The renormalized charged scalar current in the Reissner-Nordström-de Sitter spacetime

Abstract

We perform a Hadamard point-split renormalization of the current density jν of a charged scalar field in a Reissner-Nordström-de Sitter spacetime. We compute numerically the expectation values of the components jr and jt in the Unruh state in the exterior region and study their dependence on the field parameters and the position.

Quantum kicks near a Cauchy horizon

“…That horizons with equal surface gravities emerge as the exceptionally regular special case may not be surprising: that this case is special was already known from consideration of the stress-energy tensor [15][16][17] , and similar observations arise with 'lukewarm' black holes, in which two Killing horizons bound a spacetime region in which the Killing vector in question is timelike 42,43 . It is however notable that in the HHI state, the overall sign of the leading divergence is determined by which of the two surface gravities is greater, in precisely the same way for both the detector's transition rate and for the energy density seen by an observer.…”

“…When the theory is extended to include quantised fields, new issues arise from the renormalised stressenergy tensor near the Cauchy horizon, and from the back-reaction of this stress-energy on the spacetime. There is evidence that the back-reaction of the quantum fields tends to make Cauchy horizons generically unstable even in situations where classical surface gravity considerations would suggest stability [13][14][15][16][17] .…”

“…The main difference is that the energy density generically diverges proportionally to the inverse square, rather than the inverse, of the proper time separation from the Cauchy horizon; however, in the energy density averaged over the trajectory, the divergence is again proportional to the inverse of the proper time separation from the Cauchy horizon. The divergence in the stress-energy tensor, including the special role of the equal surface gravity case therein, has been studied in the context of back-reaction, in both 1 + 1 dimensions and in 3 + 1 dimensions [15][16][17] .…”