"However I want to share alot of variables and some might be rather large so I don't want to be creating copies of them like above."
That doesn't make a copy (especially with String, but even objects are pass by value of the reference, not the object itself, and getter's like that are fine to use -- arguably better to use than other means because they are common and well understood). The older "performance myths," such as not using getters and setters, still have some value, but have also been updated in the docs.
But if you don't want to do that, you could also just make the variables public or protected in GlobalState and access them directly. And, you can make a static singleton as the Application object JavaDoc indicates:
There is normally no need to subclass Application. In most situation, static singletons can provide the same functionality in a more modular way. If your singleton needs a global context (for example to register broadcast receivers), the function to retrieve it can be given a Context which internally uses Context.getApplicationContext() when first constructing the singleton.
Using Intent data, as other answers here note is another way to pass data, but it's usually used for smaller data and simple types. You can pass larger/more complex data, but it's more involved than just using a static singleon. The Application object is still my personal favorite for sharing larger/more complex non persistent data between Android application components though (because it has a well defined lifecycle in an Android app).
Also, as others have noted, if the data gets very complex and needs to be persistent then you can use SQLite or the filesystem too.