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In this thesis, we study the structure of Group Field Theories (GFTs) from the point of view of renormalization theory. Such quantum field theories are found in approaches to quantum gravity related to Loop Quantum Gravity (LQG) on the one…
This paper presents a practical and scalable grid-based state estimation method for high-dimensional models with invertible linear dynamics and with highly non-linear measurements, such as the nearly constant velocity model with…
An analytical expression is derived for the rate of gravitational Faraday rotation measured by Eulerian observers. The reference frame is a Fermi-Walker triad aligned with the spatial wave vector. Attention is restricted to the ADM split of…
This paper investigates charged particle deflection in a Kerr spacetime background with a dipole magnetic field, focusing on the equatorial plane and employing the weak field approximation. We employ the Jacobi-Randers metric to unify the…
All powered spacecraft experience residual systematic acceleration due to anisotropy of the thermal radiation pressure and fuel leakage. The residual acceleration limits the accuracy of any test of gravity that relies on the precise…
We develop a novel approach to gravity that we call `matrix general relativity' (MGR) or `gravitational chromodynamics' (GCD or GQCD for quantum version). Gravity is described in this approach not by one Riemannian metric (i.e. a symmetric…
With advanced X-ray source and detector technologies being continuously developed, non-traditional CT geometries have been widely explored. Generalized-Equiangular Geometry CT (GEGCT) architecture, in which an X-ray source might be…
Recent feed-forward networks have achieved remarkable progress in sparse-view 3D reconstruction by predicting dense point maps directly from RGB images. However, they often suffer from geometric inconsistencies and limited fine-grained…
A new scalar measure of the gyrotropy of a pressure tensor is defined. Previously suggested measures are shown to be incomplete by means of examples for which they give unphysical results. To demonstrate its usefulness as an indicator of…
The advanced world-wide network of gravitational waves (GW) observatories is scheduled to begin operations within the current decade. Thanks to their improved sensitivity, they promise to yield a number of detections and thus to open a new…
In a previous article [Phys. Rev. D 82 104040 (2010)], we derived an energy-momentum tensor for linear gravity that exhibited positive energy density and causal energy flux. Here we extend this framework by localizing the angular momentum…
In the tensor network approach to statistical physics, properties of the critical point of a 2D lattice model are encoded by a four-legged tensor which is a fixed point of an RG map. The traditional way to find the fixed point tensor…
The center of gravity as an algorithm for position measurements is analyzed for a two-dimensional geometry. Several mathematical consequences of discretization for various types of detector arrays are extracted. Arrays with rectangular,…
The task of strapdown inertial navigation system (SINS) initial alignment is to calculate the attitude transformation matrix from body frame to navigation frame. In this paper, such attitude transformation matrix is divided into two parts…
The metric-affine gravity provides a useful framework for analyzing gravitational dynamics since it treats metric tensor and affine connection as fundamentally independent variables. In this work, we show that, a metric-affine gravity…
The determination of the absolute and relative position of a spacecraft is critical for its operation, observations, data analysis, scientific studies, as well as deep space exploration in general. A spacecraft that can determine its own…
The emergence of quantum technologies, including cold atom based accelerometers, offers an opportunity to improve the performances of space geodesy missions. In this context, CNES initiated an assessment study called GRICE (GRadiom\'etrie…
We study a method to induce resonant transitions between antihydrogen ($\bar{H}$) quantum states above a material surface in the gravitational field of the Earth. The method consists of applying a gradient of magnetic field, which is…
In this paper, we adopt minimal gravitational decoupling scheme to extend a non-static spherically symmetric isotropic composition to anisotropic interior in…
In this paper, we study the \texttt{Ehlers' transformation} (sometimes called gravitational duality rotation) for \texttt{reciprocal} static metrics. First we introduce the concept of reciprocal metric. We prove a theorem which shows how we…