At the ergospheres (shown here in violet for the outer and red for the inner one), the temporal metric coefficient g becomes negative, i.e., acts like a purely spatial metric component. Consequently, timelike or lightlike worldlines within this region must co-rotate with the inner mass. Cartesian projection, equatorial perspective.1
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Footnotes
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Visser, Matt (15 Jan 2008). “The Kerr spacetime: A brief introduction”. p. 35. arXiv:0706.0622 [gr-qc]. ↩