Display a list of posts whose meta field values are equal to the ID of the post being viewed?

For the author single page

$query = new WP_Query(array(
    'post_type' => 'books',
    'meta_key' => 'author',
    'meta_value' => get_the_ID() // assuming you're inside the loop
));

while($query->have_posts()) {
    $query->the_post();
    the_title();
}
wp_reset_query();

For the books archive page

// assuming you're inside the loop
$author = get_post(get_post_meta(get_the_ID(), 'author', true));