Reissner-Nordstr\"om Metric in the Friedman-Robertson-Walker Universe

The metric for a Reissner-Nordstr$\ddot{o}$m black hole in the background of the Friedman-Robertson-Walker universe is obtained. Then we verified it and discussed the influence of the evolution of the universe on the size of the black hole. To study the problem of the orbits of a planet in the expanding universe, we rewrote the metric in the Schwarzschild coordinates system and deduced the equation of motion for a planet.Comment: 8 pages, no figure

ATRank: An Attention-Based User Behavior Modeling Framework for Recommendation

A user can be represented as what he/she does along the history. A common way to deal with the user modeling problem is to manually extract all kinds of aggregated features over the heterogeneous behaviors, which may fail to fully represent the data itself due to limited human instinct. Recent works usually use RNN-based methods to give an overall embedding of a behavior sequence, which then could be exploited by the downstream applications. However, this can only preserve very limited information, or aggregated memories of a person. When a downstream application requires to facilitate the modeled user features, it may lose the integrity of the specific highly correlated behavior of the user, and introduce noises derived from unrelated behaviors. This paper proposes an attention based user behavior modeling framework called ATRank, which we mainly use for recommendation tasks. Heterogeneous user behaviors are considered in our model that we project all types of behaviors into multiple latent semantic spaces, where influence can be made among the behaviors via self-attention. Downstream applications then can use the user behavior vectors via vanilla attention. Experiments show that ATRank can achieve better performance and faster training process. We further explore ATRank to use one unified model to predict different types of user behaviors at the same time, showing a comparable performance with the highly optimized individual models.Comment: AAAI 201

Dilaton Black Holes in de Sitter or Anti-de Sitter Universe

Poletti and Wiltshire have shown that, with the exception of a pure cosmological constant, the solution of a dilaton black hole in the background of de Sitter or anti-de Sitter universe, does not exist in the presence of one Liouville-type dilaton potential. Here with the combination of three Liouville-type dilaton potentials, we obtain the dilaton black hole solutions in the background of de Sitter or anti-de Sitter universe.Comment: 13 pages,to appear in Phys. Rev.

Higher Dimensional Dilaton Black Holes with Cosmological Constant

The metric of a higher-dimensional dilaton black hole in the presence of a cosmological constant is constructed. It is found that the cosmological constant is coupled to the dilaton in a non-trivial way. The dilaton potential with respect to the cosmological constant consists of three Liouville-type potentials.Comment: 8 pages,to appear in Phys. Lett.

Arbitrary Dimensional Schwarzschild-FRW Black Holes

The metric of arbitrary dimensional Schwarzschild black hole in the background of Friedman-Robertson-Walker universe is presented in the cosmic coordinates system. In particular, the arbitrary dimensional Schwarzschild-de Sitter metric is rewritten in the Schwarzschild coordinates system and basing on which the even more generalized higher dimensional Schwarzschild-de Sitter metric with another extra dimensions is found. The generalized solution shows that the cosmological constant may roots in the extra dimensions of space.Comment: 10 page