Quantum-induced trans-Planckian energy near horizon

Abstract

We study the loop effects on the geometry and boundary conditions of several black hole spacetimes one of which is time-dependent and analyze the energy measured by an infalling observer near their horizons. The finding in the previous works that the loop effects can be drastic is reinforced: they play an important role in the boundary conditions and non-perturbative geometry deformation. One of the channels through which the quantum gravitational effects enter is generation of the cosmological constant. The cosmological constant feeds part of the time-dependence of a solution. We obtain a trans-Planckian energy in the time-dependent case. The importance of time-dependence for the trans-Planckian energy and black hole information is discussed.

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

“…In section 3.1 we start by reviewing our earlier work of [7] on an Einsteinscalar case. We highlight some salient results of the analysis and point out an undesirable feature of the solution therein obtained.…”

“…Let us warm up by reviewing the case considered in [7], in which an Einsteinscalar system was considered. The classical action of [7] is…”

“…Therefore the focus of one's quest should be the physics that can produce various extreme-high-energy particles -such as gamma ray photons, protons, heavier ions, and neutrinos -in massive volume. Motivated by this and more theoretically-oriented issues, such as black hole information (see, e.g., [1] [2] for reviews) and Firewall [3] [4], we have initiated in [5][6][7][8] the study of quantum gravitational effects as the potential agent behind certain astrophysical phenomena, including the generation of the UHECR particles.…”

“…In section 2, before embarking on the technical analysis, we give a qualitative reasoning on why there ought to be a trans-Planckian energy behavior near the event horizon. In section 3, after reviewing the Einstein-scalar system analyzed in [7], we obtain a time-dependent quantum-level solution of an Einstein-Maxwell-scalar system. We consider the Λ 0 = 0 case -where Λ 0 = 0 denotes the classical part of the cosmological constant -for a reason to be explained; extension to the Λ 0 = 0 case is left for future.…”

On Firewalls in quantum-corrected General Relativity

“…A natural way to this end is to take into account the loop perturbative corrections to the standard gravitational action, coming either from the direct quantization of GR [44] or from String Theory and its effective low-energy supergravity actions [6]. Going beyond the semi-classical approximation we have shown a principle possibility of arising the quantum-induced trans-Plankian energy densities near the BHs horizons [43] at their birth and early stages of evolution. It means that we have found something different to the original AMPS proposal, since the Firewall prescription of [34] supposes the formation of this object at the late stages of the BH evolution.…”