It is demonstrated that the generic four-dimensional Taub-Newman-Unti-Tamburino (Taub-NUT) spacetimes can be perfectly described in terms of three or four different kinds of thermodynamic hairs: the Komar mass (M ¼ m), the "angular momentum" (J n ¼ mn), the gravitomagnetic charge (N ¼ n), and/or the dual (magnetic) mass (M ¼ n). In other words, the NUT charge is a thermodynamic multihair which means that it simultaneously has both rotation-like and electromagnetic charge-like characteristics; this is in sharp contrast with the previous knowledge that it has only one physical feature, or that it is purely a single solution parameter. To arrive at this novel result, we put forward a simple, systematic way to investigate the consistent thermodynamic first law and Bekenstein-Smarr mass formulas of all fourdimensional spacetimes that contain a nonzero NUT charge, facilitated by first deriving a meaningful Christodoulou-Ruffini-type squared-mass formula. In this way, not only can the elegant Bekenstein-Hawking one-quarter area-entropy relation be naturally restored in the Lorentzian and Euclidian sectors of generic Taub-NUT-type spacetimes without imposing any constraint condition, but also the physical meaning of the NUT parameter as a poly-facet can be completely clarified in the thermodynamic sense for the first time.

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Context. In Gaia DR2, an unprecedented high level of precision has been reached at sub-milliarcsecond for astrometry and millimagnitudes for photometry. Using cluster members identified with the astrometry and photometry in Gaia DR2, we can obtain a reliable determination of cluster properties. However, because of the shortcomings of Gaia spectroscopic observations in dealing with densely crowded cluster regions, the RVs and metallicity values for cluster member stars from Gaia DR2 are still lacking. It is necessary to combine the Gaia data with the data from large spectroscopic surveys, such as LAMOST, APOGEE, GALAH, and Gaia-ESO. Aims. In this study our aim is to improve the cluster properties by combining the LAMOST spectra. In particular, we provide the list of cluster members with spectroscopic parameters as an add-value catalog in LAMOST DR5, which can be used to perform a detailed study for a better understanding of the stellar properties, by using their spectra and fundamental properties from the host cluster. Methods. We cross-matched the spectroscopic catalog in LAMOST DR5 with the identified cluster members in Cantat-Gaudin et al. (2018, A&A, 618, A93). We then used members with spectroscopic parameters to derive statistical properties of open clusters. Results. We obtained a list of 8811 members with spectroscopic parameters and a catalog of 295 cluster properties. The provided cluster properties include astrometric parameters, spectroscopic parameters, derived kinematic and orbital parameters, and isochrone fitting results. In addition, we study the radial and vertical metallicity gradient and age-metallicity relation with the compiled open clusters as tracers, finding slopes of −0.053 ± 0.004 dex kpc−1, −0.252 ± 0.039 dex kpc−1, and 0.022 ± 0.008 dex Gyr−1, respectively. The slopes of the metallicity distribution relation for young clusters (0.1 Gyr < Age < 2 Gyr) and the age-metallicity relation for clusters within 6 Gyr are both consistent with the literature results. In order to fully study the chemical evolution history in the disk, more spectroscopic observations for old and distant open clusters are needed for further investigation.

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In this paper, utilizing the generalized off-shell Helmholtz free energy, we explore the topological numbers of the four-dimensional static accelerating black hole and its AdS extension, as well as the static charged accelerating black hole and its AdS extension. Our analysis reveals a profound and significant impact of the acceleration parameter on the topological numbers associated with the static black holes. In addition, we demonstrate that the electric charge parameter has an important effect on the topological number of the static neutral accelerating black holes. What is more, we also indicate that the cosmological constant has a remarkable influence on the topological number of the static accelerating black hole.

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