相关论文: The Vector Volume and Black Holes
Numerical tests of volume formulae are presented to compute efficiently the volume enclosed between flux surfaces for integrable 3D vector fields with various degrees of symmetry. In the process, a new case is proposed and tested.
We present a new approach to the study of vacuum spacetimes with a Killing symmetry. The central quantity in this approach is the exterior derivative of the Killing vector field, which is a test electromagnetic field. Considering the…
We construct an asymptotically flat Morris-Thorne wormhole solution supported by anisotropic matter fluid and a vector field which is coupled to gravity in a non-minimal way with broken Abelian gauge symmetry. In this paper, a specific…
Vector resonant relaxation (VRR) is known to be the fastest gravitational process that shapes the geometry of stellar orbits in nuclear star clusters. This leads to the realignment of the orbital planes on the corresponding VRR time scale…
In his calculation of the spacetime volume of a small Alexandrov interval in 4 dimensions Myrheim introduced a term which he referred to as a surface integral [1]. The evaluation of this term has remained opaque and led subsequent authors…
Scale invariance is considered in the context of gravitational theories where the action, in the first order formalism, is of the form $S = \int L_{1} \Phi d^4x$ + $\int L_{2}\sqrt{-g}d^4x$ where the volume element $\Phi d^4x$ is…
In spite of considerable progress, computing curvature in Volume of Fluid (VOF) methods continues to be a challenge. The goal is to develop a function or a subroutine that returns the curvature in computational cells containing an interface…
This article reports on three-dimensional (3-D) MHD simulations of non-rotating and rapidly rotating black holes and the adjacent black hole accretion disk magnetospheres. A particular emphasis is placed on the vertical magnetic flux that…
The convex hull of several i.i.d. beta distributed random vectors in $\mathbb R^d$ is called the random beta polytope. Recently, the expected values of their intrinsic volumes, number of faces, normal and tangent angles and other quantities…
Consider vector valued harmonic maps of at most linear growth, defined on a complete non-compact Riemannian manifold with non-negative Ricci curvature. For the norm square of the pull-back of the target volume form by such maps, we report a…
We describe 4D evaporating black holes as quantum field configurations by solving the semi-classical Einstein equation $G_{\mu\nu}=8\pi G \langle \psi|T_{\mu\nu}|\psi \rangle$ and quantum matter fields in a self-consistent manner. As the…
We consider a one-brane probe in the presence of a five-dimensional black hole in the classical limit. The velocity-dependent force on a slowly-moving probe is characterized by a metric on the probe moduli space. This metric is computed for…
We introduce an adelic Cartier divisor over a trivially valued field and discuss the bigness of it. For bigness, we give the integral representation of the arithmetic volume and prove the existence of limit of it. Moreover, we show that the…
We study the global distribution and morphology of dark matter voids in a LCDM universe using density fields generated by N-body simulations. Voids are defined as isolated regions of the low-density excursion set specified via density…
Given a basic compact semi-algebraic set $\K\subset\R^n$, we introduce a methodology that generates a sequence converging to the volume of $\K$. This sequence is obtained from optimal values of a hierarchy of either semidefinite or linear…
We compute the volumes of convex bodies that are given by inequalities of concave polynomials. These volumes are found to arbitrary precision thanks to the representation of periods by linear differential equations. Our approach rests on…
Given a finite metric CW complex $X$ and an element $\alpha \in \pi_n(X)$, what are the properties of a geometrically optimal representative of $\alpha$? We study the optimal volume of $k\alpha$ as a function of $k$. Asymptotically, this…
The classical cosmological V/Vm-test is introduced and elaborated. Use of the differential distribution p(V/Vm) of the V/Vm-variable rather than just the mean <V/Vm> leads directly to the cosmological number density without any need for…
In this work, we focus on the dynamics of a massive one-form field, \textbf{B}, often referred to simply as a vector field, that is minimally coupled to standard Einstein gravity. In the framework of four-dimensional spacetimes, the theory…
We first present an overview of the Schwarzschild vacuum spacetime within general relativity, with particular emphasis on the role of scalar polynomial invariants and the null frame approach (and the related Cartan invariants), that…