Abstract
Static, spherically symmetric black hole solutions to the semi-classical Einstein equation are studied, including the effect of the quantum energy-momentum tensor for conformal matters with 4D Weyl anomaly. Through both perturbative and non-perturbative methods, we show that the quantum effect can play a crucial role in shaping the nearhorizon geometry, and that the existence of the horizon requires fine-tuning.
Highlights
Since Hawking’s proposal [1] that a black hole can completely evaporate through Hawking radiation, physicists have realized that quantum effects, despite its weakness, have the potential to affect the large-scale structure of black holes
Pei-Ming Ho,a Hikaru Kawai,b Yoshinori Matsuoa and Yuki Yokokurac aDepartment of Physics and Center for Theoretical Physics, National Taiwan University, Taipei 106, Taiwan, R.O.C. bDepartment of Physics, Kyoto University, Kitashirakawa, Kyoto 606-8502, Japan ciTHEMS Program, RIKEN, Wako, Saitama 351-0198, Japan E-mail: pmho@phys.ntu.edu.tw, hkawai@gauge.scphys.kyoto-u.ac.jp, matsuo@phys.ntu.edu.tw, yuki.yokokura@riken.jp Abstract: Static, spherically symmetric black hole solutions to the semi-classical Einstein equation are studied, including the effect of the quantum energy-momentum tensor for conformal matters with 4D Weyl anomaly. Through both perturbative and non-perturbative methods, we show that the quantum effect can play a crucial role in shaping the nearhorizon geometry, and that the existence of the horizon requires fine-tuning
When the conformal charges c4, a4 vanish, in the absence of the pressure Tθθ(z0), this expression reproduces the result B2 = 1 of the Schwarzschild solution. (But there is no neck in the Schwarzschild solution at z = z0 because it coincides with the horizon.) For a large black hole, since κ is very small, B2 is positive unless Tθθ(z0) O(κ−1), and there is a local minimum of the areal radius at z = z0
Summary
Since Hawking’s proposal [1] that a black hole can completely evaporate through Hawking radiation, physicists have realized that quantum effects, despite its weakness, have the potential to affect the large-scale structure of black holes To this day, there has not yet been a satisfactory understanding on this topic, leaving many unsettled issues, including most notably the information loss paradox [2,3,4,5] and related proposals such as the fuzzball [6,7,8,9,10] and the firewall [11,12,13]. Vacuum energy-momentum tensors derived from 2D models of quantum field theories are extensively studied in ref. It was shown that, depending on the quantum model of vacuum energy-momentum tensor and the vacuum state, the backreacted near-horizon geometry falls into three qualitatively different classes. The progress achieved in this work is mainly the use of 4D (instead of 2D) models of quantum vacuum energy-momentum, and its generality that covers all static solutions with spherical symmetry. The perturbative and non-perturbative solutions together depict a comprehensive picture of the black-hole geometry
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