如何根据Firebase Auth错误消息在Flutter中显示自定义警报对话框？

import 'package:flutter/material.dart';
import 'package:firebase_auth/firebase_auth.dart';

class MyLoginPage extends StatefulWidget {
  @override
  _MyLoginPageState createState() => _MyLoginPageState();
}

class _MyLoginPageState extends State<MyLoginPage> {
  String _errorMessage = '';

  void _signInWithEmailAndPassword(String email, String password) {
    FirebaseAuth.instance
        .signInWithEmailAndPassword(email: email, password: password)
        .then((userCredential) {
      // 登录成功
    }).catchError((error) {
      // 登录失败，显示错误消息
      setState(() {
        _errorMessage = error.message;
      });
      _showErrorDialog();
    });
  }

  void _showErrorDialog() {
    showDialog(
      context: context,
      builder: (BuildContext context) {
        return AlertDialog(
          title: Text('登录失败'),
          content: Text(_errorMessage),
          actions: <Widget>[
            FlatButton(
              child: Text('确定'),
              onPressed: () {
                Navigator.of(context).pop();
              },
            ),
          ],
        );
      },
    );
  }

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        title: Text('登录页面'),
      ),
      body: Center(
        child: Column(
          mainAxisAlignment: MainAxisAlignment.center,
          children: <Widget>[
            Text(
              '错误消息：$_errorMessage',
              style: TextStyle(color: Colors.red),
            ),
            RaisedButton(
              child: Text('登录'),
              onPressed: () {
                _signInWithEmailAndPassword('example@example.com', 'password');
              },
            ),
          ],
        ),
      ),
    );
  }
}