Rotating and Charged Black Holes

Real black holes generally spin, and the Kerr solution describing rotating black holes, together with its charged generalizations, exhibits new features absent from the Schwarzschild case, including an ergosphere and frame dragging.

Definition

Rotating and charged black holes are stationary solutions of the Einstein (and Einstein-Maxwell) equations characterized by mass together with angular momentum and electric charge, whose geometry features dragging of inertial frames and, for rotating cases, an ergosphere outside the horizon.

Scope

This topic covers the Kerr metric for rotating black holes, the Reissner-Nordstrom solution for charged ones, and the Kerr-Newman metric combining both; it treats the ergosphere and the Penrose process for energy extraction, frame dragging, the inner and outer horizons, the extremal limit, and the central role of these solutions in astrophysics.

Core questions

• How does rotation change the structure of a black hole compared with Schwarzschild?
• What is the ergosphere and how can it be used to extract energy?
• Why are astrophysical black holes expected to be rotating but nearly uncharged?

Key concepts

• Kerr metric
• Reissner-Nordstrom and Kerr-Newman metrics
• Ergosphere
• Frame dragging
• Inner and outer horizons
• Penrose process

Key theories

Kerr geometry and frame dragging

The Kerr metric describes a rotating black hole whose angular momentum drags surrounding spacetime around it, producing an ergosphere outside the event horizon within which no observer can remain static.

Penrose process and energy extraction

Because particles in the ergosphere can have negative energy relative to infinity, a process splitting a particle there can extract rotational energy from the black hole, reducing its spin, a mechanism underlying astrophysical jet-powering models.

Clinical relevance

Astrophysical black holes are essentially uncharged but often rapidly spinning, so the Kerr solution governs the dynamics of accretion disks, the innermost stable circular orbit setting disk efficiency, and the spin inferred from X-ray spectra and from the ringdown of gravitational-wave signals.

History

Reissner and Nordstrom found the charged solution around 1916-1918, but the rotating case resisted solution until Kerr's breakthrough in 1963; Newman and collaborators combined charge and spin in the Kerr-Newman metric in 1965, and the Penrose process for energy extraction followed in 1969.

Key figures

• Roy Kerr
• Roger Penrose
• Hans Reissner
• Ezra Newman

Seminal works

• kerr1963
• wald1984

Frequently asked questions

Why are real black holes assumed to be uncharged?

Any net charge on an astrophysical black hole would quickly attract opposite charges from the surrounding plasma and neutralize, so charge is dynamically negligible; spin, by contrast, is conserved and commonly large, making Kerr the relevant solution.

What is frame dragging?

Frame dragging is the twisting of spacetime by a rotating mass, which forces nearby objects and even light to be carried around in the direction of rotation; near a Kerr black hole it becomes so strong inside the ergosphere that nothing can remain still.