• Journal of the Korean Physical Society
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• 제73권10호
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• pp.1420-1430
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• 2018

We investigate an entangled system, which is analogous to a composite system of a black hole and Hawking radiation. If Hawking radiation is well approximated by an outgoing particle generated from pair creation around the black hole, such a pair creation increases the total number of states. There should be a unitary mechanism to reduce the number of states inside the horizon for black hole evaporation. Because the infalling antiparticle has negative energy, as long as the infalling antiparticle finds its partner such that the two particles form a separable state, one can trace out such a zero energy system by maintaining unitarity. In this paper, based on some toy model calculations, we show that such a unitary tracing-out process is only possible before the Page time while it is impossible after the Page time. Hence, after the Page time, if we assume that the process is unitary and the Hawking pair forms a separable state, the internal number of states will monotonically increase, which is supported by the Almheiri-Marolf-Polchinski-Sully (AMPS) argument. In addition, the Hawking particles cannot generate randomness of the entire system; hence, the entanglement entropy cannot reach its maximum. Based on these results, we modify the correct form of the Page curve for the remnant picture. The most important conclusion is this: if we assume unitarity, semi-classical quantum field theory, and general relativity, then the black hole should violate the Bekenstein-Hawking entropy bound around the Page time at the latest; hence, the infinite production arguments for remnants might be applied for semi-classical black holes, which seems very problematic.

• Journal of Korean Neurosurgical Society
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• 제64권5호
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• pp.705-715
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• 2021

Objective : Through our previous clinical trials, the demonstrated therapeutic effects of MSC in chronic spinal cord injury (SCI) were found to be not sufficient. Therefore, the need to develop stem cell agent with enhanced efficacy is increased. We transplanted enhanced Wnt3-asecreting human mesenchymal stem cells (hMSC) into injured spines at 6 weeks after SCI to improve axonal regeneration in a rat model of chronic SCI. We hypothesized that enhanced Wnt3a protein expression could augment neuro-regeneration after SCI. Methods : Thirty-six Sprague-Dawley rats were injured using an Infinite Horizon (IH) impactor at the T9-10 vertebrae and separated into five groups : 1) phosphate-buffered saline injection (injury only group, n=7); 2) hMSC transplantation (MSC, n=7); 3) hMSC transfected with pLenti vector (without Wnt3a gene) transplantation (pLenti-MSC, n=7); 4) hMSC transfected with Wnt3a gene transplantation (Wnt3a-MSC, n=7); and 5) hMSC transfected with enhanced Wnt3a gene (1.7 fold Wnt3a mRNA expression) transplantation (1.7 Wnt3a-MSC, n=8). Six weeks after SCI, each 5×10⁵ cells/15 µL at 2 points were injected using stereotactic and microsyringe pump. To evaluate functional recovery from SCI, rats underwent Basso-Beattie-Bresnahan (BBB) locomotor test on the first, second, and third days post-injury and then weekly for 14 weeks. Axonal regeneration was assessed using growth-associated protein 43 (GAP43), microtubule-associated protein 2 (MAP2), and neurofilament (NF) immunostaining. Results : Fourteen weeks after injury (8 weeks after transplantation), BBB score of the 1.7 Wnt3a-MSC group (15.0±0.28) was significantly higher than that of the injury only (10.0±0.48), MSC (12.57±0.48), pLenti-MSC (12.42±0.48), and Wnt3a-MSC (13.71±0.61) groups (p<0.05). Immunostaining revealed increased expression of axonal regeneration markers GAP43, MAP2, and NF in the Wnt3a-MSC and 1.7 Wnt3a-MSC groups. Conclusion : Our results showed that enhanced gene expression of Wnt3a in hMSC can potentiate axonal regeneration and improve functional recovery in a rat model of chronic SCI.