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

Abstract

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. We stretch the study of the conformal equivalence of the physical quantities in these two frames by following the ADT formalism. Our further study reveals that there is a connection between the ADT and the Noether conserved quantities, which signifies that the ADT approach provide the equivalent thermodynamic description in the two frames as obtained in Noether prescription. Our whole analysis is very general as the conserved Noether and ADT currents and potentials are formulated {\it off-shell} and the analysis is exempted from any prior assumption or boundary condition.

Published Version

References in corpus (11)

• Scalar-tensor theories and modified gravity in the wake of GW170817
• The (pseudo)issue of the conformal frame revisited
• Black hole mass and angular momentum in topologically massive gravity
• Physical non-equivalence of the Jordan and Einstein frames
• Invariant quantities in the scalar-tensor theories of gravitation
• Frame-dependence of higher-order inflationary observables in scalar-tensor theories
• One-loop divergences for gravity non-minimally coupled to a multiplet of scalar fields: calculation in the Jordan frame. I. The main results
• Quantum equivalence of $f(R)$ gravity and scalar-tensor theories
• Thermodynamics of charged rotating black branes in Brans-Dicke theory with quadratic scalar field potential
• More on the conformal mapping of quasi-local masses: The Hawking-Hayward case
• Conformal Properties of Charges in Scalar-Tensor Gravities

Cited by in corpus (17)

• Selected topics in scalar-tensor theories and beyond
• Equivalence of inflationary models between the metric and Palatini formulation of scalar-tensor theories
• Frame-invariant approach to higher-dimensional scalar-tensor gravity
• "Conserved charges" of the Bondi-Metzner-Sachs algebra in the Brans-Dicke theory
• Extended phase space thermodynamics of black holes: A study in Einstein's gravity and beyond
• Thermodynamic structure of a generic null surface and the zeroth law in scalar-tensor theory
• Fluid-gravity correspondence in the scalar-tensor theory of gravity: (in)equivalence of Einstein and Jordan frames
• Black hole mechanics and thermodynamics in the light of Weyl transformations
• Jordan and Einstein Frames from the perspective of $\omega =-3/2$ Hamiltonian Brans-Dicke theory
• Scalar-tensor gravity from thermodynamic and fluid-gravity perspective
• An issue with the classification of the scalar-tensor theories of gravity
• Abbott-Deser-Tekin like conserved quantities in Lanczos-Lovelock gravity: beyond Killing diffeomorphisms
• Scalar-tensor theories of gravity from a thermodynamic viewpoint
• Scalar fluid in scalar-tensor gravity from an equivalent picture of thermodynamic and fluid descriptions of gravitational dynamics
• Boundary terms and Brown-York quasi-local parameters for scalar-tensor theory: a study on both timelike and null hypersurfaces
• Mass and angular momentum of charged rotating Gödel black holes in five-dimensional minimal supergravity
• Thermodynamic parameters of fluids on conformally connected spacetimes