Rotating bodies; the Kerr metric

Spacetime around a general rigidly rotating body is discussed, and the Kerr solution explored in detail. First we obtain generic properties of stationary, axisymmetric metrics. The stationary limit surface and ergoregion is defined. Then the Kerr metric is presented (without derivation) and discussed. Horizons and limit surfaces are obtained, and the overall structure of the Kerr black hole deduced. The mass and angular momentum is extracted. Equations for particle orbits are obtained, and their properties discussed.

Laplace surface dynamics, revisited: satellites, exo-planets and debris with distant, eccentric companions

To date, studies of Laplace Surface dynamics have concerned themselves with test particle orbits of fixed shape and orientation in the combined field of an oblate central body (to which the particle is bound) and a distant, inclined, companion which is captured to quadrupolar order. While amply sufficient for satellites around planets on near-circular orbits, the quadrupolar approximation fails to capture essential dynamical features induced by a wide binary companion (be it a star, a planet or a black hole) on a fairly eccentric orbit. With similar such astronomical settings in mind, we extend the classical Laplace framework to higher multipoles, and map out the backbone of stationary orbits, now complexified by the broken axial symmetry. Eccentric and inclined Laplace equilibria, which had been presaged in systems of large enough mutual inclination, are here delineated over a broad range of mutually inclined perturbations. We recover them for test particles in the field of a hot Jupiter and a wide eccentric stellar binary, highlighting their relevance for the architecture of multi-planet systems in binaries. We then extend and deploy our machinery closer to home, as we consider the secular dynamics of Trans-Neptunian Objects (TNOs) in the presence of a putative ninth planet. We show how generalized Laplace equilibria seed islands for Trans-Neptunian objects to be sheltered around, islands within chaotic seas which we capture via Poincaré sections, while highlighting a beautiful interplay between Laplace and Kozai-Lidov secular dynamical structures. An eminently classical tale revived for the exo-planetary 21st century!

Can accretion properties distinguish between a naked singularity, wormhole and black hole?

We first advance a mathematical novelty that the three geometrically and topologically distinct objects mentioned in the title can be exactly obtained from the Jordan frame vacuum Brans I solution by a combination of coordinate transformations, trigonometric identities and complex Wick rotation. Next, we study their respective accretion properties using the Page–Thorne model which studies accretion properties exclusively for $$r\ge r_{\text {ms}}$$ r ≥ r ms (the minimally stable radius of particle orbits), while the radii of singularity/throat/horizon $$r<r_{\text {ms}}$$ r < r ms . Also, its Page–Thorne efficiency $$\epsilon $$ ϵ is found to increase with decreasing $$r_{\text {ms}}$$ r ms and also yields $$\epsilon =0.0572$$ ϵ = 0.0572 for Schwarzschild black hole (SBH). But in the singular limit $$r\rightarrow r_{s}$$ r → r s (radius of singularity), we have $$\epsilon \rightarrow 1$$ ϵ → 1 giving rise to $$100 \%$$ 100 % efficiency in agreement with the efficiency of the naked singularity constructed in [10]. We show that the differential accretion luminosity $$\frac{d{\mathcal {L}}_{\infty }}{d\ln {r}}$$ d L ∞ d ln r of Buchdahl naked singularity (BNS) is always substantially larger than that of SBH, while Eddington luminosity at infinity $$L_{\text {Edd}}^{\infty }$$ L Edd ∞ for BNS could be arbitrarily large at $$r\rightarrow r_{s}$$ r → r s due to the scalar field $$\phi $$ ϕ that is defined in $$(r_{s}, \infty )$$ ( r s , ∞ ) . It is concluded that BNS accretion profiles can still be higher than those of regular objects in the universe.

How accurately can we detect the splashback radius of dark matter haloes and its correlation with accretion rate?

ABSTRACT The splashback radius (Rsp) of dark matter haloes has recently been detected using weak gravitational lensing and cross-correlations with galaxies. However, different methods have been used to measure Rsp and to assess the significance of its detection. In this paper, we use simulations to study the precision and accuracy to which we can detect the splashback radius with 3D density, 3D subhalo, and weak lensing profiles. We study how well various methods and tracers recover Rsp by comparing it with the value measured directly from particle dynamics. We show that estimates of Rsp from density and subhalo profiles correspond to different percentiles of the underlying Rsp distribution of particle orbits. At low accretion rates, a second caustic appears and can bias results. Finally, we show that upcoming lensing surveys may be able to constrain the Rsp–Γdyn relation directly.