Gauge freedom of plane-symmetric line elements with semi-plane-symmetric null electromagnetic fields

Abstract

Previously, we gave two classes of plane-symmetric line elements associated with semi-planesymmetric null electromagnetic fields. Different functions J ( V ) in those line elements may represent the same geometry. Two criteria on this "gauge freedom" are proven in the present paper. The line elements of class B are identified with the conformally flat plane-fronted gravitational waves with parallel rays (pp waves), and the gauge freedom on the function, W v ) , appearing in the line element of the pp waves is also derived.

The causal boundary of product spacetimes

“…However, they have not obtained totally satisfactory results up to date (see [1,[10][11][12]; see also [13,14] for interesting reviews on the subject).…”

“…Many authors have tried different methods to establish these identifications [4,5,6,7]; indeed, this question is related to the introduction of a satisfactory topology for the completion. However, they have not obtained totally satisfactory results up to date (see [8,9,10,1]). See also [11], [12] for interesting reviews on the subject.…”