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Abstract Systems consisting of spheres rolling on elastic membranes have been used to introduce a core conceptual idea of General Relativity: how curvature guides the movement of matter. However, such schemes cannot accurately represent relativistic dynamics in the laboratory because of the dominance of dissipation and external gravitational fields. Here we demonstrate that an “active” object (a wheeled robot), which moves in a straight line on level ground and can alter its speed depending on the curvature of the deformable terrain it moves on, can exactly capture dynamics in curved relativistic spacetimes. Via the systematic study of the robot’s dynamics in the radial and orbital directions, we develop a mapping of the emergent trajectories of a wheeled vehicle on a spandex membrane to the motion in a curved spacetime. Our mapping demonstrates how the driven robot’s dynamics mix space and time in a metric, and shows how active particles do not necessarily follow geodesics in the real space but instead follow geodesics in a fiducial spacetime. The mapping further reveals how parameters such as the membrane elasticity and instantaneous speed allow the programming of a desired spacetime, such as the Schwarzschild metric near a non-rotating blackhole. Our mapping and framework facilitate creation of a robophysical analog to a general relativistic system in the laboratory at low cost that can provide insights into active matter in deformable environments and robot exploration in complex landscapes. 

Abstract Mechanisms have been proposed to enhance the merger rate of stellar-mass black hole binaries, such as the Von Zeipel–Lidov–Kozai mechanism (vZLK). However, high inclinations are required in order to greatly excite the eccentricity and to reduce the merger time through vZLK. Here, we propose a novel pathway through which compact binaries could merge due to eccentricity increase in general, including in a near coplanar configuration. Specifically, a compact binary migrating in an active galactic nucleus disk could be captured in an evection resonance, when the precession rate of the binary equals the orbital period around the supermassive black hole. In our study we include precession due to first-order post-Newtonian precession as well as that due to disk around one or both components of the binary. Eccentricity is excited when the binary sweeps through the resonance, which happens only when it migrates on a timescale 10–100 times the libration timescale of the resonance. Libration timescale decreases as the mass of the disk increases. The eccentricity excitation of the binary can reduce the merger timescale by up to a factor of ∼10 3−5 . 

Abstract Systems with ultra-short-period (USP) planets tend to possess larger mutual inclinations compared to those with planets located farther from their host stars. This could be explained due to precession caused by stellar oblateness at early times when the host star was rapidly spinning. However, stellar oblateness reduces over time due to the decrease in the stellar rotation rate, and this may further shape the planetary mutual inclinations. In this work, we investigate in detail how the final mutual inclination varies under the effect of a decreasing J 2 . We find that different initial parameters (e.g., the magnitude of J 2 and planetary inclinations) will contribute to different final mutual inclinations, providing a constraint on the formation mechanisms of USP planets. In general, if the inner planets start in the same plane as the stellar equator (or coplanar while misaligned with the stellar spin axis), the mutual inclination decreases (or increases then decreases) over time due to the decay of the J 2 moment. This is because the inner orbit typically possesses less orbital angular momentum than the outer ones. However, if the outer planet is initially aligned with the stellar spin while the inner one is misaligned, the mutual inclination nearly stays the same. Overall, our results suggest that either USP planets formed early and acquired significant inclinations (e.g., ≳30° with its companion or ≳10° with its host star spin axis for Kepler-653 c) or they formed late (≳Gyr) when their host stars rotated slower. 

ABSTRACT Having a massive moon has been considered as a primary mechanism for stabilized planetary obliquity, an example of which being our Earth. This is, however, not always consistent with the exoplanetary cases. This article details the discovery of an alternative mechanism, namely that planets orbiting around binary stars tend to have low spin-axis variations. This is because the large quadrupole potential of the stellar binary could speed up the planetary orbital precession, and detune the system out of secular spin-orbit resonances. Consequently, habitable zone planets around the stellar binaries in low inclination orbits hold higher potential for regular seasonal changes comparing to their single star analogues. 

Abstract HD 106906 is a planetary system that hosts a wide-orbit companion, as well as an eccentric and flat debris disk, which hold important constraints on its formation and subsequent evolution. The recent observations of the companion constrain its orbit to be eccentric and inclined relative to the plane of the debris disk. Here, we show that, in the presence of the inclined companion, the debris disk quickly (≲5 Myr) becomes warped and puffy. This suggests that the current configuration of the system is relatively recent. We explore the possibility that a recent close encounter with a free-floating planet could produce a companion with orbital parameters that agree with observations of HD 106906 b. We find that this scenario is able to recreate the structure of the debris disk while producing a companion in agreement with observation.