Object Oriented PHP Url Router
This is not OOP.

Observe how your class contains only static functions.  There are no class properties.  This can be written equivalently:

namespace Router;

function getPath($uri = null){
    // Same implementation (I have just cut it out for readability).
}

function getQuery($uri = null){
    // Same implementation.
}

function follow($uri = null){
    // Same implementation.
}


Usage from anywhere can be compared (First your code):

Router::getPath($uri);
Router::getQuery($uri);
Router::follow($uri);


Then the equivalent:

Router\getPath($uri);
Router\getQuery($uri);
Router\follow($uri);


Note how no object is required to be used (that is a good hint that its not OO).

The following question would be worth reading:

User class design

I have an answer to that question which covers in more detail some of the problems with using static in OOP.