R-Patz and the pop beauty, Katy Perry, got close as they attended a Bjork concert in the city together — but left separately to avoid photographers outside.

Their romance is said to have blossomed as Katy comforted him over his split with Twilight co-star Kristen Stewart — who romped behind his back last year with director Rupert Sanders.

A source revealed yesterday: “They are both good friends but have been hanging out more and more recently. Rob poured out his heart to Katy about Kristen cheating on him. She proved to be a really good shoulder to cry on. ”

“He stayed at her house in LA after they went away to Santa Barbara together for few days over American Memorial Day weekend late last month. ”

“Their friends say they have now fallen for each other.”

The couple are now planning a romantic Caribbean summer getaway. The source went on: “They are talking about going to the Bahamas in the next few weeks to visit some friends of Katy’s. ”