arXiv subjects

James W. York Jr

Publications and source records attributed to James W. York Jr.

3 recordsLinked to original sources

arXiv2006

Self-Renormalization of the Classical Quasilocal Energy

Pointlike objects cause many of the divergences that afflict physical theories. For instance, the gravitational binding energy of a point particle in Newtonian mechanics is infinite. In general relativity, the analog of a point particle is a black hole and the notion of binding energy must be replaced by quasilocal energy. The quasilocal energy (QLE) derived by York, and elaborated by Brown and York, is finite outside the horizon but it was not considered how to evaluate it inside the horizon. We present a prescription for finding the QLE inside a horizon, and show that it is finite at the singularity for a variety of types of black hole. The energy is typically concentrated just inside the horizon, not at the central singularity.

gr-qc↗

arXiv2004

Velocities and Momenta in an Extended Elliptic Form of the Initial Value Conditions

The complete form of the constraints following from their conformal structure is extended so as to include constant mean curvature and other mean curvature foliations. This step is demonstrated using the momentum phase space approach. This approach yields equations of exactly the same form as the extended conformal thin sandwich approach. In solving the equations, it is never necessary actually to perform a tensor decomposition.

gr-qc↗

arXiv1999

Einstein's Equations and Equivalent Hyperbolic Dynamical Systems

We discuss several explicitly causal hyperbolic formulations of Einstein's dynamical 3+1 equations in a coherent way, emphasizing throughout the fundamental role of the ``slicing function,'' $α$---the quantity that relates the lapse $N$ to the determinant of the spatial metric $\bar{g}$ through $N = \bar{g}^{1/2} α$. The slicing function allows us to demonstrate explicitly that every foliation of spacetime by spatial time-slices can be used in conjunction with the causal hyperbolic forms of the dynamical Einstein equations. Specifically, the slicing function plays an essential role (1) in a clearer form of the canonical action principle and Hamiltonian dynamics for gravity and leads to a recasting (2) of the Bianchi identities $\nabla_βG^β\mathstrut_α\equiv 0$ as a well-posed system for the evolution of the gravitational constraints in vacuum, and also (3) of $\nabla_βT^β\mathstrut_α\equiv 0$ as a well-posed system for evolution of the energy and momentum components of the stress tensor in the presence of matter, (4) in an explicit rendering of four hyperbolic formulations of Einstein's equations with only physical characteristics, and (5) in providing guidance to a new ``conformal thin sandwich'' form of the initial value constraints.

gr-qc↗