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There is no proof that black holes contain singularities when they are generated by real physical bodies. Roger Penrose claimed sixty years ago that trapped surfaces inevitably lead to light rays of finite affine length (FALL's). Penrose and Stephen Hawking then asserted that these must end in actual singularities. When they could not prove this they decreed it to be self evident. It is shown that there are counterexamples through every point in the Kerr metric. These are asymptotic to at least one event horizon and do not end in singularities.

Stellar positions and velocities from Gaia are yielding a new view of open cluster dispersal. Here we present an analysis of a group of stars spanning Cepheus to Hercules, hereafter the Cep-Her complex. The group includes four Kepler Objects of Interest: Kepler-1643 b ($2.32 \pm 0.13$ Earth-radii, 5.3 day orbital period), KOI-7368 b ($2.22 \pm 0.12$ Earth-radii, 6.8 days), KOI-7913 Ab ($2.34 \pm 0.18$ Earth-radii, 24.2 days), and Kepler-1627 Ab ($3.85 \pm 0.11$ Earth-radii, 7.2 days). The latter Neptune-sized planet is in part of the Cep-Her complex called the $\delta$ Lyr cluster (Bouma et al. 2022). Here we focus on the former three systems, which are in other regions of the association. Based on kinematic evidence from Gaia, stellar rotation periods from TESS, and spectroscopy, these three objects are also approximately 40 million years (Myr) old. More specifically, we find that Kepler-1643 is $46^{+9}_{-7}$ Myr old, based on its membership in a dense sub-cluster of the complex called RSG-5. KOI-7368 and KOI-7913 are $36^{+10}_{-8}$ Myr old, and are in a diffuse region that we call CH-2. Based on the transit shapes and high resolution imaging, all three objects are most likely planets, with false positive probabilities of $6 \times 10^{-9}$, $4 \times 10^{-3}$, and $1 \times 10^{-4}$ for Kepler-1643, KOI-7368, and KOI-7913 respectively. These planets demonstrate that mini-Neptunes with sizes of approximately 2 Earth radii exist at ages of 40 million years., Comment: AJ accepted. Tables 2 and 3 uploaded

We show that the gravitomagnetic interaction of a Kerr black hole (BH) with a surrounding magnetic field induces an electric field that accelerates charged particles to ultra-relativistic energies in the vicinity of the BH. Along the BH rotation axis, these electrons/protons can reach energies of even thousands of PeV, so stellar-mass BHs in long gamma-ray bursts (GRBs) and supermassive BHs in active galactic nuclei (AGN) can contribute to the ultrahigh-energy cosmic rays (UHECRs) thorough this mechanism. At off-axis latitudes, the particles accelerate to energies of hundreds of GeV and emit synchrotron radiation at GeV energies. This process occurs within $60^\circ$ around the BH rotation axis, and due to the equatorial-symmetry, it forms a double-cone emission. We outline the theoretical framework describing these acceleration and radiation processes, how they extract the rotational energy of the Kerr BH and the consequences for the astrophysics of GRBs., Comment: Accepted for publication in the ApJ

The Arecibo Observatory (AO) is a multidisciplinary research and education facility that is recognized worldwide as a leading facility in astronomy, planetary, and atmospheric and space sciences. AO's cornerstone research instrument was the 305-m William E. Gordon telescope. On December 1, 2020, the 305-m telescope collapsed and was irreparably damaged. In the three weeks following the collapse, AO's scientific and engineering staff and the AO users community initiated extensive discussions on the future of the observatory. The community is in overwhelming agreement that there is a need to build an enhanced, next-generation radar-radio telescope at the AO site. From these discussions, we established the set of science requirements the new facility should enable. These requirements can be summarized briefly as: 5 MW of continuous wave transmitter power at 2 - 6 GHz, 10 MW of peak transmitter power at 430 MHz (also at 220MHz under consideration), zenith angle coverage 0 to 48 deg, frequency coverage 0.2 to 30 GHz and increased Field-of-View. These requirements determine the unique specifications of the proposed new instrument. The telescope design concept we suggest consists of a compact array of fixed dishes on a tiltable, plate-like structure with a collecting area equivalent to a 300m dish. This concept, referred to as the Next Generation Arecibo Telescope (NGAT), meets all of the desired specifications and provides significant new science capabilities to all three research groups at AO. This whitepaper presents a sample of the wide variety of the science that can be achieved with the NGAT, the details of the telescope design concept and the need for the new telescope to be located at the AO site. We also discuss other AO science activities that interlock with the NGAT in the white paper., Comment: 82 pages (executive summary 10 pages), 21 figures, Arecibo observatory white paper (Updated with the complete author list and minor edits)

