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A stationary observer in the Kerr spacetime has zero angular momentum ifhis/her angular velocity $\omega$ has a particular value, which depends on theposition of the observer. Worldlines of such zero angular momentum observers(ZAMOs) with the same value of the angular velocity $\omega$ form a threedimensional surface, which has the property that the Killing vectors generatingtime translation and rotation are tangent to it. We call such a surface arigidly rotating ZAMO surface. This definition allows a natural generalizationto the surfaces inside the black hole, where ZAMO's trajectories formallybecome spacelike. A general property of such a surface is that there existlinear combinations of the Killing vectors with constant coefficients whichmake them orthogonal on it. In this paper we discuss properties of the rigidlyrotating ZAMO surfaces both outside and inside the black hole and relevance ofthese objects to a couple of interesting physical problems.

Rigidly rotating ZAMO surfaces in the Kerr spacetime