I remember watching it a long time ago but I can't seem to remember its name.

Its about how a phone gets dropped into a blackhole and ends up in the hands of a girl in the edo period (I think). The guy in this story is living in the present.

The guy and the girl chat through the phone and eventually fall in love.

I thought it was called Tokyo Girl but I can't seem to find it through that.

Hope someone here can help me out with the name of the drama. 

sounds interesting. sadly i also don't know the title sorry