Rotating Killing horizons in generic $F(R)$ gravity theories

Understand

We discuss various properties of rotating Killing horizons in generic $F(R)$ theories of gravity in dimension four for spacetimes endowed with two commuting Killing vector fields.

• Assuming there is no curvature singularity anywhere on or outside the horizon, we construct a suitable $(3+1)$-foliation.
• We show that similar to Einstein's gravity, we must have $T_{ab}k^ak^b=0$ on the Killing horizon, where $k^a$ is a null geodesic tangent to the horizon.
• For axisymmetric spacetimes, the effective gravitational coupling $\sim\,F'^{-1}(R)$ should usually depend upon the polar coordinate and hence need not necessarily be a constant on the Killing horizon.