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For any configuration of a static plane-symmetric distribution of matter along space-time, there are coordinates where the metric can be put explicitly as a functional of the energy density and pressures. It satisfies Einstein equations as…
Online augmentation of an oblique aerial image sequence with structural information is an essential aspect in the process of 3D scene interpretation and analysis. One key aspect in this is the efficient dense image matching and depth…
The direct gravimetry problem is solved using the subdivision of each body of a deposit into a set of vertical adjoining bars, and in the inverse problem each body of a deposit is modeled by a uniform ellipsoid of revolution (spheroid).…
General relativity can be presented in terms of other geometries besides Riemannian. In particular, teleparallel geometry (i.e., curvature vanishes) has some advantages, especially concerning energy-momentum localization and its…
Accurate weather and climate prediction relies on data assimilation (DA), which estimates the Earth system state by integrating observations with models. While exascale computing has significantly advanced earth simulation, scalable and…
I propose that the proper framework for gravitational scattering theory is the rep- resentation theory of the super-BMS algebra of Awada, Gibbons and Shaw[1], and its generalizations. Certain representation spaces of these algebras…
We propose and investigate a numerical shooting method for computing geodesics in the Weil-Petersson ($WP$) metric on the universal Teichm\"uller space T(1). This space, or rather the coset subspace $\PSL_2(\R)\backslash\Diff(S^1)$, has…
Detecting and confirming terrestrial planets is incredibly difficult due to their tiny size and mass relative to Sun-like host stars. However, recent instrumental advancements are making the detection of Earth-like exoplanets…
Gravitating bodies significantly alter the flow pattern (density and velocity) of the gas that attempts to stream past. Still, small protoplanets in the Mars--super-Earth range can only bind limited amounts of nebular gas; until the…
Atmospheric refraction affects to various degrees exoplanet transit, lunar eclipse, as well as stellar occultation observations. Exoplanet retrieval algorithms often use analytical expressions for the column abundance along a ray traversing…
Using a three-dimensional general circulation model, we show that the atmospheric dynamics on a tidally locked Earth-like exoplanet, simulated with the planetary and orbital parameters of Proxima Centauri b, support a longitudinally…
We develop a generalized projective gauge theory of gravity and spinorial matter, incorporating both non-metricity and torsion. The work is divided into three parts. Part I provides a thorough review of General Relativity, Metric-Affine…
Gas giants are the most readily detectable exoplanets but fundamental questions about their system architectures, formation, migration, and atmospheres have been unanswerable with the current generation of ground- and space-based…
Tropical Geometry and Mathematical Morphology share the same max-plus and min-plus semiring arithmetic and matrix algebra. In this chapter we summarize some of their main ideas and common (geometric and algebraic) structure, generalize and…
In the restricted four-body problem consisting of the Earth, the Moon and the Sun as the primaries and a spacecraft as the planetoid, we take into account the solar perturbation in the description of the motion of a spacecraft in the…
We present a simplified expression for the gravitational angular momentum in the framework of the teleparallel equivalent of general relativity (TEGR). The expression arises from the constraints equations of the Hamiltonian formulation of…
Tetrahedral configurations of spacecraft on unperturbed heliocentric orbits allow for highly precise observations of small spatial changes in the gravitational field, especially those affecting the gravity gradient tensor (GGT). The…
Given two distributions $P$ and $S$ of equal total mass, the Earth Mover's Distance measures the cost of transforming one distribution into the other, where the cost of moving a unit of mass is equal to the distance over which it is moved.…
Let $\Omega\subset\mathbb{R}^{n+1}$ have minimal Gaussian surface area among all sets satisfying $\Omega=-\Omega$ with fixed Gaussian volume. Let $A=A_{x}$ be the second fundamental form of $\partial\Omega$ at $x$, i.e. $A$ is the matrix of…
Bearing the thermodynamic arguments together with the two definitions of mass in mind, we try to find metrics with spherical symmetry. We consider the adiabatic condition along with the Gong-Wang mass, and evaluate the $g_{rr}$ element…