A Mode-Sum Prescription for Vacuum Polarization in Odd Dimensions

Understand

We present a new mode-sum regularization prescription for computing the vacuum polarization of a scalar field in static spherically-symmetric black hole spacetimes in odd dimensions.

• This is the first general and systematic approach to regularized vacuum polarization in higher dimensions.
• Remarkably, the regularization parameters can be computed in closed form in arbitrary dimensions and for arbitrary metric function $f(r)$.
• In fact, we show that in spite of the increasing severity and number of the divergences to be regularized, the method presented is mostly agnostic to the number of dimensions.