论文标题
部分可观测时空混沌系统的无模型预测
Testing strong gravitational lensing effects by supermassive compact objects with regular spacetimes
论文作者
论文摘要
我们通过球形对称的球形在球形对称的常规电动电荷（rec）黑洞（$ 0 <b \ leq b_e $）中比较和对比度重力镜头，并与相应的rec no-horizon spaceTimes（$ b> b_e $）进行比较。在这里，$ b $是由于充电而引起的附加参数，并且值$ b = b_e \大约0.226 $对应于具有退化视野的极端黑洞。有趣的是，时空以$ 0 <b \ leq b_p \约0.247 $和抗photon Sphere仅适用于$ b_e <b \ b \ leq b_p $。使用无旋转的时空，也可以出现从光子球内部（$ u <u_ {ps} $）镜头的图像。有趣的是，对于$ u <u_ {ps} $，偏转角$α_d$随$ u $增加。我们通过将紧凑的对象SGR A*，M87*，NGC4649和NGC1332建模为黑洞和无抗原空间来分析镜头可观察物。角位置$θ_ {\ infty} $和光子球半径$ x_ {ps} $随着参数$ b $的增加而减小。我们的发现表明，光子球内的相对论图像的角度分离（$ s $）和放大倍率（$ r $）可能高于外部。此外，SGR A*和M87*的时间延迟分别可以达到$ \ sim $ 8.8809分钟和$ \ sim $ 12701.8分钟，$ b = 0.2 $，偏离了Schwarzschild Black Holes的$ \ sim $ \ sim $ 2.615 min和$ \ sim $ \ sim $ 4677分钟。这些偏差对于SGR A*而言是微不足道的，因为它太小了，但是它们足以对M87*和其他一些黑洞进行天文观察。在$θ_{sh} $上的EHT界限的情况下，Sgr a*和m 87*在$1σ$区域内，在参数$ b $上放置了界限，我们的分析得出结论，rec黑洞与EHT相一致，导致有限的空间，而相应的相应的空间空间完全不可用。
We compare and contrast gravitational lensing, in the strong-field limit, by photon sphere in spherically symmetric regular electrically charged (REC) black holes ($0<b\leq b_E$) and with those by corresponding REC no-horizon spacetimes ($b>b_E$). Here, $b$ is additional parameter due to charge and the value $b=b_E \approx 0.226$ corresponds to an extremal black hole with degenerate horizons. Interestingly, the spacetime admits photon sphere for $0<b\leq b_P \approx 0.247$ and an anti-photon sphere only for $b_E < b \leq b_P$. With no-horizon spacetime, images by lensing from the inside of the photon sphere ($u<u_{ps}$) can also appear. Interestingly, for the case $u<u_{ps}$ the deflection angle $α_D$ increases with $u$. We analyse the lensing observables by modelling compact objects Sgr A*, M87*, NGC4649, and NGC1332 as black holes and no-horizon spacetimes. The angular position $θ_{\infty}$ and photon sphere radius $x_{ps}$ decrease with increasing parameter $b$. Our findings suggest that the angular separations ($s$) and magnification ($r$) of relativistic images inside the photon sphere may be higher than those outside. Moreover, the time delay for Sgr A* and M87* can reach $\sim$ 8.8809 min and $\sim$ 12701.8 min, respectively, at $b = 0.2$, deviating from Schwarzschild black holes by $\sim$ 2.615 min and $\sim$ 4677 min. These deviations are insignificant for Sgr A* because it is too small, but they are sufficient for astronomical observation of M87* and some other black holes. With EHT bounds on $θ_{sh}$ of Sgr A* and M 87*, within $1 σ$ region, placing bounds on the parameter $b$, our analysis concludes that the REC black holes agree with the EHT results in finite space, whereas the corresponding REC no-horizon spacetimes are completely ruled out.
