We refute recent claims in the literature that stars with relativistically deep potentials cannot exist in $f(R)$ gravity. Numerical examples of stable stars, including relativistic ($GM_\star/r_\star \sim 0.1$), constant density stars, are studied. As a star is made larger, non-linear "chameleon" effects screen much of the star's mass, stabilizing gravity at the stellar center. Furthermore, we show that the onset of this chameleon screening is unrelated to strong gravity. At large central pressures $P>ρ/3$, $f(R)$ gravity, like general relativity, does have a maximum gravitational potential, but at a slightly smaller value: $GM_\star/r_\star = 0.345 < 4/9$ for constant density and one choice of parameters. This difference is associated with negative central curvature $R$ under general relativity not being accessed in the $f(R)$ model, but does not apply to any known astrophysical object.
Possible altitudinal, latitudinal and directional dependence of relativistic Sagnac effect in Chern-Simons modified gravity
为了检验引力理论中的宇称破缺，最近讨论了Chern-Simons引力对干涉仪的可能影响。在早期出版物[Okawara，Yamada和Asada，Phys. Rev. Lett. 109，231101（2012）]，我们研究了CS修正引力中相对论Sagnac效应可能的高度和方向依赖性。我们比较了Sagnac干涉仪的CS效应与广义相对论的Lense-Thirring（LT）效应。数值计算表明，东向Sagnac干涉仪可能是首选的测试CS单独，因为LT的影响，这个干涉仪抵消。在CS模型中引起的相移的大小可能也有振荡依赖于通过CS质量参数$m_{CS}$的干涉仪的高度。因此，对国际空间站选址以及进行地基实验也进行了讨论。
The physical foundations for the geometric structure of relativistic theories of gravitation. From General Relativity to Extended Theories of Gravity through Ehlers-Pirani-Schild approach
A free parametrized TOV: Modified Gravity from Newtonian to Relativistic Stars
我们测试一个自由的{\it ad hoc}参数化的托尔曼-奥本海默-托洛霍夫（TOV）方程。我们没有想到任何具体的引力扩展理论（ETG），但引入的每个新参数都有物理解释。我们的目标完全是教学性的，而不是提出一个新的ETG。给定一个现实的中子星状态方程，我们将每个新参数的贡献映射到质量半径图的轨迹中。这个练习使我们能够使每个TOV扇区与可能的重力修改之间的对应关系，并澄清中子星观测如何有助于区分理论。
Non-vacuum relativistic extensions of MOND using metric theories of gravity with curvature-matter couplings and their applications to the accelerated expansion of the Universe without dark components
Test of relativistic gravity using microlensing of relativistically broadened lines in gravitationally lensed quasars
我们表明，在强透镜类星体中观测相对论性加宽的发射线（例如X射线中的Fe K α线）的微透镜效应的时间依赖性，可以提供超大质量黑洞视界附近圆形轨道的天体力学数据。该信息可以从放大线的红/蓝边缘的演化的观察中提取，所述红/蓝边缘刚好在微透镜焦散线穿过最内侧稳定圆形轨道的周期之前和之后。这种演化的函数形式对吸积黑洞和微透镜焦散网络系统的许多天体物理参数不敏感（与全谱线的演化相反）。测量红/蓝边缘的时间演化可以精确测量引力红移和圆形轨道速度的径向依赖性，直到最里面的稳定圆形轨道。这些测量可以用来区分广义相对论和相对论引力的替代模型，其中光子和大质量物体绕引力中心的动力学不同于史瓦西或克尔时空中的测地线。
