Justin Bieber Serenades Hailey Baldwin Outside of Buckingham Palace

Just a few days after their rumored wedding ceremony inside a New York City courthouse, Justin Bieber & Hailey Baldwin have been spotted vacationing [honeymooning?!] in London

On Tuesday afternoon, the PrObABLy NeWLyWeDs stopped by Buckingham Palace -- where Justin sat down with his guitar to serenade Hailey in front of everyone

It's disgusting how cute this is, right?

"I love you babe. I love you so much -- it hurts. My favorite. That girl, that girl right there is the love of my life," Bieber crooned.  

Naturally, tons of fans have uploaded pictures and videos since the impromptu performance.