Quantum‐corrected Geometry of Horizon Vicinity

Abstract

We study the deformation of the horizon-vicinity geometry caused by quantum gravitational effects. Departure from the semi-classical picture is noted, and the fact that the matter part of the action comes at a higher order in Newton's constant than does the Einstein-Hilbert term is crucial for the departure. The analysis leads to a Firewalltype energy measured by an infalling observer for which quantum generation of the cosmological constant is critical. The analysis seems to suggest that the Firewall should be a part of such deformation and that the information be stored both in the horizon-vicinity and asymptotic boundary region. We also examine the behavior near the cosmological horizon.

Quantum-Gravitational Trans-Planckian Energy of a Time-Dependent Black Hole

“…The analysis consists of three components: computation of the quantum action (for which we referred to the previous works) and its time-dependent solution, computation of the four-velocity of the observer, as well as evaluation of the energy after expansion around the location of the horizon. As in the previous works [6] [7], a trans-Planckian energy has resulted. Concerning the physical origin of the trans-Planckian energy behavior, the loop effects become important near the horizon.…”

“…Such effects may be behind some of the highly energetic astrophysical phenomena. In the previous works [6] [7], we considered an Einstein-scalar system and examined the possibility that the quantum corrections may produce a violent energy behavior in the vicinity of the event horizon. It was shown that for a time-dependent solution, one indeed encounters such a behavior.…”

“…It turns out that this is not a genuine problem: one can set Λ 0 = 0 from the beginning. 6 Not unrelated to this, one of the mode relations, m 2 = 2Λ 0 3 , does not look natural. These observations motivate introduction of the scalar potential and, while doing so, we also introduce a Maxwell's field to make the system even more realistic.…”

“…What sets the present work apart from the previous works is that the system being considered is more realistic: we consider an Einstein-Maxwellscalar system with a Higgs-type potential and its rotating black hole solution. As in [6] [7] 2 , the analysis leads to a trans-Planckian energy. The trans-Planckian energy behavior may well be a generic feature of a time-dependent black hole configuration at the quantum level.…”

Foliation-Based Approach to Quantum Gravity and Applications to Astrophysics

“…Due to this there may again be "order-1" modifications to the classical picture. In [92] and [93] (see an earlier related work [94]), the energy measured by an infalling observer was studied for two different cases: quantum-corrected time-dependent dS-Schwarzschild and AdS black holes. It turns out that the infalling observer encounters a trans-Planckian energy near the horizon of the black hole, which is consistent with the Firewall proposal [95] [96].…”