Tightening the Penrose Inequality

The Penrose inequality estimates the lower bound of the mass of a black hole in terms of the area of its horizon. This bound is not very ``tight'' for extremal or near extremal black holes. We propose a new Penrose-like inequality for static black holes involving the mass, the area of black hole event horizon and the temperature. Our inequality includes the Penrose inequality as its corollary and it is saturated by both the Schwarzschild black hole and Reissner-Nordstr\"om (RN) black hole. In the spherically-symmetric case, we prove this new inequality by assuming both the null and trace energy conditions.Comment: latex, 19 page

Physical origin of color changes in lutetium hydride under pressure

Recently, near-ambient superconductivity was claimed in nitrogen-doped lutetium hydride (LuH$_{3-\delta}$N$_{\epsilon}$) . Unfortunately, all follow-up research still cannot find superconductivity signs in successfully synthesized lutetium dihydride (LuH$_2$) and N-doped LuH$_{2\pm x}$N$_y$. However, a similar intriguing observation was the pressure-induced color changes (from blue to pink and subsequent red). The physical understanding of its origin and the correlation between the color, crystal structure, and chemical composition of Lu-H-N is still lacking. In this work, we theoretically study the optical properties of LuH$_2$, LuH$_3$, and some potential N-doped compounds using the first-principles calculations by considering both interband and intraband contributions. Our results show that LuH$_2$ has an optical reflectivity peak around blue light up to 10 GPa. Under higher pressure, the reflectivity of red light gradually becomes dominant. This evolution is driven by changes in the direct band gap and the Fermi velocity of free electrons under pressure. In contrast, LuH$_3$ exhibits gray and no color change up to 50 GPa. Furthermore, we considered different types of N-doped LuH$_2$ and LuH$_3$. We find that N-doped LuH$_2$ with the substitution of a hydrogen atom at the tetrahedral position maintains the color change when the N-doping concentration is low. As the doping level increases, this trend becomes less obvious. While other N-doped structures do not show significant color change. Our results can clarify the origin of the experimental observed blue-to-red color change in lutetium hydride and also provide a further understanding of the potential N-doped lutetium dihydride

Universal bounds on the size of a black hole

For static black holes in Einstein gravity, if matter fields satisfy a few general conditions, we conjecture that three characteristic parameters about the spatial size of black holes, namely the outermost photon sphere area $A_{\text{ph,out}}$, the corresponding shadow area $A_{\text{sh,out}}$ and the horizon area $A_{H}$ satisfy a series of universal inequalities $9A_{H}/4\leq A_{\text{ph,out}}\leq A_{\text{sh,out}}/3\leq 36\pi M^2$, where $M$ is the ADM mass. We present a complete proof in the spherically symmetric case and some pieces of evidence to support it in general static cases. We also discuss the properties of the photon spheres in general static spacetimes and show that, similar to horizon, photon spheres are also conformal invariant structures of the spacetimes.Comment: latex, 8 pages, 5 figures, typos and errors corrected, references adde

Erratum

'Beibinghong': A new grape cultivar for brewing ice red wineVitis 53 (2), 85-89 (2014

hCLP46 Increases Smad3 Protein Stability Via Inhibiting its Ubiquitin-Proteasomal Degradation

hCLP46 (human CAP10-like protein 46 kDa) was initially isolated and identified from human acute myeloid leukemia transformed from myelodysplastic syndrome (MDS-AML) CD34+ cells (Teng et al., 2006) and we demonstrated previously that hCLP46 is abnormally expressed in many hematopoietic malignancies (Wang et al., 2010). Studies fromits Drosophila homolog, Rumi, suggested that Notch is a potential target of hCLP46 (Acar et al., 2008). We also found that overexpression of hCLP46 enhances Notch activation and regulates cell proliferation in a cell type-dependent manner (Ma et al., 2011; Chu et al., 2013). However, hCLP46−/− embryos show more severe phenotypes compared to those displayed by other global regulators of canonical Notch signaling, suggesting that hCLP46 is likely to have additional important targets during mammalian development (Fernandez- Valdivia et al., 2011). Based on the crosstalk between Notch and the transforming growth factor-β (TGF-β) signaling, we proposed that hCLP46 might be involved in TGF-β signal regulation, but the detail mechanism remains unclear