want to be global through here
myPassedVariable={this.variable}/>
);
})}/>
}
}
class SceneComponent extends Component {
render() {
return(
<Text>{this.props.myPassedVariable}</Text>
);
}
}