Related papers: Higher Conservation Law for the Multi-Centre Metri…
The multi-centre metrics are a family of euclidean solutions of the empty space Einstein equations with self-dual curvature. For this full class, we determine which metrics do exhibit an extra conserved quantity quadratic in the momenta,…
We consider a class of axially symmetric solutions to Einstein's equations incorporating a $\theta$-dependent scalar field and extend these solutions by introducing electric and magnetic charges via Harrison transformations. Subsequently,…
Hidden symmetries of generalized Kaluza-Klein-type metrics are studied using van Holten's systematic analysis \cite{vH} based on Killing tensors. Applied to generalized Taub-NUT metrics, Kepler-type symmetries with associated…
A numerical scheme is developed for systems of conservation laws on manifolds which arise in high speed aerodynamics and magneto-aerodynamics. The systems are presented in an arbitrary coordinate system on the manifold and involve source…
We classify super-symmetric solutions of the minimal $N=2$ gauged Euclidean supergravity in four dimensions. The solutions with anti-self-dual Maxwell field give rise to anti-self-dual Einstein metrics given in terms of solutions to the…
Axially symmetric stationary metrics governed by the Einstein-Euler equations for slowly rotating perfect fluids have been constructed in an arbitrarily large bounded domain containing the support of the mass density. However the problem of…
We investigate solutions of the classical Einstein or supergravity equations that solve any set of quantum corrected Einstein equations in which the Einstein tensor plus a multiple of the metric is equated to a symmetric conserved tensor…
The Cauchy problem for the complete Euler system is in general ill posed in the class of admissible (entropy producing) weak solutions. This suggests there might be sequences of approximate solutions that develop fine scale oscillations.…
It is well known that any 4-dimensional hyperkahler metric with two commuting Killing fields may be obtained explicitly, via the Gibbons-Hawking Ansatz, from a harmonic function invariant under a Killing field on R^3. In this paper, we find…
A new methodology is developed to integrate numerically the equations of motion for classical many-body systems in molecular dynamics simulations. Its distinguishable feature is the possibility to preserve, independently on the size of the…
We present a construction of complete self-dual Einstein metrics of negative scalar curvature on an uncountable family of manifolds of infinite topological type, which are enumerated by continued fraction expansions of irrational numbers.…
We investigate entanglement properties at quantum phase transitions of an integrable extended Hubbard model in the momentum space representation. Two elementary subsystems are recognized: the single mode of an electron, and the pair of…
High-order accurate, $\textit{entropy stable}$ numerical methods for hyperbolic conservation laws have attracted much interest over the last decade, but only a few rigorous convergence results are available, particularly in multiple space…
In finite-dimensional dynamical systems, stochastic stability provides the selection of physical relevant measures from the myriad invariant measures of conservative systems. That this might also apply to infinite-dimensional systems is the…
We study the dynamics of the Gaudin magnet ("central-spin model") using machine-learning methods. This model is of practical importance, e.g., for studying non-Markovian decoherence dynamics of a central spin interacting with a large bath…
We study Hermitian metrics with constant second scalar curvature on compact manifolds. We first consider a Yamabe-type problem for the second Bismut scalar curvature under a natural topological condition, and then analyze elliptic equations…
A new class of higher-dimensional exact solutions of Einstein's vacuum equation is presented. These metrics are written in terms of the exponential of a symmetric matrix and when this matrix is diagonal the solution reduces to…
In this paper we show how Einstein metrics are naturally described using the quantization of the algebra of functions on a Kahler manifold M. In this setup one interprets M as the phase space itself, equipped with the Poisson brackets…
On a spacetime $(M,g)$ endowed with a density function $h$, we consider the vacuum weighted Einstein field equations: \[h\rho-\operatorname{Hes}_h+\Delta h g=0.\] First, it is shown that the equation characterizes critical metrics for an…
Stable numerical simulations for a hyperbolic system of conservation laws of relaxation type but not in divergence form are obtained by incorporating the physical entropy into the simulations. The entropy balance is utilized as an…