The debris disk surrounding $\beta$ Pictoris has a gas composition rich in carbon and oxygen, relative to solar abundances. Two possible scenarios have been proposed to explain this enrichment. The preferential production scenario suggests that the gas produced may be naturally rich in C and O, while the alternative preferential depletion scenario states that the enrichment has evolved to the current state from a gas with solar-like abundances. In the latter case, the radiation pressure from the star expels the gas outwards, leaving behind species less sensitive to stellar radiation such as C and O. Nitrogen is also not sensitive to radiation pressure due to its low oscillator strength, which would make it also overabundant under the preferential depletion scenario. As such, the abundance of N in the disk may provide clues to why C and O are overabundant. We aim to measure the N column density in the direction of $\beta$ Pic, and use this information to disentangle these different scenarios explaining the C and O overabundance. Using far-UV spectroscopic data collected by the HST's Cosmic Origins Spectrograph (COS) instrument, we analyse the spectrum and characterise the NI triplet by modelling the absorption lines. We measure the N column density in the direction of $\beta$ Pic for the first time, and find it to be $\log(N_{\mathrm{NI}}/1\,\mathrm{cm}^2) = 14.9\pm0.7$. The N gas is found to be consistent with solar abundances and Halley dust. The solar N abundance supports the preferential production hypothesis, in which the composition of gas in $\beta$\,Pic is the result of photodesorption from icy grains rich in C and O or collisional vaporisation of C and O rich dust in the disk. It does not support the hypothesis that C and O are overabundant due to the insensitivity of C and O to radiation pressure thereby leaving them to accumulate in the disk., Comment: 8 pages, 3 figures. Accepted for publication in A&A

Chemical clock reactions are characterised by a relatively long induction period followed by a rapid `switchover' during which the concentration of a \emph{clock chemical} rises rapidly. In addition to their interest in chemistry education, these reactions are relevant to industrial and biochemical applications. A substrate-depletive, non-autocatalytic clock reaction involving household chemicals (vitamin C, iodine, hydrogen peroxide and starch) is modelled mathematically via a system of nonlinear ordinary differential equations. Following dimensional analysis the model is analysed in the phase plane and via matched asymptotic expansions. Asymptotic approximations are found to agree closely with numerical solutions in the appropriate time regions. Asymptotic analysis also yields an approximate formula for the dependence of switchover time on initial concentrations and the rate of the slow reaction. This formula is tested via `kitchen sink chemistry' experiments, and is found to enable a good fit to experimental series varying in initial concentrations of both iodine and vitamin C. The vitamin C clock reaction provides an accessible model system for mathematical chemistry., Comment: 17 pages, 5 figures

The issue of intermittency in numerical solutions of the 3D Navier-Stokes equations on a periodic box $[0,\,L]^{3}$ is addressed through four sets of numerical simulations that calculate a new set of variables defined by $D_{m}(t) = \left(\varpi_{0}^{-1}\Omega_{m}\right)^{\alpha_{m}}$ for $1 \leq m \leq \infty$ where $\alpha_{m}= \frac{2m}{4m-3}$ and $\left[\Omega_{m}(t)\right]^{2m} = L^{-3}\I |\bom|^{2m}dV$ with $\varpi_{0} = \nu L^{-2}$. All four simulations unexpectedly show that the $D_{m}$ are ordered for $m = 1\,,...,\,9$ such that $D_{m+1} < D_{m}$. Moreover, the $D_{m}$ squeeze together such that $D_{m+1}/D_{m}\nearrow 1$ as $m$ increases. The first simulation is of very anisotropic decaying turbulence\,; the second and third are of decaying isotropic turbulence from random initial conditions and forced isotropic turbulence at constant Grashof number respectively\,; the fourth is of very high Reynolds number forced, stationary, isotropic turbulence at up to resolutions of $4096^{3}$.

Non-positive definite, global inviscid invariants similar to helicity are discussed for two types of shell models and evidence for a new role for helicity in Navier-Stokes turbulence is presented. It is suggested that the extra invariants play the role of triggering the intermittent cascade of energy to small scales characterized by pulses. These invariants also determine where a transition to chaos appears. New analysis of numerical experiments with existing models is suggested and a new class of shell-models where the dynamical interactions of a second quadratic invariant are closer to those of helicity in the Navier-Stokes equations is introduced. The place of the popular GOY model within this class is discussed., Comment: 7 figures not included, available upon request from the author or on WWW in: http://www.mmm.ucar.edu/blt/kerr_shells.html

The Kerr solution is defined by a null congruence which is geodesic and shear free and has a singular line contained in a bounded region of space. A generalization of the Kerr congruence for nonstationary case is obtained. We find a nonstationary shear free geodesic null congruence which is generated by a given analytical complex world line. Solutions of the Einstein equations are analyzed. It is shown that there exists complex radiative solution which is generalization of the Kerr solution and the Kinnersley accelerating solution for "photon rocket"., Comment: 17 pages., AmS-TeX