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We model the general relativistic interaction of a small hyperelastic sphere with a Schwarzschild black hole as it follows an initially marginally-bound orbit through a close encounter. While the interaction reveals effects that are encoded by the Mathisson-Papapetrou-Dixon (MPD) multipolar equations through quadrupole order, the calculation is made using an independent general relativistic finite element scheme that we described earlier (Phys. Rev. D 108(8):084020, October 2023). The finite element calculation is done in Schwarzschild coordinates, following a large and scalable number of mass elements in interaction with each other through elastic forces derived from a potential energy function and with the spacetime geometry. After the fact, we analyze the dynamics using a local Fermi coordinate system, computing (1) the deviation of the center of mass of the body relative to the initial marginally-bound orbit, (2) changes in orbital and spin angular momenta, and (3) the decrease in orbital energy and accompanying deposition of energy into internal elastic dynamics. The interaction leads to the capture of the small body into a highly eccentric orbit (e ≃ 0.99998 in a sample calculation). 

Efforts are underway to accurately model extreme-mass-ratio inspirals for binaries with a spinning (Kerr) primary. At lowest order the adiabatic evolution depends on the radiation fluxes. Fluxes and other self-force quantities can be expanded analytically in post-Newtonian (PN) series allowing the early evolutionary phase to be understood. When it comes to more complicated background geodesic orbits, it proves useful to use the scalar field model problem to guide development and testing of techniques. In this paper, we present analytical expressions for the scalar fluxes from a scalar point charge in inclined-spherical orbit about a Kerr black hole up to 12PN relative order, with expressions that are exact in terms of the inclination parameter $x$and black hole spin $a$. The expressions are constructed using the Mano, Suzuki, and Takasugi method of solving the scalar wave equation in a Kerr background. We compare the numerical evaluation of these flux expressions to full numerical ( $s=0$) eukolsky code results, examining their degree of utility as the strong-field region is approached. 

Highly alloyed (Al,Gd)N is of potential interest in a variety of applications, including neutron detection and in devices such as non-volatile memory. Gd has been shown to have very low equilibrium solubility in AlN at room temperature; however, non-equilibrium deposition techniques such as sputtering are able to deposit thin films, which incorporate large amounts of Gd. Here, we characterize a highly-alloyed (Al,Gd)N combinatorial thin film grown by RF sputtering on a GaN substrate, looking for any evidence of chemical or phase segregation or structural disorder in the films. Compositions with between 13% and 32% Gd (on a cation basis) were studied. No evidence was found for chemical or phase segregation in any studied composition. Higher degrees of Gd incorporation led to greater structural disorder in the film and a tendency toward amorphization; however, electron diffraction shows that the film does not become fully amorphous at any of the studied compositions, instead retaining textured local order even at 32% Gd. Electron energy loss spectra suggest that the material retains a locally wurtzite-like tetrahedral bonding environment at all studied compositions. 

Abstract: The PostNewtonianSelfForce package provides a set of functions for working with post-Newtonian expansions in the self-force regime. See the package website for further details and installation instructions. What's New Add series for scalar field spherical orbits What's Changed Fixed issues with Schwarzschild eccentric redshift series in https://github.com/BlackHolePerturbationToolkit/PostNewtonianSelfForce/issues/7 and https://github.com/BlackHolePerturbationToolkit/PostNewtonianSelfForce/pull/8 Update README.md by @davidtrestini in https://github.com/BlackHolePerturbationToolkit/PostNewtonianSelfForce/pull/9 New Contributors @davidtrestini made their first contribution in https://github.com/BlackHolePerturbationToolkit/PostNewtonianSelfForce/pull/9 Full Changelog: https://github.com/BlackHolePerturbationToolkit/PostNewtonianSelfForce/compare/0.5.0...0.6.0 Other: If you use this software, please cite its Zenodo record and include the acknowledgment "This work makes use of the Black Hole Perturbation Toolkit." in any papers. 

