Non-existence of quantum black hole horizons in the improved dynamics approach

On the improved dynamics approach in loop quantum black holes

“…Then, we found that black/white hole horizons do not exist. This conclusion is consistent with what we obtained previously by adopting a different gauge [22]. This is quite expected, as the physics should not depend on the gauge choice.…”

“…On the other hand, in [23] the proof that the BV model is geodesically complete was carried out in the cosmic time coordinate, in which the lapse function was set to one. In this paper, we shall adopt the Saini-Singh (SS) gauge, N = 1, and show that indeed black/white horizons never exist in the BV model, as expected from what we obtained in [22], since the physics should not depend on the choice of the gauge.…”

“…Note that in writing down the above equations, we had used the Hamiltonian constraint H eff ≈ 0. It should be also noted that there exists a typo in the EoM of c(τ) given in [23], where the last term should be p p )| t as those given in [22]. In order to compare the results obtained in this two papers, where 1.11068 t   corresponds to the location of the first transition surface of the BV model, and 0 H GR t = to the location of the classical Schwarzschild black hole horizon.…”

“…Then, we expect that there are large departures from the classical theory very near the classical black hole horizon even for massive black holes, for which the curvatures at the horizon become very low [11,[19][20][21]. As a matter of fact, recently we found that the effects are so large that black/white horizons never exist in the BV model [22].…”

“…Hamiltonian, where b and c are the moment conjugates of p b and p c , with {c, p c } = 2Gγ, {b, p b } = Gγ, and δ b and δ c are the corresponding two polymerization parameters, given by [21]To understand the quantum effects, let us first note that in the interior of the Schwarzschild black hole we have[22] the black hole singularity is located at T = -∞, while its horizon is located at T T m ln 2H GR ( ) = º. Thus, near the singular point we have δ b ∝ e −T → ∞ , although δ c ∝ e T/2 → 0.…”