Effective theory of Black Holes in the 1/D expansion

The gravitational field of a black hole is strongly localized near its horizon when the number of dimensions D is very large. In this limit, we can effectively replace the black hole with a surface in a background geometry (eg Minkowski or Anti-deSitter space). The Einstein equations determine the effective equations that this 'black hole surface' (or membrane) must satisfy. We obtain them up to next-to-leading order in 1/D for static black holes of the Einstein-(A)dS theory. To leading order, and also to next order in Minkowski backgrounds, the equations of the effective theory are the same as soap-film equations, possibly up to a redshift factor. In particular, the Schwarzschild black hole is recovered as a spherical soap bubble. Less trivially, we find solutions for 'black droplets', ie black holes localized at the boundary of AdS, and for non-uniform black strings.Comment: 32 pages, 3 figure

Structure of the Milky Way stellar halo out to its outer boundary with blue horizontal-branch stars

We present the structure of the Milky Way stellar halo beyond Galactocentric distances of $r = 50$ kpc traced by blue horizontal-branch (BHB) stars, which are extracted from the survey data in the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP). We select BHB candidates based on $(g,r,i,z)$ photometry, where the $z$-band is on the Paschen series and the colors that involve the $z$-band are sensitive to surface gravity. About 450 BHB candidates are identified between $r = 50$ kpc and 300 kpc, most of which are beyond the reach of previous large surveys including the Sloan Digital Sky Survey. We find that the global structure of the stellar halo in this range has substructures, which are especially remarkable in the GAMA15H and XMM-LSS fields in the HSC-SSP. We find that the stellar halo can be fitted to a single power-law density profile with an index of $\alpha \simeq 3.3$ ($3.5$) with (without) these fields and its global axial ratio is $q \simeq 2.2$ ($1.3$). Thus, the stellar halo may be significantly disturbed and be made in a prolate form by halo substructures, perhaps associated with the Sagittarius stream in its extension beyond $r \sim 100$ kpc. For a broken power-law model allowing different power-law indices inside/outside a break radius, we obtain a steep power-law slope of $\alpha \sim 5$ outside a break radius of $\simeq 100$ kpc ($200$ kpc) for the case with (without) GAMA15H and XMM-LSS. This radius of $200$ kpc might be as close as a halo boundary if there is any, although larger BHB sample is required from further HSC-SSP survey to increase its statistical significance.Comment: 12 pages, 8 figures, revised version, accepted for publication in PAS

A cross-licensing system discourages R&D investments in completely complementary technologies.

We consider the R&D investments competition of the duopolistic firms in completely complementarty technologies. By "completely complementary technologies" ,we mea that each firm cannot produce the goods without both of the technologies. We derive the investments competiton equilibria in R&D of the two completely complementary technologies with and without the cross-licensing system. By comparing the R&D incestment levels in the two equilibria, we show that the crosslicensing system discourages the R&D investments when the duopolistic firms produce goods by using the two completely complementary technologies

Licensing (cross-licensing) system and R&D investments in a weakly complementary technologies economy

We consider the R&D investments competition of the two duopolistic firms in a weakly complementary technologies economy. By “the weakly complementary technologies”, we mean that each firm can produce goods without both of the two technologies but it incurs more redundant costs than that in the case each or both of the technologies may be available for it. By “the strongly complementary technologies,” we mean that the firm cannot produce the goods at all without the use of both of them. We derive the investments competition equilibria in R&D of the two weakly complementary technologies with and without the (cross-) licensing system. By comparing of the R&D investment levels in the two equilibria, we show that the (cross-) licensing system promotes the R&D investments when the duopolistic firms can produce goods by using of the two weakly complementary technologies