Problem in Flutter. Conflict between Firebase previous and last version Authentication - flutter

Question

I am trying to make login and Signup features for my project but stuck in converting from Firebase old version to the new latest one. As I want to check if user signed in or not, I have added currentUser() method but then I got an error.
As I understand FirebaseUser class has replaced by AuthResult class
The main problem comes from currentUser() method: Error is the following and when I want to register, app shuts down;
(NoSuchMethodError: The getter 'uid' was called on null. Receiver: null Tried calling: uid)
This the old:
import 'dart:async';
import 'package:firebase_auth/firebase_auth.dart';
abstract class BaseAuth {
Future<String> signInWithEmailAndPassword(String email, String password);
Future<String> createUserWithEmailAndPassword(String email, String password);
Future<String> currentUser();
Future<void> signOut();
}
class Auth implements BaseAuth {
final FirebaseAuth _firebaseAuth = FirebaseAuth.instance;
#override
Future<String> signInWithEmailAndPassword(String email, String password) async {
final FirebaseUser user = await _firebaseAuth.signInWithEmailAndPassword(email: email, password: password);
return user?.uid;
}
#override
Future<String> createUserWithEmailAndPassword(String email, String password) async {
final FirebaseUser user = await _firebaseAuth.createUserWithEmailAndPassword(email: email, password: password);
return user?.uid;
}
#override
Future<String> currentUser() async {
final FirebaseUser user = await _firebaseAuth.currentUser();
return user?.uid;
}
#override
Future<void> signOut() async {
return _firebaseAuth.signOut();
}
}
This is the new one:
abstract class BaseAuth{
Future<String> signInWithEmailAndPassword (String email, String password);
Future<String> createUserWithEmailAndPassword (String email, String password);
Future<String> currentUser();
}
class Auth implements BaseAuth{
#override
Future<String> signInWithEmailAndPassword (String email, String password) async {
final AuthResult user = await FirebaseAuth.instance
.signInWithEmailAndPassword(email: email, password: password);
return user.user.uid;
}
#override
Future<String> createUserWithEmailAndPassword (String email, String password) async {
final AuthResult user = await FirebaseAuth.instance
.createUserWithEmailAndPassword(email: email, password: password);
return user.user.uid;
}
#override
Future<String> currentUser() async {
final FirebaseUser user = await FirebaseAuth.instance.currentUser();
return user.uid; //Error comes from here
}
#override
Future<void> signOut() async {
return _firebaseAuth.signOut();
}
}