Ruby では結論としては、空文字列と、. で同じ結果になる

require "pathname"

p path = Pathname.new( "" ) #=> #<Pathname:>
p path.to_path #=> ""

p path_ab = path.join( "a/b" ) #=> #<Pathname:a/b>
p path_ab.to_path #=> "a/b"

# --------

p path_2 = Pathname.new( "." ) #=> #<Pathname:.>
p path_2.to_path #=> "."

p path_2_ab = path_2.join( "a/b" ) #=> #<Pathname:a/b>
p path_2_ab.to_path #=> "a/b"