We study the causal structure of dynamical charged black holes, with a sufficient number of massless fields, using numerical simulations. Neglecting Hawking radiation, the inner horizon is a null Cauchy horizon and a curvature singularity due to mass inflation. When we include Hawking radiation, the inner horizon becomes spacelike and is separated from the Cauchy horizon, which is parallel to the out-going null direction. Since a charged black hole must eventually transit to a neutral black hole, we studied the neutralization of the black hole and observed that the inner horizon evolves into a space-like singularity, generating a Cauchy horizon which is parallel to the ingoing null direction. Since the mass function is finite around the inner horizon, the inner horizon is regular and penetrable in a general relativistic sense. However, since the curvature functions become trans-Planckian, we cannot say more about the region beyond the inner horizon, and it is natural to say that there is a "physical" space-like singularity. However, if we assume an exponentially large number of massless scalar fields, our results can be extended beyond the inner horizon. In this case, strong cosmic censorship and black hole complementarity can be violated. ‡ In this paper, we use the outer and inner horizons in a local sense, i.e. we will use "apparent" or "trapping" horizons [29].
We investigate the internal structure of charged black holes with a spherically symmetric model in the double-null coordinate system. Hawking radiation is considered using the S-wave approximation of semiclassical back-reaction and discharge is simulated by supplying an oppositely charged matter to the black hole. In the stage of formation, the internal structure is determined by the mass and charge of collapsing matter. When the charge-mass ratio is small, a wormhole-like internal structure is observed. The structure becomes analogous to the static limit as the ratio reaches unity. After the formation, mass inflation induces large curvature in the internal structure, which makes the structure insensitive to the late-time perturbations. The internal structure determined from the formation seems to be maintained during a substantial mass reduction. The discharge and neutralization of charged black holes is also investigated for both non-evaporating and evaporating cases. Finally, we discuss the implications of the wormhole-like structure inside of charged black holes.Comment: 32 pages, 23 figure
In this article, we study the no-boundary wave function in scalar-tensor gravity with various potentials for the non-minimally coupled scalar field. Our goal is to calculate probabilities for the scalar field -and hence the effective gravitational coupling and cosmological constant -to take specific values. Most calculations are done in the minisuperspace approximation, and we use a saddle point approximation for the Euclidean action, which is then evaluated numerically.We find that for potentials that have several minima, none of them is substantially preferred by the quantum mechanical probabilities. We argue that the same is true for the stable and the runaway solution in the case of a dilaton-type potential. Technically, this is due to the inclusion of quantum mechanical effects (fuzzy instantons).These results are in contrast to the often held view that vanishing gravitation or cosmological constants would be exponentially preferred in quantum cosmology, and they may be relevant to the cosmological constant problem and the dilaton stabilization problem.
In this paper, we discuss the black hole complementarity and the firewall proposal at length. Black hole complementarity is inevitable if we assume the following five things: unitarity, entropy-area formula, existence of an information observer, semi-classical quantum field theory for an asymptotic observer, and the general relativity for an in-falling observer. However, large N rescaling and the AMPS argument show that black hole complementarity is inconsistent. To salvage the basic philosophy of the black hole complementarity, AMPS introduced a firewall around the horizon. According to large N rescaling, the firewall should be located close to the apparent horizon.We investigate the consistency of the firewall with the two critical conditions: the firewall should be near the time-like apparent horizon and it should not affect the future infinity. Concerning this, we have introduced a gravitational collapse with a false vacuum lump which can generate a spacetime structure with disconnected apparent horizons. This reveals a situation that there is a firewall outside of the event horizon, while the apparent horizon is absent. Therefore, the firewall, if it exists, not only does modify the general relativity for an in-falling observer, but also modify the semi-classical quantum field theory for an asymptotic observer.
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