Killing Tensor and Carter Constant for Painlevé–Gullstrand Form of Lense–Thirring Spacetime

Recently, the authors have formulated and explored a novel Painlevé–Gullstrand variant of the Lense–Thirring spacetime, which has some particularly elegant features, including unit-lapse, intrinsically flat spatial 3-slices, and some particularly simple geodesics—the “rain” geodesics. At the linear level in the rotation parameter, this spacetime is indistinguishable from the usual slow-rotation expansion of Kerr. Herein, we shall show that this spacetime possesses a nontrivial Killing tensor, implying separability of the Hamilton–Jacobi equation. Furthermore, we shall show that the Klein–Gordon equation is also separable on this spacetime. However, while the Killing tensor has a 2-form square root, we shall see that this 2-form square root of the Killing tensor is not a Killing–Yano tensor. Finally, the Killing-tensor-induced Carter constant is easily extracted, and now, with a fourth constant of motion, the geodesics become (in principle) explicitly integrable.

Blandford-Znajek mechanism in the general stationary axially-symmetric black-hole spacetime

We consider the Blandford-Znajek process of electromagnetic extraction of energy from a general axially symmetric asymptotically flat slowly rotating black hole. Using the general parametrization of the black-hole spacetime we construct formulas for the flux of the magnetic field and the rate of energy extraction, which are valid not only for the Kerr spacetime, but also for its arbitrary axially symmetric deformations. We show that in the dominant order these quantities depend only on a single deformation parameter, which relates the spin frequency of a black hole with its rotation parameter.

MMX geodesy investigations: science requirements and observation strategy

In order to investigate the origin of Phobos and Deimos, the Japanese Martian Moons eXploration (MMX) mission is scheduled for launch in 2024. MMX will make comprehensive remote-sensing measurements of both moons and return regolith samples from Phobos to Earth. Geodetic measurements of gravity, shape, and rotation parameter of a body provides constraints on its internal structure reflecting its origin and evolution. Moments of inertia are important parameters to constrain the internal mass distribution, but they have not been well determined for the Martian moons yet. We discuss the mission requirements related to the moments of inertia to detect a potential heterogeneity of the mass distribution inside Phobos. We introduce mission instruments and operational strategies to meet the mission requirements. We present a preliminary imaging strategy from a quasi-satellite orbit for a base shape model that is expected to be created at the early stage of the mission. Geodetic products including ephemeris, gravity field, rotation parameter of Phobos, and spacecraft orbit are of importance not only for the geodetic study, but also for interpreting data from various mission instruments and selecting possible landing sites. Graphical Abstract

Electro-Magnetohydrodynamic Two Fluid Flow of Ionized-Gases with Hall and Rotation Effects

An electro-magnetohydrodynamic (EMHD) two fluid flow and heat transfer of ionized gases through a horizontal channel surrounded by non-conducting plates in a rotating framework with Hall currents is investigated. The Hall effect is considered with an assumption that the gases are completely ionized and the strength of the applied transverse magnetic field is strong. The governing equations are solved analytically for the temperature and velocity distributions in two fluid flow regions. The numerical solutions are demonstrated graphically for various physical parameters such the Hartmann number, Hall parameter, rotation parameter, and so on. It was noticed that an increment is either due to the Hall parameter or the rotation parameter reduces the temperature in the two regions.

Shadow and deflection angle of charged rotating black hole surrounded by perfect fluid dark matter

We analysed the shadow cast by charged rotating black hole (BH) in presence of perfect fluid dark matter (PFDM). We studied the null geodesic equations and obtained the shadow of the charged rotating BH to see the effects of PFDM parameter $\gamma$, charge $Q$ and rotation parameter $a$, and it is noticed that the size as well as the shape of BH shadow is affected due to PFDM parameter, charge and rotation parameter. Thus, it is seen that the presence of dark matter around a BH affects its spacetime. We also investigated the influence of all the parameters (PFDM parameter $\gamma$, BHs charge $Q$ and rotational parameter $a$) on effective potential, energy emission by graphical representation, and compare all the results with the non rotating case in usual general relativity. To this end, we have also explored the effect of PFDM on the deflection angle and the size of Einstein rings.

Photon boomerang in a nearly extreme Kerr metric

The Kerr rotating black hole metric has unstable photon orbits that orbit around the hole at fixed values of the Boyer-Lindquist coordinate r that depend on the axial angular momentum of the orbit, as well as on the parameters of the hole. For zero orbital axial angular momentum, these orbits cross the rotational axes at a fixed value of r that depends on the mass M and angular momentum J of the black hole. Nonzero angular momentum of the hole causes the photon orbit to rotate so that its direction when crossing the north polar axis changes from one crossing to the next by an angle I shall call ∆φ, which depends on the black hole dimensionless rotation parameter a/M = cJ/(GM2) by an equation involving a complete elliptic integral of the first kind. When the black hole has a/M ≈ 0.994 341 179 923 26, which is nearly maximally rotating, a photon sent out in a constant-r direction from the north polar axis at r ≈ 2.423 776 210 035 73 GM/c2returns to the north polar axis in precisely the opposite direction (in a frame nonrotating with respect to the distant stars), a photon boomerang.

