Properties of the instantaneous Ergo Surface of a Kerr Black Hole

Details Properties of the instantaneous Ergo Surface of a Kerr Black Hole Properties of the instantaneous Ergo Surface of a Kerr Black Hole

2000-12-15

arxiv.org/abs/gr-qc/0012052v2

Class.Quant.Grav. 18 (2001) 1319-1332

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages, 11 figures, also on the web at http://grtensor.phy.queensu.ca/ergo/

Scientific paper

10.1088/0264-9381/18/7/314

This paper explores properties of the instantaneous ergo surface of a Kerr black hole. The surface area is evaluated in closed form. In terms of the mass ($m$) and angular velocity ($a$), to second order in $a$, the area of the ergo surface is given by $16 \pi m^2 + 4 \pi a^2$ (compared to the familiar $16 \pi m^2 - 4 \pi a^2$ for the event horizon). Whereas the total curvature of the instantaneous event horizon is $4 \pi$, on the ergo surface it ranges from $4 \pi$ (for $a=0$) to 0 (for $a=m$) due to conical singularities on the axis ($\theta=0,\pi$) of deficit angle $2 \pi (1-\sqrt{1-(a/m)^2})$. A careful application of the Gauss-Bonnet theorem shows that the ergo surface remains topologically spherical. Isometric embeddings of the ergo surface in Euclidean 3-space are defined for $0 \leq a/m \leq 1$ (compared to $0 \leq a/m \leq \sqrt{3}/2$ for the horizon).

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