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

Abstract

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

Typos corrected, published in Phys. Rev. D

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• Physical non-equivalence of the Jordan and Einstein frames
• Holography of Gravitational Action Functionals
• Noether current from the surface term of gravitational action, Virasoro algebra and horizon entropy
• Thermodynamics of charged rotating black branes in Brans-Dicke theory with quadratic scalar field potential
• Holography in Action
• Revisiting the Brans solutions of scalar-tensor gravity
• Conformal Transformation, Near Horizon Symmetry, Virasoro Algebra and Entropy
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• Quantized Brans Dicke Theory: Phase Transition and Strong Coupling (Large $\omega$) Limit & General Relativity
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• Ultra long lived quasinormal modes of neutron stars in massive scalar-tensor gravity
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• 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
• Thermodynamics of $f(R)$ Gravity with Disformal Transformation
• Revisiting black holes and wormholes under Weyl transformations
• Noncommutative Heisenberg algebra in the neighbourhood of a generic null surface
• Black hole mechanics and thermodynamics in the light of Weyl transformations
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• An issue with the classification of the scalar-tensor theories of gravity
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• Scalar fluid in scalar-tensor gravity from an equivalent picture of thermodynamic and fluid descriptions of gravitational dynamics
• Black Hole Entropy and Boundary Conditions
• Scalar-tensor theories of gravity from a thermodynamic viewpoint
• Boundary terms and Brown-York quasi-local parameters for scalar-tensor theory: a study on both timelike and null hypersurfaces