Will wp_get_attachment_metadata display PDF metadata (eg: keyword, author, description)?

I’d say you’re gonna need external assistance…

Zend Framework
https://stackoverflow.com/a/4520725

$pdf = Zend_Pdf::load($pdfPath);

echo $pdf->properties['Title'] . "\n";
echo $pdf->properties['Author'] . "\n";

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XMP PHP Toolkit
https://stackoverflow.com/a/8862702

XMP Toolkit PHP Extension is a PHP module which includes the Adobe XMP
Toolkit SDK. This PHP5 extension will provide classes and methods to
manipulate XMP Metadatas from files like jpegs, tiff, png, but also
wav, mp3, avi, mpeg4, pdf, ai, eps… It’s based from the Adobe XMP
Toolkit SDK 4.4.2. The goal of this extension is to have php classes
which can open files, extract metadatas, manipulate them, and put them
back within few lines of php code. This project is under GPL v3
License.