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We examine the relative performance of algorithms for the calculation of curvature in spacetime. The classical coordinate component method is compared to two distinct versions of the Newman-Penrose tetrad approach for a variety of…
Quantum computers have long been expected to efficiently solve complex classical differential equations. Most digital, fault-tolerant approaches use Carleman linearization to map nonlinear systems to linear ones and then apply quantum…
We develop quantum electrodynamics into a kinetic-theory-like evolution equation for electrons, positrons and photons. To keep the "collision rules" simple, we make use of longitudinal and temporal photons in addition to the usual…
The paper presents equations determining the particle spin evolution in the post-Newtonian approximation in the problem of motion of two mass and spin possessing particles. The equations are derived with the Einstein-Infeld-Hoffmann method…
In this work, we introduce a fast numerical algorithm to solve the time-dependent radiative transport equation (RTE). Our method uses the integral formulation of RTE and applies the treecode algorithm to reduce the computational complexity…
Parton distribution functions and hadronic tensors may be computed on a universal quantum computer without many of the complexities that apply to Euclidean lattice calculations. We detail algorithms for computing parton distribution…
We consider the Dirac equation coupled to an external electromagnetic field in curved four-dimensional spacetime with a given timelike worldline $\gamma$ representing a classical clock. We use generalised Fermi normal coordinates in a…
The geodesics of Kerr's metric are described by the four-dimensional Hamiltonian dynamics integrable in the Arnold--Liouville sense. It can be reduced to two-dimensional one by the use of Fermat's principle. The resulting Hamiltonian is,…
Stars near the Galactic center reach a few percent of light speed during pericenter passage, which makes post-Newtonian effects potentially detectable. We formulate the orbit equations in Hamiltonian form such that the $O(v^2/c^2)$ and…
The astrophysics of compact objects, which requires Einstein's theory of general relativity for understanding phenomena such as black holes and neutron stars, is attracting increasing attention. In general relativity, gravity is governed by…
We construct a new type of Chandrasekhar transformation in Kerr spacetime using the different tortoise coordinate, which is useful for exact analysis to study Teukolsky equation with arbitrary frequency. We also give the interpretation of…
We propose a Fast Marching based implementation for computing sub-Riemanninan (SR) geodesics in the roto-translation group SE(2), with a metric depending on a cost induced by the image data. The key ingredient is a Riemannian approximation…
Starting from the Mandelstam-Leibbrandt prescription, we introduce a general rule for the null vector $\bar{n}$ to compute any $SIM(2)$ integral and diagram with an arbitrary number of external legs. Using the new prescription, the…
The studies of influence of spin on a photon's motion in a Schwartzschild spacetime is continued. In the previous paper [13] the first order correction to the geodesic motion is found for the first half of the photon world line. The system…
A new Kerr-like metric with quadrupole moment is obtained by means of perturbing the Kerr spacetime. The form of this new metric is simple as the Kerr metric. By comparison with the exterior Hartle-Thorne metric, it is shown that it could…
Closed optical trajectories in Kerr spacetime are engineered to exhibit a marked lack of symmetry. The eccentricity manifests as a holonomy in gravitational Faraday rotation that can be made arbitrarily large by radial translation of the…
The transition from reversible microdynamics to irreversible transport can be studied very efficiently with the help of the so-called projection method. We give a concise introduction to that method, illustrate its power by using it to…
Complete sequences of new analytic solutions of Einstein's equations which describe thin super massive disks are constructed. These solutions are derived geometrically. The identification of points across two symmetrical cuts through a…
We report on a new capability added to our general relativistic radiation-magnetohydrodynamics code, Cosmos++: an implicit Monte Carlo (IMC) treatment for radiation transport. The method is based on a Fleck-type implicit discretization of…
The equations governing null and timelike geodesics are derived within the 3+1 formalism of general relativity. In addition to the particle's position, they encompass an evolution equation for the particle's energy leading to a 3+1…