In an ongoing effort to explore quantum effects on the interior geometry of black holes, we explicitly compute the semiclassical flux components Tuu ren and Tvv 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-Nordström black hole. These two flux components turn out to dominate the effect of backreaction in the vicinity of the IH; 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 Tuu ren and Tvv ren in the vicinity of the IH for a wide range of Q/M values. We find that both Tuu ren and Tvv ren attain finite asymptotic values at the IH. These asymptotic values are found to be either positive or negative (or vanishing in-between), depending on the Q/M parameter. Note that having a nonvanishing Tvv 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.
We numerically compute the renormalized expectation value Φ 2 ren of a minimally-coupled massless quantum scalar field in the interior of a four-dimensional Reissner-Nordstrom black hole, in both the Hartle-Hawking and Unruh states. To this end we use a recently developed mode-sum renormalization scheme based on covariant point splitting. In both quantum states, Φ 2 ren is found to approach a finite value at the inner horizon (IH). The final approach to the IH asymptotic value is marked by an inverse-power tail r −n * , where r * is the Regge-Wheeler "tortoise coordinate", and with n = 2 for the Hartle-Hawking state and n = 3 for the Unruh state. We also report here the results of an analytical computation of these inverse-power tails of Φ 2 ren near the IH. Our numerical results show very good agreement with this analytical derivation (for both the power index and the tail amplitude), in both quantum states. Finally, from this asymptotic behavior of Φ 2 ren we analytically compute the leading-order asymptotic behavior of the trace T µ µ ren of the renormalized stress-energy tensor at the IH. In both quantum states this quantity is found to diverge like b(r − r−) −1 r −n−2 * (with n specified above, and with a known parameter b). To the best of our knowledge, this is the first fully-quantitative derivation of the asymptotic behavior of these renormalized quantities at the inner horizon of a four-dimensional Reissner-Nordstrom black hole.
We evolve stellar models to study the rotational profiles of the pre-explosion cores of single massive stars that are progenitors of core collapse supernovae (CCSNe), and find large rotational shear above the iron core that might play an important role in the jet feedback explosion mechanism by amplifying magnetic fields before and after collapse. Initial masses of 15M and 30M and various values of the initial rotation velocity are considered, as well as a reduced mass-loss rate along the evolution and the effect of core-envelope coupling through magnetic fields. We find that the rotation profiles just before core collapse differ between models, but share the following properties. (1) There are narrow zones of very large rotational shear adjacent to convective zones.(2) The rotation rate of the inner core is slower than required to form a Keplerian accretion disk. (3) The outer part of the core and the envelope have non-negligible specific angular momentum compared to the last stable orbit around a black hole (BH). Our results suggest the feasibility of magnetic field amplification which might aid a jet-driven explosion leaving behind a neutron star. Alternatively, if the inner core fails in exploding the star, an accretion disk from the outer parts of the core might form and lead to a jet-driven CCSN which leaves behind a BH.
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