Related papers: Junctions and thin shells in general relativity us…
We formulate the junction conditions for Scalar-Tensor-Vector Gravity (STVG/MOG), proposed by J.~W.~Moffat. Using these conditions, the theory of gravitational collapse is constructed. In the collapsing process, an interior…
We construct generic spherically symmetric thin-shell gravastars by using the cut-and-paste procedure. We take considerable effort to make the analysis as general and unified as practicable; investigating both the internal physics of the…
Real algebraic geometry adapts the methods and ideas from (complex) algebraic geometry to study the real solutions to systems of polynomial equations and polynomial inequalities. As it is the real solutions to such systems modeling…
We propose a containment query that is robust to the watertightness of regions bound by trimmed NURBS surfaces, as this property is difficult to guarantee for in-the-wild CAD models. Containment is determined through the generalized winding…
We present GRAMSES, a new pipeline for nonlinear cosmological $N$-body simulations in General Relativity (GR). This code adopts the Arnowitt-Deser-Misner (ADM) formalism of GR, with constant mean curvature and minimum distortion gauge…
The method of refined algebraic quantization of constrained systems which is based on modification of the inner product of the theory rather than on imposing constraints on the physical states is generalized to the case of constrained…
Interpreting gravitational wave observations and understanding the physics of astrophysical compact objects such as black holes or neutron stars requires accurate theoretical models. Here, we present a new numerical relativity computer…
We propose a second order, fully semi-Lagrangian method for the numerical solution of systems of advection-diffusion-reaction equations, which employs a semi-Lagrangian approach to approximate in time both the advective and the diffusive…
We present some Maple procedures using the GrTensorII package for teaching purposes in the study of the canonical version of the general relativity based on the ADM formalism
We discuss three applications of a gauge theory of gravity to rotating astrophysical systems. The theory employs gauge fields in a flat Minkowski background spacetime to describe gravitational interactions. The iron fluorescence line…
The double wall-ring (DWR) rotational configuration is nowadays the instrument of choice regarding interfacial shear rheometers (ISR) in rotational configurations. Complex numerical schemes must be used in the analysis of the output data in…
In 2000, Darmon described a program to study the generalized Fermat equation using modularity of abelian varieties of $\mathrm{GL}_2$-type over totally real fields. The original approach was based on hard open conjectures, which have made…
Understanding the behavior and evolution of a dynamical many-body system by analyzing patterns in their experimentally captured images is a promising method relevant for a variety of living and non-living self-assembled systems. The arrays…
Current Lagrangian (particle-tracking) algorithms used to simulate diffusion-reaction equations must employ a certain number of particles to properly emulate the system dynamics---particularly for imperfectly-mixed systems. The number of…
In the context of extended Teleparallel gravity theories, we address the issue of junction conditions required to guarantee the correct matching of different regions of spacetime. In the absence of shells/branes, these conditions turn out…
We consider the numerical discretization of the time-domain Maxwell's equations with an energy-conserving discontinuous Galerkin finite element formulation. This particular formulation allows for higher order approximations of the electric…
We construct a rotating thin-shell wormhole using a Myers-Perry black hole in five dimensions, using the Darmois-Israel junction conditions. The stability of the wormhole is analyzed under perturbations. We find that exotic matter is…
We study the general dynamics of the spherically symmetric gravitational collapse of a massless scalar field. We apply the Galerkin projection method to transform a system of partial differential equations into a set of ordinary…
We review recent developments and results in testing general relativity (GR) at cosmological scales. The subject has witnessed rapid growth during the last two decades with the aim of addressing the question of cosmic acceleration and the…
This is a first graduate course in algebraic geometry. It aims to give the student a lift up into the subject at the research level, with lots of interesting topics taken from the classification of surfaces, and a human-oriented discussion…