Quantum fluxes at the inner horizon of a spherical charged black hole


Abstract in English

In an ongoing effort to explore quantum effects on the interior geometry of black holes, we explicitly compute the semiclassical flux components $leftlangle T_{uu}rightrangle _{ren}$ and $leftlangle T_{vv}rightrangle _{ren}$ ($u$ and $v$ being the standard Eddington coordinates) of the renormalized stress-energy tensor for a minimally-coupled massless quantum scalar field, in the vicinity of the inner horizon (IH) of a Reissner-Nordstrom black hole. These two flux components seem to dominate the effect of backreaction in the IH vicinity; and furthermore, their regularization procedure reveals remarkable simplicity. We consider the Hartle-Hawking and Unruh quantum states, the latter corresponding to an evaporating black hole. In both quantum states, we compute $leftlangle T_{uu}rightrangle _{ren}$ and $leftlangle T_{vv}rightrangle _{ren}$ in the IH vicinity for a wide range of $Q/M$ values. We find that both $leftlangle T_{uu}rightrangle _{ren}$ and $leftlangle T_{vv}rightrangle _{ren}$ attain finite asymptotic values at the IH. Depending on $Q/M$, these asymptotic values are found to be either positive or negative (or vanishing in-between). Note that having a nonvanishing $leftlangle T_{vv}rightrangle _{ren}$ at the IH implies the formation of a curvature singularity on its ingoing section, the Cauchy horizon. Motivated by these findings, we also take initial steps in the exploration of the backreaction effect of these semiclassical fluxes on the near-IH geometry.

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