Accretion onto Reissner-Nordström naked singularities

TL;DR

This work investigates accretion onto Reissner-Nordström naked singularities using GR hydrodynamics, focusing on the zero-gravity radius as a critical scale that enables levitating atmospheres and cusped tori. Through 2D axisymmetric simulations with the Koral+ code, the authors show that accretion naturally forms a toroidal inner structure near $r_0$ and drives strong winds, with the fluid's angular momentum decreasing from the initial value due to heating, yielding a nearly constant $l$ inside the inner torus. The results across three representative $Q/M$ cases reveal consistent inner-torus formation and characteristic outflows, highlighting potential observational signatures distinct from black-hole accretion and motivating future MHD and ray-tracing work to assess detectability in AGN and EHT-like observations. Overall, the study demonstrates that naked RN spacetimes can host complex, partially levitating accretion flows and significant outflows, offering a framework to test non-Kerr spacetimes against high-resolution astrophysical data.

Abstract

Nearly every galactic core contains a supermassive compact object, hypothesized to be a Kerr black hole. It was only with the advent of Event Horizon Telescope observations that the predictions of this hypothesis could be observationally tested for our own Galaxy, and the nearby elliptical M87, on spatial scales comparable to the gravitational radius. At the same time it became possible to test whether alternatives such as naked singularities in general relativity, or similar objects in alternative theories of gravity, are excluded by the data. These and other observational developments renewed interest in non-Kerr spacetime metrics, also in the context of active galactic nuclei at cosmological distances. Recently, we have shown that accreting naked singularities in the Reissner-Nordström metric of general relativity tend to produce strong outflows. The geometry and origin of these winds is studied here, and their parameter dependence is investigated. To this end we performed numerical GR hydrodynamical simulations of accretion of electrically neutral matter in the Reissner-Nordström metric and discussed the results in the context of analytic predictions of fluid motion in this spacetime.

Figures (49)

• Figure 1: The time-time component of the Reissner-Nordström metric as a function of the radius for various values of the charge to mass ratio $Q/M$. Blue solid line: $-g_{tt} = f(r)$ for naked singularity with $Q / M = 1.2$. Green dashed line: extremal black hole $Q = M$, for which only one horizon exists. Red dotted-dashed line: black hole with $Q / M= 0.85$. For comparison, $-g_{tt}$ of Schwarzschild black-hole metric ($Q=0$) is plotted as dotted yellow line.
• Figure 2: Radial dependence of Keplerian frequency, $\Omega_\mathrm{K}$, in circular orbits for Reissner-Nordström NkS with charge $Q$ and mass $M$, for (top to bottom) $Q/M = 1.02$, $1.07$, $1.09$, $1.14$. Solid lines represent stable orbits, dotted lines represent unstable orbits. The green curve is disrupted by the forbidden region between the photon orbits (c.f. Fig. \ref{['fig:stability_plot']}).
• Figure 3: Keplerian angular momentum, $l_\mathrm{K}$, of circular orbits for Reissner-Nordström NkS, with (top to bottom) $Q/M = 1.02$, $1.07$, $1.09$, $1.14$. Solid lines represent stable orbits and dotted ones unstable orbits. The green curve is disrupted by the forbidden region between photon orbits. Circular orbits are stable when they satisfy the Rayleigh criterion, $dl_\mathrm{K}/dr>0$.
• Figure 4: Stability of circular orbits in Reissner-Nordström metric with charge $Q$ and mass $M$. Black patch corresponds to region between horizons. Solid green line: the zero-gravity radius. Dashed dotted yellow line: the radii of photon orbits. Dotted red line: radii of marginally stable orbits. Blue dashed line: radii of marginally bound orbits. Cyan line: location of the maximum of Keplerian frequency of circular orbits. Stable circular timelike geodesics exist in the shaded red region. In the shaded yellow region (sandwiched between the red and white ones) only unstable circular timelike geodesics exist.
• Figure 5: Effective potential $W(r,\theta)$ in the equatorial plane ($\theta = \pi/2$) as a function of the radius $r$ for Reissner-Nordström NkS metric with $Q/M = 1.02$ for a selected value of $l_0=3.22$.