Hello everyone, can you help me?
I need to add Author name wich is located in Author Id object into Book object and after that i need to send email. Both fields are in junction object AuthorToBook. Explain me whats wrong with my code?

public class BatchUpdateBookAuthors implements Database.Batchable<sObject>, Database.Stateful {
    public Integer recordsProcessed = 0;
    public Database.QueryLocator start(Database.BatchableContext bc) {
        return Database.getQueryLocator(
            'SELECT ID, Author__c FROM Book__c WHERE Author__c = null' +
            'SELECT ID, Author__c, Book__c (SELECT Id FROM Author__c) FROM AuthorToBook__c'
        );
    }
    public void execute(Database.BatchableContext bc, List<AuthorToBook__c> scope){
        // process each batch of records
        List<Book__c> books = new List<Book__c>();
        for (AuthorToBook__c authors : scope) {
            for (Book__c book : books) {
                book.Author__c = authors.Author__c;
                books.add(book);
                recordsProcessed = recordsProcessed + 1;
            }
        }
        update books;
    }
    public void finish(Database.BatchableContext bc){
        System.debug(recordsProcessed + ' records processed!');
        AsyncApexJob job = [SELECT Id, Status, NumberOfErrors,
            JobItemsProcessed,
            TotalJobItems, CreatedBy.Email
            FROM AsyncApexJob
            WHERE Id = :bc.getJobId()];
        
        Messaging.SingleEmailMessage message = new Messaging.SingleEmailMessage();
        message.toAddresses = new String[] { 'olga.luckina@gmail.com' };
        message.optOutPolicy = 'FILTER';
        message.subject = 'Books';
        message.plainTextBody = 'Books are updated';
        Messaging.SingleEmailMessage[] messages =   new List<Messaging.SingleEmailMessage> {message};
        Messaging.SendEmailResult[] results = Messaging.sendEmail(messages);

        if (results[0].success) {
            System.debug('The email was sent successfully.');
        } else {
            System.debug('The email failed to send: ' + results[0].errors[0].message);
        }
    }
}