Abstract
We present spherically symmetric solutions to Einstein's equations which are equivalent to canonical Schwarzschild and Reissner-Nordstrom black holes on the exterior, but with singular (Planck-density) shells at their respective event and inner horizons. The locally measured mass of the shell and the singularity are much larger than the asymptotic ADM mass. The area of the shell is equal to that of the corresponding canonical black hole, but the physical distance from the shell to the singularity is a Planck length, suggesting a natural explanation for the scaling of the black hole entropy with area. The existence of such singular shells enables solutions to the black hole information problem of Schwarzschild black holes and the Cauchy horizon problem of Reissner-Nordstrom black holes. While we cannot rigorously address the formation of these solutions, we suggest plausibility arguments for how normal black hole solutions may evolve into such states. We also comment on the possibility of negative mass Schwarzschild solutions that could be constructed using our methods. Requirements for the non-existence of negative-mass solutions may put restrictions on the types of singularities allowed in an ultraviolet theory of gravity.
Highlights
The black hole information problem seemingly causes a conflict between general relativity and quantum mechanics at energy scales where both theories are known to be valid [1]
We have shown that charge and mass separation within the interior of a black hole can lead to dramatic changes to the interior geometry while leading to the same exterior
The interior geometry can lead to the existence of singular firewalls at the event horizon of a Schwarzschild black hole and the inner horizon of a Reissner-Nordstrom black hole
Summary
The black hole information problem seemingly causes a conflict between general relativity and quantum mechanics at energy scales where both theories are known to be valid [1]. By appropriate choice of coefficients, we can get jpj < ρ so that the shell obeys the dominant energy condition, plausibly enabling the matter on the shell to be provided by canonical classical fluids For these parameters, RμνλσRμνλσ is ∼M4pl at r1o, implying the breakdown of general relativity just within the inner horizon of the exterior black hole. We posit how such a naked singularity could be the end point of the evolution of a traditional black hole Note that this solution can be extended to a Reissner-Nordstrom exterior (charged black hole) with a shell placed just outside its outer horizon. Þ, with r1 and r2 being the inner and outer horizons of the interior Reissner-Nordstrom black hole and C is again a constant redefinition of the local clocks in the interior in order to facilitate the matching of the metrics across the surface.
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