Energy Extraction from Higher Dimensional Black Holes and Black Rings

TL;DR

This work analyzes energy extraction from higher-dimensional rotating black holes and black rings via the Penrose process, showing that extraction efficiency can greatly exceed the four-dimensional Kerr case and can diverge when a single rotation parameter vanishes. It derives explicit maximal- efficiency formulas for Myers–Perry black holes in both even and odd dimensions and for the five-dimensional black ring, highlighting that black rings can outperform black holes in energy extraction for fixed parameters, with a divergence as the ring thickness parameter $\nu$ approaches unity. The authors apply catastrophe theory to map stability in the black-hole/black-ring phase space, identifying a cusp that signals a stability change and distinguishing a distinct instability mechanism from Gregory–Laflamme-type modes. They discuss irreducible mass, rotational energy, and limits such as boosted black strings, noting that quantum effects (Hawking radiation, superradiance) require separate treatment. Overall, the paper suggests that higher-dimensional gravity offers qualitatively new energy-extraction behavior and stability features that could, in principle, distinguish higher-dimensional objects from four-dimensional Kerr black holes.

Abstract

We analyze the energy extraction by the Penrose process in higher dimensions. Our result shows the efficiency of the process from higher dimensional black holes and black rings can be rather high compared with than that in four dimensional Kerr black hole. In particular, if one rotation parameter vanishes, the maximum efficiency becomes infinitely large because the angular momentum is not bounded from above. We also apply a catastrophe theory to analyze the stability of black rings. It indicates a branch of black rings with higher rotational energy is unstable, which should be a different type of instability from the Gregory-Laflamme's one.

Figures (7)

• Figure 1: The momenta $p_{(I)}$ lie in the local light cone. The maximum efficiency of the Penrose process is achieved when the radial velocities $v_{(I)}$ vanish, assuming $p_{(1)}$ and $p_{(2)}$ are null.
• Figure 2: The energy extraction efficiency in terms of a reduced spin. The solid line corresponds to a black ring and the fine line to a black hole.
• Figure 3: Reduced rotational energy ($\varepsilon_R$) is shown in terms of a reduced spin $j$. The fine line corresponds to a black hole solution, while the solid line to a ring solution. The overlapped point $(j^2,\varepsilon_R)=(1,1)$ is a naked singularity. The point $(0,0)$ represents the Tangherlini-Schwarzschild solution, so in this case we cannot extract energy from a black hole.
• Figure 4: Two smooth curves in the equilibrium space ${\cal V}= (\bar{R}^2, j^2, \varepsilon _R)$:One (the fine line) corresponds to a set of black hole solutions and the other (the solid line) to that of black rings.
• Figure 5: The projection of the curve in the $(\bar{R}^2, j^2, \varepsilon _R)$ space onto the $(\bar{R}^2, j^2)$ plane and the $(\bar{R}^2,\varepsilon _R)$ plane.