Actress Vanessa Hudgens and her boyfriend Austin Butler are under investigation for reportedly carving their names in a heart into a rock formation in Sedona, Arizona.

A public affairs officer for Coconino National Forest has said the incident involving Hudgens and Butler "is under investigation", reports etonline.com.

"Officials at the Coconino National Forest became aware of the incident (Monday) when the media alerted them of the situation," the officer said.

"There is no deadline for this investigation -- it takes as long as it takes. The maximum punishment for this is $5,000 and/or six months behind bars."

Eyebrows were raised after Hudgens posted a photograph of the carving on Instagram, but the post has since been deleted.