Scalar fluid in scalar-tensor gravity from an equivalent picture of thermodynamic and fluid descriptions of gravitational dynamics

TL;DR

This paper develops a unified thermodynamic framework for scalar fluids in scalar-tensor gravity, using an equivalent gravitational dynamics approach in different frames, and challenges the traditional Eckart's formalism for ideal fluids.

Contribution

It introduces a novel method to identify scalar fluid energy-momentum tensors via gravitational dynamics in Jordan and Einstein frames, and proposes an alternative to Eckart's formalism for ideal fluids.

Findings

Unified thermodynamic description in both frames.

Scalar fluid energy-momentum tensor as ideal fluid.

Eckart's frame may not be suitable for ideal fluids.

Abstract

We revisit the thermodynamic description of fluid, represented by scalar field in scalar-tensor gravity theory through a general approach to study the thermodynamics of relativistic fluids. In order to identify the fluid energy-momentum tensor, contrary to the existing way, we use equivalent description of gravitational dynamics both in Jordan and Einstein frames as thermodynamical identity and fluid equation on a generic null surface. Such an approach provides the energy-momentum tensors for scalar fluid as that of an ideal fluid in both the frames. We then mention few issues in the existing way of using Eckart's formalism for an ideal fluid. Our investigation suggests that the Eckart's frame may not be suitable to consider ideal fluid. Consequently a possible alternative description, valid in other than Eckart's frame, is being suggested for a general ideal fluid. Based on this we obtain a unified thermodynamic description in both Jordan and Einstein frames from our identified energy-momentum tensors. Finally, the relations between thermodynamic entities on different frames are being put forwarded. Thus, the description in either of the frames is enough to provide the complete picture.