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We investigate the stationary, spherically symmetric accretion of a degenerate relativistic Fermi gas onto a Reissner-Nordstr\"{o}m black hole. The accretion theory is based on the Boyer-Lindquist coordinates and the Fermi gas follows Fermi-Dirac statistics at infinity. We have derived the expression for the particle current density, the stress energy-momentum tensor, and three accretion rates. As the charged particle falls into the black hole, both the mass and the charge of the black hole increase. Consequently, the mass accretion rate and charge accretion rate are proportional to the particle accretion rate. We have also provided analytical results at infinity and numerical results within a finite range for these quantities. Our results indicate that the accretion rate decreases as the charge of the black hole increases, suggests that the presence of naked singularities is avoided in black hole accretion theory. In this paper, we also discovered that the accretion model of Vlasov gas behaves as an anisotropic fluid containing two perfect-fluid components. One component represents the isotropic fluid of Fermi gas, while the other represents a null fluid. When using the Boyer-Lindquist coordinate system, we observed that the contribution from the null fluid persists even at infinity, which led to the radial pressure always smaller than the tangential pressure. Therefore, it's not appropriate to treat the accretion model as a perfect fluid at infinity.

In this paper, we extend Chandrasekhar's method of calculating rotating black holes into $f(R)$ theory. We consider the Ricci scalar is a constant and derive the Kerr and Kerr-Ads metric by using the analytical mathematical method. Suppose that the spacetime is a 4-dimensional Riemannian manifold with a general stationary axisymmetric metric, we calculate Cartan's equation of structure and derive the Einstein tensor. In order to reduce the solving difficulty, we fix the gauge freedom to transform the metric into a more symmetric form. We solve the field equations in the two cases of the Ricci scalar $R=0$ and $R\neq 0$. In the case of $R=0$, the Ernst's equations are derived. We give the elementary solution of Ernst's equations and show the way to obtain more solutions including Kerr metric. In the case of $R\neq 0$, we reasonably assume that the solution to the equations consists of two parts: the first is Kerr part and the second is introduced by the Ricci scalar. Giving solution to the second part and combining the two parts, we obtain the Kerr-Ads metric. The calculations are carried out in a general $f(R)$ theory, indicating the Kerr and Kerr-Ads black holes exist widely in general $f(R)$ models. Furthermore, the whole solving process can be treated as a standard calculation procedure to obtain rotating black holes, which can be applied to other modified gravities.

In this work, the support vector machine (SVM) method is adopted to separate BL Lacertae objects (BL Lacs) and flat spectrum radio quasars (FSRQs) in the plots of photon spectrum index against the photon flux, $\alpha_{\rm ph} \sim {\rm log}\,F$, that of photon spectrum index against the variability index, $\alpha_{\rm ph} \sim {\rm log}\, \textit{V\!I}$, and that of variability index against the photon flux, ${\rm log}\,{V\!I} \sim {\rm log}\,F$. Then we used the dividing lines to tell BL Lacs from FSRQs in the blazars candidates of uncertain types from \textit{Fermi}/LAT catalogue. Our main conclusions are: 1. We separate BL Lacs and FSRQs by $\alpha_{\rm ph} = -0.123\,{\rm log}\,F + 1.170$ in the $\alpha_{\rm ph} \sim {\rm log}\,F$ plot, $\alpha_{\rm ph} = -0.161\,{\rm log}\,{V\!I} + 2.594$ in the $\alpha_{\rm ph} \sim {\rm log}\,{V\!I}$ plot, and ${\rm log}\,{V\!I} = 0.792\,{\rm log}\,F + 9.203$ in the ${\rm log}\,{V\!I} \sim {\rm log}\,F$ plot. 2. We obtained 932 BL Lac candidates and possible BL Lac candidates, and 585 FSRQ candidates and possible FSRQ candidates. 3. Some discussions are given for comparisons with those in literature., Comment: Accepted to Universe

