Related papers: Discrete Relativistic Positioning Systems
Binary pulsars provide an excellent system for testing general relativity because of their intrinsic rotational stability and the precision with which radio observations can be used to determine their orbital dynamics. Measurements of the…
The Kruskal-Szekeres coordinates construction for the Schwarzschild spacetime could be viewed geometrically as a squeezing of the $t$-line associated with the asymptotic observer into a single point, at the event horizon $r=2M$. Starting…
This research presents a novel method of determining relative bearing and elevation measurements, to a remote signal, that is suitable for implementation on small embedded systems - potentially in a GPS denied environment. This is an…
In this paper we seek static spherically symmetric solutions of Horava-Lifshitz-like gravity with projectability condition. We consider the most general form of gravity action without detailed balance, and require the spacetime metric to…
We employ Maxwell's equations formulated in Space-Time Algebra to perform discretization of moving geometries directly in space-time. All the derivations are carried out without any non-relativistic assumptions, thus the application area of…
Spontaneous collapse models are modifications of standard quantum mechanics in which a physical mechanism is responsible for the collapse of the wavefunction, thus providing a way to solve the so-called "measurement problem". The two most…
Between Snyder's quantized space-time model in de Sitter space of momenta and the \dS special relativity on \dS-spacetime of radius $R$ with Beltrami coordinates, there is a one-to-one dual correspondence supported by a minimum…
We prove the global asymptotic stability of the Minkowski space for the massless Einstein-Vlasov system in wave coordinates. In contrast with previous work on the subject, no compact support assumptions on the initial data of the Vlasov…
We revisit and improve the analytic study arXiv:1804.03462 of spherically symmetric but dynamical black holes in Einstein's gravity coupled to a real scalar field. We introduce a series expansion in a small parameter $\epsilon$ that…
In the former part, we study the gravitational collapse of pressureless dust and find special solutions, where, in both the physical and fiducial sectors, the exterior and interior spacetime geometries are given by the Schwarzschild…
PoseNet can map a photo to the position where it is taken, which is appealing in robotics. However, training PoseNet requires full supervision, where ground truth positions are non-trivial to obtain. Can we train PoseNet without knowing the…
By assuming a certain localized energy estimate, we prove the existence portion of the Strauss conjecture on asymptotically flat manifolds, possibly exterior to a compact domain, when the spatial dimension is 3 or 4. In particular, this…
A complete exposition of the rest-frame instant form of dynamics for arbitrary isolated systems (particles, fields, strings, fluids)admitting a Lagrangian description is given. The starting point is the parametrized Minkowski theory…
Accurate and robust extrinsic calibration is necessary for deploying autonomous systems which need multiple sensors for perception. In this paper, we present a robust system for real-time extrinsic calibration of multiple lidars in vehicle…
We discuss the Minkowski stability problem in modified gravity by using dynamical system approach. The method to investigate dynamical stability of Minkowski space was proposed. This method was applied for some modified gravity theories,…
Localization is a fundamental challenge for any wireless network of nodes, in particular when the nodes are mobile. We present an extension of the classical Multidimensional scaling (MDS) for an anchorless network of mobile nodes, wherein…
The present work describes an immersion in 5D of the interior Schwarzschild solution of the general relativity equations. The model theory is defined in the context of a flat 5D space time matter Minkowski model, using a Tolman like…
Space-time symmetries are a crucial ingredient of any theoretical model in physics. Unlike internal symmetries, which may or may not be gauged and/or spontaneously broken, space-time symmetries do not admit any ambiguity: they are gauged by…
The state of a non-relativistic gravitational dynamical system is known at any time $t$ if the dynamical rule, i.e. Newton's equations of motion, can be solved; this requires specification of the gravitational potential. The evolution of a…
The main constraint on relative position of geometric objects, used in spatial planning for computing the C-space maps (for example, in robotics, CAD, and packaging), is the relative non-overlapping of objects. This is the simplest…