Quantum Gravitational Effects on the Boundary

Fortschritte der Physik

2017

Self Cite

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.

Section: Resultsmentioning

confidence: 93%

“…It has been shown in [] that the 1PI action at the first few leading orders is given by

\begin{matrix} true \\ right S & = & left \frac{1}{κ^{2}} \int d^{4} x \sqrt{- g} false(R - 2 normalΛ false) - \int d^{4} x \sqrt{- g} [\frac{1}{2} {false(\partial_{μ} ϕ false)}^{2} + scriptV (ϕ)] \\ left + \frac{1}{κ^{2}} \int d^{4} x \sqrt{- g} [e_{1} κ^{4} R ϕ^{2} + e_{2} κ^{2} R^{2} + e_{3} κ^{2} R_{μ ν} R^{μ ν} + \dots] \end{matrix}

where the subscript ‘ r ’ (denoting ‘renormalized’ quantities) has been omitted. The coefficient e 's are to be determined by divergence‐cancelling conditions.…”

Section: Graviton Quantum‐field‐theoretic Effectsmentioning

confidence: 99%

“…It was shown in [] that the renormalization procedure requires a metric field redefinition of the form

\begin{matrix} true \\ right g_{μ ν} & \to & left g_{μ ν} + κ^{2} true[l_{0} g_{μ ν} + l_{1} g_{μ ν} R + l_{2} R_{μ ν} + l_{3} g_{μ ν} {false(\partial ϕ false)}^{2} \\ left + l_{4} \partial_{μ} ϕ \partial_{ν} ϕ + l_{5} g_{μ ν} ϕ^{2} \\ left + κ^{2} true(l_{6} R \partial_{μ} ϕ \partial_{ν} ϕ + l_{7} R_{μ ν} {false(\partial ϕ false)}^{2} + l_{8} R_{μ ν} ϕ^{2} + l_{9} g_{μ ν} R {false(\partial ϕ false)}^{2} \\ left + l_{10} g_{μ ν} R^{α β} \partial_{α} ϕ \partial_{β} ϕ + l_{11} R^{α}_{μ ν}^{β} \partial_{α} ϕ \partial_{β} ϕ + l_{12} g_{μ ν} R ϕ^{2} true) \\ left + κ^{4} ((l_{13} g_{μ ν} {(\partial ϕ)}^{4} + l_{14} \partial_{μ} ϕ \partial_{ν} ϕ {(\partial ϕ)}^{2} + l_{15} g_{μ ν} ϕ^{4}) \\ left + () l_{16} g_{μ ν} {(\partial ϕ)}^{2} ϕ^{2} + l_{17} \partial_{μ} ϕ \partial_{ν} ϕ ϕ^{2}) + \dots true] \end{matrix}

…”

Section: Graviton Quantum‐field‐theoretic Effectsmentioning

confidence: 99%

See 1 more Smart Citation

Quantum‐corrected Geometry of Horizon Vicinity

Fortschritte der Physik

2017

Self Cite

“…Constructing the Green's function will be technically involved too but it should be possible to employ a certain approximation method. If one's focus is on the vacuum transition, the AdS case analyzed in [33,78] should presumably serve the purpose better.…”

Section: Resultsmentioning

confidence: 99%

Foliation-based quantization and black hole information

2017

Class. Quantum Grav.

We extend the foliation-based quantization scheme of [19] to arbitrary asymptotically flat backgrounds including time-and positiondependent ones. One of the ingredients to accomplish the extension is imposition of a Neumann-type boundary condition. The quantization procedure, especially the gauge-fixing-induced reduction, provides a new insight into the black hole information paradox. The hypersurface degrees of freedom in the asymptotic region -whose dynamics should be responsible for part of the 'hair' -and transitions among various excitations play a central role in the global formulation of the information and proposed solution of the information paradox. In retrospect, the quantization scheme reveals the origin of the difficulty of the information problem: the problem's ties with the quantization of gravity and subtle boundary dynamics as well as the multilayered techniques required for its setup and study. We also comment on the implications of the asymptotic symmetries for the present quantization framework.arXiv:1707.04803v1 [hep-th]

“…The classical part of the quantum-level solution is required to settle down to a Kerr geometry. A novel feature observed in [15,16] is shared: the quantum effects remove the time-dependence of the classical part, which is crucial for the subsequent energy analysis. In section 4, we analyze the energy observed near horizon by an infalling observer and are led to a trans-Planckian energy.…”

Section: Introductionmentioning

confidence: 99%

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

Nurmagambetov

2019

Symmetry

Self Cite

We continue our recent endeavor in which a time-dependent black hole solution of a one-loop quantum-corrected Einstein-scalar system was obtained and its near-horizon behavior was analyzed. The energy analysis led to a trans-Planckian scaling behavior near the event horizon. In the present work the analysis is extended to a rotating black hole solution of an Einstein-Maxwell-scalar system with a Higgs potential. Although the analysis becomes much more complex compared to that of the previous, we observe the same basic features, including the quantum-gravitational trans-Planckian energy near the horizon.