Geodesic properties in terms of multipole moments in scalar-tensor theories of gravity

The formalism for describing a metric and the corresponding scalar in terms of multipole moments has recently been developed for scalar-tensor theories. We take advantage of this formalism in order to obtain expressions for the observables that characterise geodesics in terms of the moments. These expressions provide some insight into how the structure of a scalarized compact object affects observables. They can also be used to understand how deviations from general relativity are imprinted on the observables.Comment: 16 page

Multipole moments in scalar-tensor theory of gravity

Stationary, asymptotically flat spacetimes in general relativity can be characterized by their multipole moments. The moments have proved to be very useful tools for extracting information about the spacetime from various observables and, more recently, for establishing universalities in the structure of neutron stars. As a first step toward extending these methods beyond general relativity, we develop the formalism that allows one to define and calculate the multipole moments in scalar-tensor theories of gravity.Comment: 12 pages, references added, accepted for publication as a Regular Article in Physical Review

Matching of analytical and numerical solutions for neutron stars of arbitrary rotation

We demonstrate the results of an attempt to match the two-soliton analytical solution with the numerically produced solutions of the Einstein field equations, that describe the spacetime exterior of rotating neutron stars, for arbitrary rotation. The matching procedure is performed by equating the first four multipole moments of the analytical solution to the multipole moments of the numerical one. We then argue that in order to check the effectiveness of the matching of the analytical with the numerical solution we should compare the metric components, the radius of the innermost stable circular orbit ($R_{ISCO}$), the rotation frequency $\Omega\equiv\frac{d\phi}{dt}$ and the epicyclic frequencies $\Omega_{\rho},\;\Omega_z$. Finally we present some results of the comparison.Comment: Contribution at the 13th Conference on Recent Developments in Gravity (NEB XIII), corrected typo in $M_4$ of eq. 5 of the published versio

Energy-Aware, Collision-Free Information Gathering for Heterogeneous Robot Teams

This paper considers the problem of safely coordinating a team of sensor-equipped robots to reduce uncertainty about a dynamical process, where the objective trades off information gain and energy cost. Optimizing this trade-off is desirable, but leads to a non-monotone objective function in the set of robot trajectories. Therefore, common multi-robot planners based on coordinate descent lose their performance guarantees. Furthermore, methods that handle non-monotonicity lose their performance guarantees when subject to inter-robot collision avoidance constraints. As it is desirable to retain both the performance guarantee and safety guarantee, this work proposes a hierarchical approach with a distributed planner that uses local search with a worst-case performance guarantees and a decentralized controller based on control barrier functions that ensures safety and encourages timely arrival at sensing locations. Via extensive simulations, hardware-in-the-loop tests and hardware experiments, we demonstrate that the proposed approach achieves a better trade-off between sensing and energy cost than coordinate-descent-based algorithms.Comment: To appear in Transactions on Robotics; 18 pages and 16 figures. arXiv admin note: text overlap with arXiv:2101.1109

Comparison of Branching Ratio and Sum-Rule Analyses of Magnetic Circular Dichroism in X-Ray-Absorption Spectroscopy

Two localized picture methods of analyzing the magnetic circular dichroism in x-ray absorption will be applied to experimental results: the branching ratio (BR) and sum rule (SR) approaches. A derivation of the BR formulas and detailed comparison to the SR expressions will be made, including error estimations. The BR approach will be seen to be a limiting case form of the SR spin-moment expression and provide a simple picture of the underlying physics in magnetic x-ray circular dichroism absorption in 3d magnetic materials