Ultra-spinning Chow’s black holes in six-dimensional gauged supergravity and their properties

By taking the ultra-spinning limit as a simple solution-generating trick, a novel class of ultra-spinning charged black hole solutions has been constructed from Chow’s rotating charged black hole with two equal-charge parameters in six-dimensional $$ \mathcal{N} $$ N = 4 gauged supergravity theory. We investigate their thermodynamical properties and then demonstrate that all thermodynamical quantities completely obey both the differential first law and the Bekenstein-Smarr mass formula. For the six-dimensional ultra-spinning Chow’s black hole with only one rotation parameter, we show that it does not always obey the reverse isoperimetric inequality, thus it can be either sub-entropic or super-entropic, depending upon the ranges of the mass parameter and especially the charge parameter. This property is obviously different from that of the six-dimensional singly-rotating Kerr-AdS super-entropic black hole, which always strictly violates the RII. For the six-dimensional doubly-rotating Chow’s black hole but ultra-spinning only along one spatial axis, we point out that it may also obey or violate the RII, and can be either super-entropic or sub-entropic in general.

The intelligent networks for double-diffusion and MHD analysis of thin film flow over a stretched surface

This study presents a novel application of soft-computing through intelligent, neural networks backpropagated by Levenberg–Marquardt scheme (NNs-BLMS) to solve the mathematical model of unsteady thin film flow of magnetized Maxwell fluid with thermo-diffusion effects and chemical reaction (TFFMFTDECR) over a horizontal rotating disk. The expression for thermophoretic velocity is accounted. Energy expression is deliberated with the addition of non-uniform heat source. The PDEs of mathematical model of TFFMFTDECR are transformed to ODEs by the application of similarity transformations. A dataset is generated through Adams method for the proposed NNs-BLMS in case of various scenarios of TFFMFTDECR model by variation of rotation parameter, magnetic parameter, space dependent heat sink/source parameter, temperature dependent heat sink/source parameter and chemical reaction controlling parameter. The designed computational solver NNs-BLMS is implemented by performing training, testing and validation for the solution of TFFMFTDECR system for different variants. Variation of various physical parameters are designed via plots and explain in details. It is depicted that thin film thickness increases for higher values of disk rotation parameter, while it diminishes for higher magnetic parameter. Furthermore, higher values of Dufour number and the corresponding diminishing values of Soret number causes enhancement in fluid temperature profile. Further the effectiveness of NNs-BLMS is validated by comparing the results of the proposed solver and the standard solution of TFFMFTDECR model through error analyses, histogram representations and regression analyses.

MODELING AND CALIBRATION OF UNCERTAINTY IN MATERIAL PROPERTIES OF ADDITIVELY MANUFACTURED COMPOSITES

Simulations quantifying the uncertainty in structural response and damage evolution require accurate representation of the randomness of the underlying material stiffness and strength behaviors. In this paper, the mean and variance descriptions of variability of strength and stiffness of additively manufactured composite specimens are augmented with random field correlation descriptors that represent the process dependence on the property heterogeneity through microstructure variations. Two correlation lengths and a rotation parameter are introduced into randomized stiffness and strength distribution fields to capture the local heterogeneities in the microstructure of Additively Manufactured (AM) composites. We formulated a simulation and Artificial Intelligence (AI)-based technique to calibrate the correlation length and rotation parameter measures from relatively few samples of experimentally obtained strain field observations using Digital Image Correlation (DIC). The neural networks used for calibrating the correlation lengths of Karhunen-Loève Expansion (KL expansion) from the DIC images are trained using simulated stiffness and strength fields that have known correlation coefficients. A virtual DIC filter is used to add the noise and artifacts from typical DIC analysis to the simulated strain fields. A Deep Neural Network (DNN), whose architecture is optimized using Efficient Neural Architecture Search (ENAS), is trained on 150,000 simulated DIC images. The trained DNN is then used for calibration of KL expansion correlation lengths for additively manufactured composite specimens. The AM composites are loaded in tension and DIC images of the strain fields are generated and presented to the DNNs, which produce the correlation coefficients for the random fields as outputs. Compared to classical optimization methods to calibrate model parameters iteratively, neural networks, once trained, efficiently and quickly predict parameters without the need for a robust simulator and optimization methods.

Exploring the nanomechanical concepts of development through recent updates in magnetically guided system

This article outlines an analytical analysis of unsteady mixed bioconvection buoyancy-driven nanofluid thermodynamics and gyrotactic microorganisms motion in the stagnation domain of the impulsively rotating sphere with convective boundary conditions. To make the equations physically realistic, zero mass transfer boundary conditions have been used. The Brownian motion and thermophoresis effects are incorporated in the nanofluid model. Magnetic dipole effect has been implemented. A system of partial differential equations is used to represent thermodynamics and gyrotactic microorganisms motion, which is then transformed into dimensionless ordinary differential equations. The solution methodology is involved by homotopy analysis method. The results obtained are based on the effect of dimensionless parameters on the velocity, temperature, nanoparticles concentration and density of the motile microorganisms profiles. The primary velocity increases as the mixed convection and viscoelastic parameters are increased while it decreases as the buoyancy ratio, ferro-hydrodynamic interaction and rotation parameters are increased. The secondary velocity decreases as viscoelastic parameter increases while it increases as the rotation parameter increases. Temperature is reduced as the Prandtl number and thermophoresis parameter are increased. The nanoparticles concentration is increased as the Brownian motion parameter increases. The motile density of gyrotactic microorganisms increases as the bioconvection Rayleigh number, rotation parameter and thermal Biot number are increased.