标题： 外域中本质暗能量黑洞的阴影 显示英文标题

标题： Shadows of quintessential dark energy black holes in the domain of outer communication

摘要： 旋转的暗能量五重态黑洞对应三个视界：内视界、外视界和五重态视界。 外通信区域是外视界和五重态视界之间的区域。 在此工作中，我们研究当观测者静止在外部通信区域时，五重态暗能量黑洞的光子区域和阴影。 五重态暗能量黑洞的阴影由其质量$(M)$、自旋参数$(a)$、五重态暗能量参数$(\omega_q)$和归一化因子$(\gamma)$表征。 暗能量参数$\omega_q$可以在$-1.1<\omega_q<-1/3$之间取值，并遵循状态方程$\omega_q$= 压力$(p)$/ 能量密度($\rho_q)$。 这个状态参数显著影响黑洞阴影的形状和大小。 我们推广了$\omega_q$的所有测地线运动方程，并得到关系式，通过静态观察者在外部通信区域任意距离处可视化黑洞阴影。 我们分析估计了黑洞阴影的可观测量：半径$R_s$，畸变参数$\delta_s$和阴影面积$A$。利用阴影半径$R_s$和面积$A$的数值，我们得到了黑洞阴影的角直径。 M87和Sgr A$^*$黑洞的角大小分别为$\ 42 \pm 3 \mu a s$和$48.7 \pm 7 \mu a s $，这是由事件视界望远镜(EHT)观测到的。 在这种情况下，黑洞阴影的角直径随着第五元素参数$\omega_q$增加，并在静态观测者位于$r_o=5M$的外部通信域中，取参数$-0.66 \leq \omega_q \leq -0.62$的值$\theta_d \approx 20 \pm 3{^o}$。 显示英文摘要

摘要： The rotating black holes in the quintessential dark energy correspond to three horizons: inner, outer, and quintessential horizon. The domain of outer communication is the region between outer and quintessential horizon. Here, in this work we study the photon region and shadows of the quintessential dark energy black holes when the observer stays statically in the domain of outer communication. The quintessential dark energy black holes shadow characterizes by its mass $(M)$, spin parameter $(a)$, quintessential dark energy parameter $(\omega_q)$, and normalization factor $(\gamma)$. The dark energy parameter $\omega_q$ can take values in between $-1.1<\omega_q<-1/3$ and follows the equation of state $\omega_q$=pressure$(p)$/energy density($\rho_q)$. This state parameter significantly affects the shape and size of the black hole shadow. We generalize all the geodesic equations of motion for $\omega_q$ and obtain relation to visualize the black hole shadow by a static observer at any arbitrary distance in the domain of outer communication. We analytically estimate the black hole shadow observables: radius $R_s$, distortion parameter $\delta_s$ and the shadow area $A$. Using the numerical values of shadow radius $R_s$ and area $A$, we obtain the angular diameter of the black hole shadow. The angular size of the M87 and Sgr A$^*$ black holes are $\ 42 \pm 3 \mu a s$ and $48.7 \pm 7 \mu a s $ respectively as observe by Event Horizon Telescope (EHT). In this case, the angular diameter of the black hole shadow increases with the quintessence parameter $\omega_q$ and takes values $\theta_d \approx 20 \pm 3{^o}$ with the parameter $-0.66 \leq \omega_q \leq -0.62$ for the static observer at $r_o=5M$ in the domain of outer communication.