The Bach equations in spin-coefficient form

Null Surfaces and the Bach Equations

It is shown that the integrability conditions that arise in the Null Surface Formulation (NSF) of general relativity (GR) impose a field equation on the local null surfaces which is equivalent to the vanishing of the Bach tensor. This field equation is written explicitly to second order in a perturbation expansion. The field equation is further simplified if asymptotic flatness is imposed on th...

First-Order Field Equations in Spin 1/2 Form

Consider a quantum field that is a linear combination of annihilation and creation operators for a massive particle with a given spin. Field equations like those for relativistic free spin 1/2 particles are derived. Such field equations exist for fields that transform with a reducible Lorentz representation that allows vector matrices. Vector matrices are found that replace the Dirac gamma matr...

Spin-coefficient form of the new laws of black-hole dynamics

General laws of black-hole dynamics, some of which are analogous to the laws of thermodynamics, have recently been found for a general definition of black hole in terms of a future outer trapping horizon, a hypersurface foliated by marginal surfaces of a certain type. This theory is translated here into spin-coefficient language. Second law: the area form of a future outer trapping horizon is g...

COMPARISON OF THE EQUATIONS OF STATE FROM JOULE-THOMSON COEFFICIENT

In the present work, we have examined the ability of some different equations of state in predicting the Joule-Thomson coefficient, ?J-T, of different fluids. For dense fluids, for which density is greater than the Boyle density, ?B, two appropriate equations of state, namely the linear isotherm regularity, LIR, and the dense system equation of state, DSEOS, have been examined. The results show...

Bach in Mind