First-Order Light Deflection by Einstein-Strauss Vacuole Method

A method for solving first order fuzzy differential equation

New first-order formulation for the Einstein equations

We derive a new first-order formulation for Einstein’s equations which involves fewer unknowns than other first-order formulations that have been proposed. The new formulation is based on the 311 decomposition with arbitrary lapse and shift. In the reduction to first-order form only eight particular combinations of the 18 first derivatives of the spatial metric are introduced. In the case of li...

A new first-order formulation for the Einstein equations

We derive a new first-order formulation for Einstein’s equations which involves fewer unknowns than other first-order formulations that have been proposed. The new formulation is based on the 3 + 1 decomposition with arbitrary lapse and shift. In the reduction to first order form only 8 particular combinations of the 18 first derivatives of the spatial metric are introduced. In the case of line...

First-order symmetric hyperbolic Einstein equations with arbitrary fixed gauge.

We find a one-parameter family of variables which recast the 3+1 Einstein equations into firstorder symmetric-hyperbolic form for any fixed choice of gauge. Hyperbolicity considerations lead us to a redefinition of the lapse in terms of an arbitrary factor times a power of the determinant of the 3-metric; under certain assumptions, the exponent can be chosen arbitrarily, but positive, with no i...

The observable light deflection angle

The physical deflection angle of a light ray propagating in a space-time supplied with an asymptotically flat metric has to be expressed in terms of the impact parameter.