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Spherical accretion onto higher-dimensional Reissner-Nordström Black Hole

Bibhash Das, Anirban Chanda, Bikash Chandra Paul

TL;DR

This work analyzes relativistic, spherically symmetric accretion onto a static higher-dimensional Reissner–Nordström black hole using a generalized Hamiltonian formalism. By treating isothermal ($p= ho\, extomega$) and polytropic ($p= extkappa ho^{ extGamma}$) fluids within a two-dimensional $(r,v)$ Hamiltonian framework, it characterizes sonic points, phase-space structure, and dimension-dependent trends in critical radii and Hamiltonians. The study reveals that the critical radius generally decreases with spacetime dimension while the critical Hamiltonian increases, and shows that mass accretion rates and luminosities depend sensitively on the equation of state and charge, with polytropic cases (e.g., $ extGamma=5/3$) yielding a realistic accretion profile. The results underscore how extra dimensions modify accretion dynamics and energetics near RN black holes, and set the stage for extensions to rotating geometries.

Abstract

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.

Spherical accretion onto higher-dimensional Reissner-Nordström Black Hole

TL;DR

This work analyzes relativistic, spherically symmetric accretion onto a static higher-dimensional Reissner–Nordström black hole using a generalized Hamiltonian formalism. By treating isothermal () and polytropic () fluids within a two-dimensional Hamiltonian framework, it characterizes sonic points, phase-space structure, and dimension-dependent trends in critical radii and Hamiltonians. The study reveals that the critical radius generally decreases with spacetime dimension while the critical Hamiltonian increases, and shows that mass accretion rates and luminosities depend sensitively on the equation of state and charge, with polytropic cases (e.g., ) yielding a realistic accretion profile. The results underscore how extra dimensions modify accretion dynamics and energetics near RN black holes, and set the stage for extensions to rotating geometries.

Abstract

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 () 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.

Paper Structure

This paper contains 19 sections, 84 equations, 13 figures, 12 tables.

Table of Contents

  1. Introduction
  2. Fundamental equations for spherical accretion flow
  3. Hamiltonian systems for Accretion and Sonic Points
  4. Critical analysis at the Sonic points
  5. Dynamical analysis
  6. Applications to Isothermal fluid accretion
  7. Case I : Ultra-Stiff Fluid ($\omega = 1$)
  8. Case II : Ultra Relativistic Fluid ($\omega = \frac{1}{2}$)
  9. Case III : Radiation Fluid ($\omega = \frac{1}{3}$)
  10. Case IV : Sub-Relativistic Fluid ($\omega = \frac{1}{4}$)
  11. Applications to Polytropic fluids accretion
  12. Black hole's mass accretion rate
  13. Case I: Utra-Stiff fluid ($\omega = 1$)
  14. Case II: Utra-Relativistic fluid ($\omega = \frac{1}{2}$)
  15. Case III: Radiation fluid ($\omega = \frac{1}{3}$)
  16. ...and 4 more sections

Figures (13)

  • Figure 1: Contour plots of Hamiltonian $\mathcal{H}$ with different dimensional BHs for the parameters $\omega = 1$, $M = 1.5$ and $q = 1$. The black curve corresponds to the critical Hamiltonian $\mathcal{H}_c$. The Blue and Cyan curves correspond to $\mathcal{H} > \mathcal{H}_c$, and the Orange and Brown curves represent $\mathcal{H} < \mathcal{H}_c$.
  • Figure 2: Contour plots of Hamiltonian $\mathcal{H}$ with 5D (Dashed Curve) and 6D (Line curve) BHs for the parameters $\omega = \frac{1}{2}$, $M = 1.5$ and $q = 1$. The black curve corresponds to the critical Hamiltonian $\mathcal{H}_c$. The Blue curve corresponds to $\mathcal{H} > \mathcal{H}_c$, and the Orange curve represents $\mathcal{H} < \mathcal{H}_c$
  • Figure 3: Contour plots of Hamiltonian $\mathcal{H}$ with different dimensional BHs for the parameters $\omega = \frac{1}{2}$, $M = 1.5$ and $q = 1$. The black curve corresponds to the critical Hamiltonian $\mathcal{H}_c$. The Blue curve corresponds to $\mathcal{H} > \mathcal{H}_c$, and the Orange curve represents $\mathcal{H} < \mathcal{H}_c$.
  • Figure 4: Contour plots of Hamiltonian $\mathcal{H}$ with 5D (Dashed Curve) and 6D (Line curve) BHs for the parameters $\omega = \frac{1}{2}$, $M = 1.5$ and $q = 1$. The black curve corresponds to the critical Hamiltonian $\mathcal{H}_c$. The Blue curve corresponds to $\mathcal{H} > \mathcal{H}_c$, and the Orange curve represents $\mathcal{H} < \mathcal{H}_c$.
  • Figure 5: Contour plots of Hamiltonian $\mathcal{H}$ with different dimensional BHs for the parameters $\omega = \frac{1}{3}$, $M = 1.5$ and $q = 1$. The Black curve corresponds to the critical Hamiltonian $\mathcal{H}_c$. The Blue curve corresponds to $\mathcal{H} > \mathcal{H}_c$, and the Orange curve represents $\mathcal{H} < \mathcal{H}_c$.
  • ...and 8 more figures