相关论文: Variational Principles in General Relativity

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 variational principle for a spherical configuration consisting of a thin spherical dust shell in gravitational field is constructed. The principle is consistent with the boundary-value problem of the corresponding Euler-Lagrange…

In this work, a second order smoothed particle hydrodynamics is derived for the study of relativistic heavy ion collisions. The hydrodynamical equation of motion is formulated in terms of the variational principle. In order to describe the…

Gravitational wave (GW) astronomy has consolidated its role as a new observational window to reveal the properties of compact binaries in the Universe. In particular, the discovery of the first binary neutron star coalescence, GW170817, led…

We advance a variational method to prove qualitative properties such as symmetries, monotonicity, upper and lower bounds, sign properties, and comparison principles for a large class of doubly-nonlinear evolutionary problems including…

We integrate the third and a half post-Newtonian equations of motion for a fully generic binary black hole system, allowing both for non-circular orbits, and for one or both of the black holes to spin, in any orientation. Using the second…

(Abbreviated) We extend the results of our 2021 paper concerning the problem of tidal evolution of a binary system with a rotating primary component with rotation axis arbitrarily inclined with respect to the orbital plane. Only the…

We present a new numerical scheme for solving the initial value problem for quasiequilibrium binary neutron stars allowing for arbitrary spins. We construct sequences of circular-orbit binaries of varying separation, keeping the rest mass…

With the dual variational principle and the saddle point reduction we use the abstract bifurcation theory recently developed by author in previous work to prove many new bifurcation results for solutions of four types of Hamiltonian…

We consider the evolution in full general relativity of a family of linearly unstable isolated spherical neutron stars under the effects of very small, perturbations as induced by the truncation error. Using a simple ideal-fluid equation of…

Inspiralling binary systems of neutron stars or black holes are promising sources of gravitational radiation detectable by large-scale laser interferometric gravitational observatories, such as the US LIGO and Italian-French VIRGO projects.…

The precise modeling of binary black hole coalescences in generic planar orbits is a crucial step to disentangle dynamical and isolated binary formation channels through gravitational-wave observations. The merger regime of such…

I describe the current status of a collaboration with J.D. Romano, R.H. Price, and W. Krivan to model the geometry of and gravitational radiation emitted by a binary system of compact objects in the regime where non-perturbative…

In this paper, we use a generic and general variational method to obtain solutions to the flow of generalized Newtonian fluids through circular pipes and plane slits. The new method is not based on the use of the Euler-Lagrange variational…

This article develops dual variational formulations for a large class of models in variational optimization. The results are established through basic tools of functional analysis, convex analysis and duality theory. The main duality…

In the last five years, gravitational-wave astronomy has gone from a purely theoretical field into a thriving experimental science. Many gravitational-wave signals, emitted by stellar-mass binary black holes and binary neutron stars, have…

We discuss the initial value problem of general relativity in its recently unified Lagrangian and Hamiltonian pictures and present a multi-domain pseudo-spectral collocation method to solve the resulting coupled nonlinear partial…

We derive the proper form of Virial theorem for a system of rotating self-gravitating Brownian particles. We show that, in the two-dimensional case, it takes a very simple form that can be used to obtain general results about the dynamics…

We map the general relativistic two-body problem onto that of a test particle moving in an effective external metric. This effective-one-body approach defines, in a non-perturbative manner, the late dynamical evolution of a coalescing…

A new analytical approach to the motion and radiation of (comparable mass) binary systems has been introduced in 1999 under the name of Effective One Body (EOB) formalism. We review the basic elements of this formalism, and discuss some of…