Abstract
We study the nature of the inner Cauchy horizon of a Reissner-Nordstrom black hole in a quantum context by means of the horizon wave-function obtained from modelling the electrically charged source as a Gaussian wave-function. Our main finding is that there are significant ranges for the black hole mass (around the Planck scale) and specific charge for which the probability of realising the inner horizon is negligible. This result suggests that any semiclassical instability one expects near the inner horizon may not occur in quantum black holes.
Highlights
JHEP05(2015)096 large BH can have arbitrary small curvature near its horizon, and we have numerous tests of gravity in such low density regimes
We study the nature of the inner Cauchy horizon of a Reissner-Nordstrom black hole in a quantum context by means of the horizon wave-function obtained from modelling the electrically charged source as a Gaussian wave-function
The latter is a Cauchy horizon and is sometimes associated with an instability known as “mass inflation”: any small matter perturbation will blue-shift unboundedly just outside this horizon, and inevitably produce a large deformation to the background geometry [16]. The existence of this effect is still debated, it is clear from the classical causal structure of the RN geometry that, if there is matter falling through the outer horizon, it should accumulate outside the inner Cauchy horizon, and eventually lead to a large backreaction there
Summary
The formalism introduced in refs. [5,6,7] is based on lifting the gravitational radius RH of a QM system to the rank of a quantum operator. Going back to the HWF formalism, let us start from QM states representing spherically symmetric objects, which are localized in space and at rest in the chosen reference frame. Such particles are described by wave-functions ψS ∈ L2(R3), which we assume can be decomposed into energy eigenstates,. In more details, starting from the he wave-function ψH associated with ψS, we can calculate the probability density for the particle to lie inside its own horizon of radius r = RH: P
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