[Vuejs]-Error when trying to redirect user to another page if not authenticated in Firebase

You didn’t post your main.js, but typically, in a Vue app, the router is injected into the Vue app using Vue.use(router) or something similar. Because of this, the $router variable is injected into all Vue components and you can access the variable using the this.$router syntax.

Your firebase.js file is not a Vue component and therefore there was no $router injected into it. You’ll need to access your router object by importing it directly from where it is defined instead.