First Law of Black Rings Thermodynamics in Higher Dimensional Dilaton   Gravity with p + 1 Strength Forms
  We derive the first law of black rings thermodynamics in n-dimensional Einstein dilaton gravity with additional (p+1)-form field strength being the simplest generalization of five-dimensional theory containing a stationary black ring solution with dipole charge. It was done by means of choosing any cross section of the event horizon to the future of the bifurcation surface. 
Marek Rogatko