Active galactic nuclei (AGNs) can be divided into two major classes, namely radio-loud and radio-quiet AGNs. A small subset of the radio-loud AGNs is called blazars, which are believed to be unified with Fanaroff-Riley type I and type II (FRI&II) radio galaxies. Following our previous work, we present a latest sample of 966 sources with measured radio flux densities of the core and extended components. The sample includes 83 BL Lacs, 473 FSRQs, 101 Seyferts, 245 galaxies, 52 FRIs&IIs and 12 unidentified sources. We then calculate the radio core-dominance parameters and spectral indices and study their relationship. Our analysis shows that the core-dominance parameters and spectral indices are quite different for different types of sources. We also corroborate that the correlation between core-dominance parameter and radio spectral index extends over all the sources in a large sample presented., Comment: arXiv admin note: substantial text overlap with arXiv:1811.08774

Aims. We present a sample of 4388 AGNs with available radio core-dominance parameters defined as the ratio of the core flux densities to extended ones, namely, R = Score/Sext., which includes 630 Fermi-detected AGNs respect to the catalog of 4FGL, the fourth Fermi Large Area Telescope source catalog, and the rest of them are non-Fermi-detected AGNs. In our sample, 584 blazars are Fermi-detected and 1310 are not, and also consists of other subclasses such as Seyfert, Fanaroff-Riley I/II and normal galaxies. We investigate various different properties between Fermi-detected AGNs and non-Fermi-detected ones by using the core-dominance parameters as the previous study has shown that R is a good indication of beaming effect. Methods. We then calculate the radio spectral indices for whole sample and adopt {\gamma}-ray photon indices for Fermi AGNs from 4FGL catalog for discussing their different performances on different subclasses, and obtain the relation between core-dominance parameters and radio spectral indices for both Fermi and non-Fermi sources according to the two components model on radio band, which are consistent with our previous study. Results. We found that the core-dominance parameters and radio spectral indices are quite different for different subclasses of AGNs, not only for Fermi sources but also non-Fermi sources, particularly, R for the former ones is averagely higher than later ones. We also adopt the same relation on core-dominance parameters and {\gamma}-ray photon indices for Fermi sources by taking the same assumption with two components model on {\gamma}-ray band, and obtain the fitting results indicating that the {\gamma}-ray emissions of Fermi blazars are mainly from the core component, which is perhaps associated with the beaming effect. Therefore, Fermi blazars are beamed., Comment: 14 pages, 18 figures

Active galactic nuclei (AGNs) can be divided into two major classes, namely radio loud and radio quiet AGNs. A small subset of the radio-loud AGNs is called blazars, which are believed to be unified with Fanaroff & Riley type I/II (FRI/II) radio galaxies. Following our previous work (Fan et al. 2011), we present a sample of 2400 sources with measured radio flux densities of the core and extended components. The sample contains 250 BL Lacs, 520 quasars, 175 Seyferts, 1178 galaxies, 153 Fanaroff & Riley type I and type II galaxies and 104 unidentified sources. We then calculate the radio core-dominance parameters and spectral indices and study their relationship. Our analysis shows that the core-dominance parameters and spectral indices are quite different for different types of sources. We also confirm that the correlation between core-dominance parameter and spectral index exists for a large sample presented in this work., Comment: 24 pages, 10 figures

In this paper, using the database of the university of Michigan Radio Astronomy Observatory (UMRAO) at three (4.8 GHz, 8 GHZ, and 14.5 GHz) radio frequencies, we studied the polarization properties for 47 BL Lacertae objects(38 radio selected BL Lacertae objects, 7 X-ray selected BL Lacertae, and two inter-middle objects (Mkn 421 and Mkn 501), and found that (1) The polarizations at higher radio frequency is higher than those at lower frequency, (2) The variability of polarization at higher radio frequency is higher than those at lower frequency, (3) The polarization is correlated with the radio spectral index, and (4) The polarization is correlated with core-dominance parameter for those objects with known core-dominance parameters suggesting that the relativistic beaming could explain the polarization characteristic of BL Lacs., Comment: 5 pages, 3 figures, 1 table. PASJ, in press