Wurtzite $(\mathrm{Al},\mathrm{Sc})\mathrm{N}$ferroelectrics are attractive for microelectronics applications due to their chemical and structural compatibility with wurtzite semiconductors, such as $\mathrm{Ga}\mathrm{N}$and $(\mathrm{Al},\mathrm{Ga})\mathrm{N}$. However, the leakage current in epitaxial stacks reported to date should be reduced for reliable device operation. Here, we demonstrate low leakage current in epitaxial ${\mathrm{Al}}_{0.7}{\mathrm{Sc}}_{0.3}\mathrm{N}$films on $\mathrm{Ga}\mathrm{N}$with well-saturated ferroelectric hysteresis loops that are orders of magnitude lower (i.e., 0.07 A ${\mathrm{cm}}^{-2}$) than previously reported films (1–19 A ${\mathrm{cm}}^{-2}$) having similar or better structural characteristics. We also show that, for these high-quality epitaxial $(\mathrm{Al},\mathrm{Sc})\mathrm{N}$films, structural quality (edge and screw dislocations), as measured by diffraction techniques, is not the dominant contributor to leakage. Instead, the small leakage in our films is limited by thermionic emission across the interfaces, which is distinct from the large leakage due to trap-mediated bulk transport in the previously reported $(\mathrm{Al},\mathrm{Sc})\mathrm{N}$films. To support this conclusion, we show that ${\mathrm{Al}}_{0.7}{\mathrm{Sc}}_{0.3}\mathrm{N}$on lattice-matched ${\mathrm{In}}_{0.18}{\mathrm{Ga}}_{0.82}\mathrm{N}$buffers with improved structural characteristics but higher interface roughness exhibit increased leakage characteristics. This demonstration of low leakage current in heteroepitaxial $(\mathrm{Al},\mathrm{Sc})\mathrm{N}$films and understanding of the importance of interface barrier and surface roughness can guide further efforts toward improving the reliability of wurtzite ferroelectric devices. Published by the American Physical Society2025 

We present a numerical framework for modeling extended hyperelastic bodies based on a Lagrangian formulation of general relativistic elasticity theory. We use finite element methods to discretize the body, then use the semidiscrete action to derive ordinary differential equations of motion for the discrete nodes. The nodes are evolved in time using fourth-order Runge-Kutta. We validate our code against the normal modes of oscillation of a hyperelastic sphere, which are known analytically in the limit of small (linear), slow (Newtonian) oscillations. The algorithm displays second order convergence. This numerical framework can be used to obtain the orbital motion and internal dynamics of a hyperelastic body of any shape, for any spacetime metric, and for varying hyperelastic energy models 

We calculate the high-order post-Newtonian (PN) expansion of the energy and angular momentum fluxes onto the horizon of a nonspinning black hole primary in eccentric-orbit extreme-mass-ratio inspirals. The first-order black hole perturbation theory calculation uses Mathematica and makes an analytic expansion of the Regge-Wheeler-Zerilli functions using the Mano-Suzuki-Takasugi formalism. The horizon absorption, or tidal heating and torquing, is calculated to 18PN relative to the leading horizon flux (i.e., 22PN order relative to the leading quadrupole flux at infinity). Each PN term is a function of eccentricity e and is calculated as a series to e10. A second expansion, to 10PN horizon-relative order (or 14PN relative to the flux at infinity), is computed deeper in eccentricity to e20. A number of resummed closed-form functions are found for the low PN terms in the series. Using a separate Teukolsky perturbation code, numerical comparisons are made to test how accurate the PN expansion is when extended to a close p =10 orbit. We find that the horizon absorption expansion is not as convergent as a previously computed infinity-side flux expansion. However, given that the horizon absorption is suppressed by 4PN, useful results can be obtained even with an orbit as tight as this for e ≲1 /2 . Combining the present results with our earlier expansion of the fluxes to infinity makes the knowledge of the total dissipation known to 19PN for eccentric-orbit nonspinning extreme-mass-ratio inspirals.