Self-gravitating ring of matter in orbit around a black hole: the innermost stable circular orbit

We study analytically a black-hole-ring system which is composed of a stationary axisymmetric ring of particles in orbit around a perturbed Kerr black hole of mass $M$ . In particular, we calculate the shift in the orbital frequency of the innermost stable circular orbit (ISCO) due to the finite mass $m$ of the orbiting ring. It is shown that for thin rings of half-thickness $r\ll M$ , the dominant finite-mass correction to the characteristic ISCO frequency stems from the self-gravitational potential energy of the ring (a term in the energy budget of the system which is quadratic in the mass $m$ of the ring). This dominant correction to the ISCO frequency is of order $O(\mu \ln (M/r))$ , where $\mu \equiv m/M$ is the dimensionless mass of the ring. We show that the ISCO frequency increases (as compared to the ISCO frequency of an orbiting test-ring) due to the finite-mass effects of the self-gravitating ring.     

Exceptional functions wandering on the sphere and normal families

We extend Carathéodory’s generalization of Montel’s fundamental normality test to “wandering” exceptional functions (i.e., depending on the respective function in the family under consideration), and we give a corresponding result on shared functions. Furthermore, we prove that if we have a family of pairs (a, b) of functions meromorphic in a domain such that a and b uniformly “stay away from each other,” then the families of the functions a resp. b are normal. The proofs are based on a “simultaneous rescaling” version of Zalcman’s lemma.     

Radioactivity in the Exclusive Economic Zone of east coast Peninsular Malaysia: distribution trends of <Superscript>137</Superscript>Cs in surface seawater

Large volumes of surface seawater samples were collected from thirty locations in the Exclusive Economic Zone (EEZ) of the east coast Peninsular Malaysia on June 2008 to study the activity concentrations of ¹³⁷Cs. The results will serve as additional information to the existing baseline data and is very useful for monitoring fresh input of anthropogenic radionuclide into Malaysian marine environment. In this study, the activity concentrations of ¹³⁷Cs were determined using co-precipitation technique, followed by Gamma Spectrometry measurement. The mean activity concentration of ¹³⁷Cs ranged between 3.40 and 5.89 Bq/m³. Higher activity concentrations were observed at the coastal and towards the south of Peninsular Malaysia and were aligned with the high turbidity. These may due to the rapid diffusion of ¹³⁷Cs from suspended particulates and fine sediments into surface seawater. The activity concentrations of ¹³⁷Cs observed in this study were slightly higher than the concentrations reported in seawater at the Straits of Malacca, Vietnam and Philippines. This might be because the study area received more input of ¹³⁷Cs that originated from global fallout and then deposited on land which later being transported subsequently into the coastal zone due to siltation and erosion processes. It could also be attributed to the intrusion of river waters containing higher concentrations of ¹³⁷Cs.     

Weak cosmic censorship: as strong as ever

Spacetime singularities that arise in gravitational collapse are always hidden inside of black holes. This is the essence of the weak cosmic censorship conjecture. The hypothesis, put forward by Penrose 40 years ago, is still one of the most important open questions in general relativity. In this Letter, we reanalyze extreme situations which have been considered as counterexamples to the weak cosmic censorship conjecture. In particular, we consider the absorption of scalar particles with large angular momentum by a black hole. Ignoring back reaction effects may lead one to conclude that the incident wave may overspin the black hole, thereby exposing its inner singularity to distant observers. However, we show that when back reaction effects are properly taken into account, the stability of the black-hole event horizon is irrefutable. We therefore conclude that cosmic censorship is actually respected in this type of gedanken experiments.     

Revealing Excited-State Trajectories on Potential Energy Surfaces with Atomic Resolution in Real Time

Photoexcited molecular trajectories on potential energy surfaces (PESs) prior to thermalization are intimately connected to the photochemical reaction outcome. The excited-state trajectories of a diplatinum complex featuring photo-activated metal–metal σ-bond formation and associated Pt−Pt stretching motions were detected in real time using femtosecond wide-angle X-ray solution scattering. The observed motions correspond well with coherent vibrational wavepacket motions detected by femtosecond optical transient absorption. Two key coordinates for intersystem crossing have been identified, the Pt−Pt bond length and the orientation of the ligands coordinated with the platinum centers, along which the excited-state trajectories can be projected onto the calculated PESs of the excited states. This investigation has gleaned novel insight into electronic transitions occurring on the time scales of vibrational motions measured in real time, revealing ultrafast nonadiabatic or non-equilibrium processes along excited-state trajectories involving multiple excited-state PESs.