相关论文: Regularization of spherical and axisymmetric evolu…

We present a formalism to obtain equilibrium configurations of uniformly rotating fluid in the second post-Newtonian approximation of general relativity. In our formalism, we need to solve 29 Poisson equations, but their source terms…

We give a constructive proof that coordinate transformations exist which raise the regularity of the gravitational metric tensor from $C^{0,1}$ to $C^{1,1}$ in a neighborhood of points of shock wave collision in General Relativity. The…

Smooth axially symmetric Helfrich topological spheres are either round or else they must satisfy a second order equation known as the reduced membrane equation [17]. In this paper, we show that, conversely, axially symmetric closed genus…

Axially symmetric solutions to the Navier-Stokes equations in a bounded cylinder are considered. On the boundary the normal component of the velocity and he angular components of the velocity and vorticity are assumed to vanish. If the norm…

Motivated by the gauge/gravity duality, we introduce a numerical scheme based on generalized harmonic evolution to solve the Einstein field equations on asymptotically anti-de Sitter (AdS) spacetimes. We work in global AdS5, which can be…

We present preliminary results in our long-term project of studying the evolution of matter in a dynamical spacetime. To achieve this, we have developed a new code to evolve axisymmetric initial data sets corresponding to a black hole…

We perform fully general relativistic simulations of rotating stellar core collapse in three spatial dimension. A parametric equation of state is adopted following Dimmelmeier et al. The early stage of the collapse is followed by an…

Geometric number systems, obtained by extending the real number system to include new anticommuting square roots of +1 and -1, provide a royal road to higher mathematics by largely sidestepping the tedious languages of tensor analysis and…

Robots exhibit a rich variety of symmetries arising from their mechanical structure and the properties of their tasks. Although many robotics problems exhibit several symmetries simultaneously, existing approaches typically treat them in…

Within a cosmological context, we study the behaviour of collisionless particles in the weak field approximation to General Relativity, allowing for large gradients of the fields and relativistic velocities for the particles. We consider a…

This is the first in a series of papers devoted to fully general-relativistic $N$-body simulations applied to late-time cosmology. The purpose of this paper is to present the combination of a numerical relativity scheme, discretization…

We present a new three-parameter family of self-consistent equilibrium models for quasi-relaxed stellar systems that are subject to the combined action of external tides and rigid internal rotation. These models provide an idealised…

We extend earlier numerical and analytical considerations of the conformally invariant wave equation on a Schwarzschild background from the case of spherically symmetric solutions, discussed in Class. Quantum Grav. 34, 045005 (2017), to the…

The relativistic time evolution of multi-layer spherically symmetric shell systems---consisting of infinitely thin shells separated by vacuum regions---is examined. Whenever two shells collide the evolution is continued with the assumption…

Here, we present a review about the quantization of spherically-symmetric spacetimes adopting loop quantum gravity techniques. Several models that have been studied so far share similar properties: the resolution of the classical…

We study numerically the fully nonlinear gravitational collapse of a self-gravitating, minimally-coupled, massless scalar field in spherical symmetry. Our numerical code is based on double-null coordinates and on free evolution of the…

In this paper we provide, first, a general symbolic algorithm for computing the symmetries of a given rational surface, based on the classical differential invariants of surfaces, i.e. Gauss curvature and mean curvature. In practice, the…

We deal with non-smooth differential systems $\dot{z}=X(z), z\in R^{n},$ with discontinuity occurring in a codimension one smooth surface $\Sigma$. A regularization of $X$ is a 1-parameter family of smooth vector fields…

Detailed observations of phenomena involving black holes, be it via gravitational waves or more traditional electromagnetic means, can probe the strong field regime of the gravitational interaction. The prediction of features in such…

The point-splitting renormalization method offers a prescription to calculate finite expectation values of quadratic operators constructed from quantum fields in a general curved spacetime. It has been recently shown by Levi and Ori that…