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arXiv 1404.7823gr-qcastro-ph.COhep-th
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$f(R,R_c^2,R_m^2, L_m)$引力的教训：光滑高斯-博内极限、能量-动量守恒和非最小耦合

Lessons from $f(R,R_c^2,R_m^2, L_m)$ gravity: Smooth Gauss-Bonnet limit, energy-momentum conservation and nonminimal coupling

David Wenjie Tian, Ivan Booth

备注：
Final version: 29 pages, 1 table, modified RevTex format in one column. To appear in Physical Review D
发表信息：
Physical Review D 90, 024059 (2014)
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摘要：

本文研究了具有拉格朗日密度$f(R,R_c^2,R_m^2, \mathscr{L}_m)$的一般四阶引力理论。通过考虑$R^2$的显式依赖性和引入“相干条件”$f_{R^2}\!=\!f_{R_m^2}\!=\! -f_{R_c^2}/4$，将$f(R,R^2,R_c^2,R_m^2, \mathscr{L}_m)$引力场方程光滑地约化为$f(R,\mathcal{G},\mathscr{L}_m)$广义Gauss-Bonnet引力场方程.利用Noether守恒律研究了具有非最小耦合的$\mathscr{L}_m$和黎曼不变量$ \mathcal{R}_i$的$f(\mathcal{R}_1,\mathcal{R}_2\ldots,\mathcal{R}_n,\mathscr{L}_m)$模型，并推测非最小引力耦合强度梯度$\nabla^μf_{\!\mathscr{L}_m}$是能量动量不守恒的唯一来源.将这一猜想应用到$f(R,R_c^2,R_m^2, \mathscr{L}_m)$模型中，研究了不同物质含量的连续性和非测地线运动方程。最后，导出了包含无迹Ricci方和无迹Riemann（Weyl）方不变量的Lagrange量的场方程，比较了$f(R,R_c^2,R_m^2, \mathscr{L}_m)$模型和$f(R,R_c^2,R_m^2,T)+2κ\mathscr{L}_m$模型，并考虑了非最小耦合对黑洞和虫洞物理的影响.

英文摘要：

This paper studies a generic fourth-order theory of gravity with Lagrangian density $f(R,R_c^2,R_m^2, \mathscr{L}_m)$. By considering explicit $R^2$ dependence and imposing the "coherence condition" $f_{R^2}\!=\!f_{R_m^2}\!=\! -f_{R_c^2}/4$, the field equations of $f(R,R^2,R_c^2,R_m^2, \mathscr{L}_m)$ gravity can be smoothly reduced to that of $f(R,\mathcal{G},\mathscr{L}_m)$ generalized Gauss-Bonnet gravity. We use Noether's conservation law to study the $f(\mathcal{R}_1,\mathcal{R}_2\ldots,\mathcal{R}_n,\mathscr{L}_m)$ model with nonminimal coupling between $\mathscr{L}_m$ and Riemannian invariants $ \mathcal{R}_i$, and conjecture that the gradient of nonminimal gravitational coupling strength $\nabla^μf_{\!\mathscr{L}_m}$ is the only source for energy-momentum non-conservation. This conjecture is applied to the $f(R,R_c^2,R_m^2, \mathscr{L}_m)$ model, and the equations of continuity and non-geodesic motion of different matter contents are investigated. Finally, the field equation for Lagrangians including the traceless-Ricci square and traceless-Riemann (Weyl) square invariants is derived, the $f(R,R_c^2,R_m^2, \mathscr{L}_m)$ model is compared with the $f(R,R_c^2,R_m^2,T)+2κ\mathscr{L}_m$ model, and consequences of nonminimal coupling for black hole and wormhole physics are considered.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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