Fresh look at the scalar-tensor theory of gravity in Jordan and Einstein frames from undiscussed standpoints

摘要

We study the scalar-tensor theory of gravity profoundly in the action levelas well as in the thermodynamic level. Contrary to the usual description in theliterature about the equivalence in the two conformally connected frames, thispaper addresses several incomplete inferences regarding it and mentions someinequivalences which were not pointed out earlier. In the thermodynamic level,our analysis shows the two frames are equivalent. In that process, we identifythe entropy, the energy and the temperature for the thermodynamic description,and we find these quantities are conformally invariant even without any priorassumption. The same conclusion is reached from the gravitational action aswell as from the Gibbons-Hawking-York boundary term, establishing the result ina more convincing manner.