LogicException in Model.php line 2709: Relationship method must return an object of type Illuminate\Database\Eloquent\Relations\Relation

I'm supposed to display author details in bookformat method. But facing LogicException. Any suggestions thanks in advance. Im getting error like this LogicException in Model.php line 2709: Relationship method must return an object of type Illuminate\Database\Eloquent\Relations\Relation. Any help that would be great for me. If I comment authors in bookFormat() everything works fine. But Idk why I'm unable to get author details in my bookformat().

#booksController.php
    namespace App\Http\Controllers;
    use Illuminate\Http\Request;
    use Illuminate\Support\Facades\Input;
    use App\Models\Book;
    use App\Models\Author;

    class BooksController extends Controller
    {
        public function index()
        {
            $books = Book::all();
            $results = [];
            foreach ($books as $book) {
             $results [] = $this->bookFormat($book);
         } 
         return $results; 
     }
        public function bookFormat($book){  
            return [ 
                'Id' => $book->id,
                'Title' => $book->title,
                'Author' => [ 
                    'Id' => $book->author->id,
                    'First_name' => $book->author->first_name,
                    'Last_name' => $book->author->last_name
                ],
                'Price' => $book->price,
                'ISBN' => $book->isbn,
                'Language' => $book->language,
                'Year' => $book->year_of_publisher
            ];
        }
    }

    //book.php
    namespace App\Models;
    use Illuminate\Database\Eloquent\Model;

    class Book extends Model
    {
        public $timestamps = TRUE;
        protected $table = 'books';
    //rules
        public static $rules = [
            'title' => 'required|max:255',
            'isbn' => 'required|max:50',
            'author_id' => 'required|max:255',
            'language' => 'required|max:255',
            'price' => 'required|max:255',
            'year_of_publisher' => 'required'
        ];
    //relationship
        public function author() {
            $this->belongsTo(Author::class);
        }
    }

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