论文标题
能量摩托明方重力的光弯曲和重力镜头
Light bending and gravitational lensing in energy-momentum-squared gravity
论文作者
论文摘要
在目前的工作中，我们在能量摩托明方（EMSG）的弱场极限中得出了光的运动。为此，我们介绍了这种修改后的重力理论的牛顿后（PN）扩展。结果表明，除了牛顿电位外，新的EMSG电位还会影响光子的轨迹。结果，在这一理论中，光子的行为不像一般相对论（GR）所预测的那样。为了通过太阳系测试评估EMSG理论，我们研究光偏转和夏皮罗时间延迟。关于在\ cite {bertotti2003test，shapiro2004memaurement}中获得的结果，我们限制了理论的自由参数，并表明它位于$ -4.0 \ times 10^{ - 27}}} { - 27}}}} { - \，\，\，\，\，\，\，\，\，\ text {m} {m} <8.7 \ times 10^{ - 26} \，\ text {m} \，\ text {s}^2 \，\ text {kg}^{ - 1} $。此间隔与\ cite {nazari2020限制，akarsu2018 -constraint}中得出的间隔一致。这种一致性表明，该理论通过鲜艳的色彩通过了这些太阳系测试。有趣的是，事实证明，EMSG校正的幅度在很大程度上取决于偏转器的密度。因此，我们研究了EMSG对由紧凑型密集物体（例如中子恒星）微覆盖的光源图像的可能影响。据估计，EMSG对镜头图像位置的校正可能会大至$（1-0.1）$ Micro-Arcseconds，这可能会通过未来的高分辨率任务检测到。此外，在EMSG理论中获得了总的放大倍率和光曲线的形状。据表明，除了较小的偏差之外，EMSG光曲线的总体行为与GR相似。
In the present work, we derive the motion of light in the weak-field limit of energy-momentum-squared gravity (EMSG). To do so, we introduce the post-Newtonian (PN) expansion of this modified theory of gravity. It is shown that in addition to the Newtonian potential, a new EMSG potential affects the trajectory of photons. As a result, in this theory, photons do not behave as predicted by general relativity (GR). To evaluate the EMSG theory by the solar system tests, we study light deflection and Shapiro time delay. Regarding the results obtained in \cite{bertotti2003test,shapiro2004measurement}, we restrict the free parameter of the theory and show that it lies within the range $-4.0\times 10^{-27}\, \text{m}\,\text{s}^2\,\text{kg}^{-1} < f_0' < 8.7\times 10^{-26}\,\text{m}\,\text{s}^2\,\text{kg}^{-1}$. This interval is in agreement with those derived in \cite{nazari2020Constraining,akarsu2018constraint}. This consistency manifests that this theory passes these solar system tests with flying colors. Interestingly, it turns out that the magnitude of the EMSG correction strongly depends on the density of the deflector. So, we investigate the possible effects of EMSG on images of a light source microlensed by a compact dense object such as neutron stars. It is estimated that the EMSG correction to the position of lensed images could be as large as $(1-0.1)$ micro-arcseconds which may be detected by future high-resolution missions. Moreover, the total magnification and the shape of light curves are obtained in the EMSG theory. It is revealed that except for a small deviation, the overall behavior of the EMSG light curves is similar to that in GR.
