The Extremal Reissner-Nordström Geometry

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Extremal Reissner-Nordström geometry

Embedding diagram of a near extremal Reissner-Nordström geometry with Charge/Mass = 0.9999.

Extremal Reissner-Nordström spacetime diagram

Spacetime diagram of the extremal Reissner-Nordström metric.


r+ = r- = M

Free-fall spacetime diagram for the extremal Reissner-Nordström geometry

Spacetime diagram of the free-fall metric. Space flowing into and out of an extremal charged black hole.

Watch extremal Reissner-Nordström morph into free-fall (46K movie icon GIF); or same morph, double-size on screen (same 46K GIF).

Finkelstein spacetime diagram of the extremal Reissner-Nordström geometry

Finkelstein spacetime diagram of the Reissner-Nordström geometry.

Watch extremal Reissner-Nordström morph into Finkelstein (38K movie icon GIF); or same morph, double-size on screen (same 38K GIF).

Watch Finkelstein morph into free-fall (32K movie icon GIF); or same morph, double-size on screen (same 32K GIF).

Penrose diagram of the extremal Reissner-Nordström geometry

Penrose diagram of the extremal Reissner-Nordström geometry.

Introduce a cutoff at |R| < Rc.
rP + tP = sign(R + t) ln(1 + |R + t|)  +  Rc ln(1 + Rc)
rP - tP = ± [- sign(R - t) ln(1 + |R - t|)  +  Rc ln(1 + Rc)]
where the overall sign in the last equation is positive (+) outside the horizon, r > r+, and negative (-) inside the horizon, r < r+.

Watch Finkelstein morph into Penrose (51K movie icon GIF); or same morph, double-size on screen (same 51K GIF).

Penrose diagram of the complete extremal Reissner-Nordström geometry

Penrose diagram of the complete extremal Reissner-Nordström geometry.


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Updated 19 Apr 2001