Spherical gravitational collapse towards a black hole with non-zero tangential pressure is studied.Exact solutions corresponding to different equations of state are given.We find that when taking the tangential pressure into account,the exact solutions have three qualitatively different outcomes.For positive tangential pressure,the shell around a black hole may eventually collapse onto the black hole,or expand to infinity,or have a static but unstable solution,depending on the combination of black hole mass,mass of the shell and the pressure parameter.For vanishing or negative pressure,the shell will collapse onto the black hole.For all eventually collapsing solutions,the shell will cross the event horizon,instead of accumulating outside theeventhorizon,even if clocked by a distant stationary observer.
The maximum frequency of gravitational waves(GWs) detectable with traditional pulsar timing methods is set by the Nyquist frequency( fNy) of the observation. Beyond this frequency, GWs leave no temporal-correlated signals; instead, they appear as white noise in the timing residuals. The variance of the GW-induced white noise is a function of the position of the pulsars relative to the GW source. By observing this unique functional form in the timing data, we propose that we can detect GWs of frequency >f_(Ny)(super-Nyquist frequency GWs; SNFGWs). We demonstrate the feasibility of the proposed method with simulated timing data.Using a selected dataset from the Parkes Pulsar Timing Array data release 1 and the North American Nanohertz Observatory for Gravitational Waves publicly available datasets, we try to detect the signals from single SNFGW sources. The result is consistent with no GW detection with 65.5% probability. An all-sky map of the sensitivity of the selected pulsar timing array to single SNFGW sources is generated, and the position of the GW source where the selected pulsar timing array is most sensitive to is λ_s =.0.82,β_s =-1.03(rad); the corresponding minimum GW strain is h = 6.31 × 10^(-11) at f = 1 × 10^(-5) Hz.
We compile a sample of spectral energy distributions （SEDs） of 12 GeV radio galaxies （RGs）, including eight FR I RGs and four FR II RGs. These SEDs can be represented with the one-zone leptonic model. No significant unification, as expected in the unification model, is found for the derived jet parameters between FR I RGs and BL Lacertae objects （BL Lacs） and between FR II RGs and flat spectrum radio quasars （FSRQs）. However, on average FR I RGs have a larger ＇Tb （break Lorentz factor of electrons） and lower B （magnetic field strength） than FR II RGs, analogous to the differences be- tween BL Lacs and FSRQs. The derived Doppler factors （~） of RGs are on average smaller than those of blazars, which is consistent with the unification model such that RGs are the misaligned parent pop- ulations of blazars with smaller tS. On the basis of jet parameters from SED fits, we calculate their jet powers and the powers carded by each component, and compare their jet compositions and radiation efficiencies with blazars. Most of the RG jets may be dominated by particles, like BL Lacs, not FSRQs. However, the jets of RGs with higher radiation efficiencies tend to have higher jet magnetization. A strong anticorrelation between synchrotron peak frequency and jet power is observed for GeV RGs and blazars in both the observer and co-moving frames, indicating that the ＂sequence＂ behavior among blazars, together with the GeV RGs, may be intrinsically dominated by jet power.
By modeling the broadband spectral energy distributions （SEDs） of a typical flat spectrum radio quasar （FSRQ, 3C 279） and two GeV narrow-line Seyfert 1 galaxies （NLSls, PMN J0948＋0022 and 1H 0323＋342） in different flux stages with one-zone leptonic models, we find a universal correlation between their Doppler factors （δ） and peak luminosities （Lc） of external Compton scattering bumps. Compiling a combined sample of FSRQs and GeV NLSls, it is found that both FSRQs and GeV NLSls in different stages and in different sources follow the same δ-Lc correlation well. This indicates that the variations of observed luminosities may be essentially due to the Doppler boosting effect. The universal δ-Lo relation between FSRQs and GeV NLS 1 s in different stages may be further evidence that the particle acceleration and radiation mechanisms for the two kinds of sources are similar. In addition, by replacing Lc with the observed luminosity in the Fermi/LAT band （LLAT）, this correlation holds and it may serve as an empirical indicator of δ. We estimate the δ values with LLAT for 484 FSRQs in the Fermi/LAT Catalog and they range from 3 to 41, with a median of 16, which are statistically consistent with the values derived by other methods.
