We obtain relativistic solutions of spherically symmetric accretion by a dynamical analysis of a generalised Hamiltonian for higher-dimensional Reissner–Nordström (RN) Black Hole (BH). We consider two different fluids namely, an isotropic fluid and a non-linear polytropic fluid to analyse the critical points in a higher-dimensional RN BH. The flow dynamics of the fluids are studied in different spacetime dimensions in the framework of Hamiltonian formalism. The isotropic fluid is found to have both transonic and non-transonic flow behaviour, but in the case of polytropic fluid, the flow behaviour is found to exhibit only non-transonic flow, determined by a critical point that is related to the local sound speed. The critical radius is found to change with the spacetime dimensions. Starting from the usual four dimensions it is noted that as the dimension increases the critical radius decreases, attains a minimum at a specific dimension (D > 4) and thereafter increases again. The mass accretion rate for isotropic fluid is determined using Hamiltonian formalism. The maximum mass accretion rate for RN BH with different equations of state parameters is studied in addition to spacetime dimensions. The flow behaviour and mass accretion rate for a change in BH charge is also studied analytically. It is noted that the maximum mass accretion rate in a higher-dimensional Schwarzschild BH is the lowest, which however, increases with the increase in charge parameter in a higher-dimensional RN BH.

中文翻译：

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球形吸积到高维 Reissner-Nordström 黑洞上


我们通过对高维 Reissner-Nordström （RN） 黑洞 （BH） 的广义哈密顿量进行动力学分析，获得了球对称吸积的相对论解。我们考虑两种不同的流体，即各向同性流体和非线性多方流体，以分析更高维 RN BH 中的临界点。在哈密顿形式主义的框架内，在不同的时空维度上研究了流体的流动动力学。发现各向同性流体同时具有跨音速和非跨音速流动行为，但在多方流体的情况下，发现流动行为仅表现出非跨音速流动，由与局部声速相关的临界点决定。发现临界半径随时空维度而变化。从通常的四个维度开始，值得注意的是，随着维度的增加，临界半径减小，在特定维度 （D > 4） 达到最小值，然后再次增加。各向同性流体的质量吸积率使用哈密顿形式确定。除了时空维度外，还研究了具有不同状态参数方程的 RN BH 的最大质量吸积率。还对 BH 电荷变化的流动特性和吸质量速率进行了分析研究。值得注意的是，高维 Schwarzschild BH 中的最大质量吸积率是最低的，然而，随着高维 RN BH 中电荷参数的增加而增加。