发表机构
Faculdade de Ciências da Universidade de Lisboa; Instituto de Astrofísica e Ciências do Espaço（里斯本大学理学院; 天体物理与空间科学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为框架不变的标量-张量引力构造了类Jordan框架的不变热力学表示，其中物质最小耦合，引力作用量呈Brans-Dicke-Bergmann-Wagoner形式，有效应力张量展现不完美流体特征，证明其热力学描述不限于类爱因斯坦框架的完美流体形式。
AI 中文摘要
已有研究表明，框架不变的标量-张量引力热力学允许一种类爱因斯坦框架的不变表示，其中标量扇区最小耦合，并表现为温度为零的完美流体。我们证明这并非唯一可用的不变热力学组织方式。相反，利用不变物质度规，我们构造了一种类Jordan框架的不变表示，其中物质最小耦合，引力作用量采用Brans-Dicke-Bergmann-Wagoner形式，并具有不变场$\Psi=\mathcal I_1^{-1}$、$\mathcal U(\Psi)$和$\omega_{\mathrm{inv}}(\Psi)$。在此表示中，度规场方程保留了Jordan框架标量-张量引力的Hessian扇区特征。对相应有效应力张量进行$1+3$分解，在一般类时丛中产生非零热通量和各向异性应力。在$\Psi$-共动系中，通常的一阶热力学识别以不变形式恢复，包括$K_{\mathrm J}T_{\mathrm J}=-\dot\Psi/(\kappa^2\Psi)$和$\eta_{\mathrm J}=\dot\Psi/(2\kappa^2\Psi)$，体通道在均匀各向同性扇区中获得。因此，框架不变的标量-张量引力热力学并非本质上局限于类爱因斯坦框架的完美流体描述：它还允许类Jordan框架的不变表述，其中有效不完美流体解释是明显的。
英文摘要
It has been shown that the thermodynamics of frame-invariant scalar-tensor gravity admits an Einstein-frame-like invariant representation, in which the scalar sector is minimally coupled and behaves as a perfect fluid with vanishing temperature. We show that this is not the only invariant thermodynamic organization available. Using instead the invariant matter metric, we construct a Jordan-frame-like invariant representation in which matter is minimally coupled and the gravitational action takes the Brans-Dicke-Bergmann-Wagoner form with invariant fields $Ψ=\mathcal I_1^{-1}$, $\mathcal U(Ψ)$, and $ω_{\mathrm{inv}}(Ψ)$. In this representation the metric field equations retain the Hessian sector characteristic of Jordan-frame scalar-tensor gravity. A $1+3$ decomposition of the corresponding effective stress tensor yields nonvanishing heat flux and anisotropic stress in a generic congruence. In the $Ψ$-comoving frame, the usual first-order thermodynamic identifications are recovered in invariant form, including $K_{\mathrm J}T_{\mathrm J}=-\dotΨ/(κ^2Ψ)$ and $η_{\mathrm J}=\dotΨ/(2κ^2Ψ)$, with the bulk channel obtained in homogeneous and isotropic sectors. Thus, frame-invariant scalar-tensor thermodynamics is not intrinsically restricted to an Einstein-frame-like perfect-fluid description: it also admits a Jordan-frame-like invariant formulation in which the effective imperfect-fluid interpretation is manifest.
Comments9 pages
