Noether and Abbott-Deser-Tekin conserved quantities in scalar-tensor theory of gravity both in Jordan and Einstein frames

Understand

We revisit the thermodynamic aspects of the scalar-tensor theory of gravity in the Jordan and in the Einstein frame.

• Examining the {\it missing links} of this theory carefully, we establish the thermodynamic descriptions from the conserved currents and potentials by following both the Noether and the Abbott-Deser-Tekin (ADT) formalism.
• With the help of conserved Noether current and potential, we define the thermodynamic quantities, which we show to be {\it conformally invariant}.
• Moreover, the defined quantities are shown to fit nicely in the laws of (the first and the second) black hole thermodynamics formulated by the Wald's method.