Higher-Derivative Gravity with Non-minimally Coupled Maxwell Field

We construct higher-derivative gravities with a non-minimally coupled Maxwell field. The Lagrangian consists of polynomial invariants built from the Riemann tensor and the Maxwell field strength in such a way that the equations of motion are second order for both the metric and the Maxwell potential. We also generalize the construction to involve a generic non-minimally coupled $p$-form field strength. We then focus on one low-lying example in four dimensions and construct the exact magnetically-charged black holes. We also construct exact electrically-charged $z=2$ Lifshitz black holes. We obtain approximate dyonic black holes for the small coupling constant or small charges. We find that the thermodynamics based on the Wald formalism disagrees with that derived from the Euclidean action procedure, suggesting this may be a general situation in higher-derivative gravities with non-minimally coupled form fields. As an application in the AdS/CFT correspondence, we study the entropy/viscosity ratio for the AdS or Lifshitz planar black holes, and find that the exact ratio can be obtained without having to know the details of the solutions, even for this higher-derivative theory.Comment: Latex, 23 page

Intraday pattern in bid-ask spreads and its power-law relaxation for Chinese A-share stocks

We use high-frequency data of 1364 Chinese A-share stocks traded on the Shanghai Stock Exchange and Shenzhen Stock Exchange to investigate the intraday patterns in the bid-ask spreads. The daily periodicity in the spread time series is confirmed by Lomb analysis and the intraday bid-ask spreads are found to exhibit $L$-shaped pattern with idiosyncratic fine structure. The intraday spread of individual stocks relaxes as a power law within the first hour of the continuous double auction from 9:30AM to 10:30AM with exponents $\beta_{\rm{SHSE}}=0.19\pm0.069$ for the Shanghai market and $\beta_{\rm{SZSE}}=0.18\pm0.067$ for the Shenzhen market. The power-law relaxation exponent $\beta$ of individual stocks is roughly normally distributed. There is evidence showing that the accumulation of information widening the spread is an endogenous process.Comment: 12 Elsart pages including 7 eps figure

Non-Abelian (Hyperscaling Violating) Lifshitz Black Holes in General Dimensions

We consider Einstein gravities coupled to a cosmological constant and multiple $SU(2)$ Yang-Mills fields in general dimensions and find that the theories admit colored Lifshitz solutions with dynamic exponents $z>1$. We also introduce a Maxwell field and construct exact electric charged black holes that asymptote to the $z=D-1$ colored Lifshitz spacetimes and analyse their thermodynamical first law. Furthermore, we introduce a dilaton to the system and construct Lifshitz spacetimes with hyperscaling violations. After turning on the Maxwell field, we obtain a class of hyperscaling violating Lifshitz black holes when $\theta=\frac{2}{D-2}[z-(D-1)]$.Comment: Latex, 12 pages, a published version in PL

Holographic Complexity Growth Rate in Horndeski Theory

Based on the context of complexity = action (CA) conjecture, we calculate the holographic complexity of AdS black holes with planar and spherical topologies in Horndeski theory. We find that the rate of change of holographic complexity for neutral AdS black holes saturates the Lloyd's bound. For charged black holes, we find that there exists only one horizon and thus the corresponding holographic complexity can't be expressed as the difference of some thermodynamical potential between two horizons as that of Reissner-Nordstrom AdS black hole in Einstein-Maxwell theory. However, the Lloyd's bound is not violated for charged AdS black hole in Horndeski theory.Comment: 20 pages, 6 figures, references added, typos correcte

New Active Asteroid (6478) Gault

Main-belt asteroid (6478) Gault was observed to show cometary features in early 2019. To investigate the cause, we conducted {\it BVR} observations at Xingming Observatory, China, from 2019 January to April. The two tails were formed around 2018 October 26--November 08, and 2018 December 29--2019 January 08, respectively, and consisted of dust grains of $\gtrsim$20 $\mu$m to 3 mm in radius ejected at a speed of $0.15 \pm 0.05$ m s$^{-1}$ and following a broken power-law size distribution bending at grain radius $\sim$70 $\mu$m (bulk density 1 g cm$^{-3}$ assumed). The total mass of dust within a $10^4$ km-radius aperture around Gault declined from $\sim$$9 \times 10^6$ kg since 2019 January at a rate of $2.28 \pm 0.07$ kg s$^{-1}$, but temporarily surged around 2019 March 25, because Earth thence crossed the orbital plane of Gault, within which the ejected dust was mainly distributed. No statistically significant colour or short-term lightcurve variation was seen. Nonetheless we argue that Gault is currently subjected to rotational instability. Using the available astrometry, we did not detect any nongravitational acceleration in the orbital motion of Gault.Comment: 6 pages, 4 figures, 2 table