Abstract
Among the known exact solutions of Einstein's vacuum field equations the Manko–Novikov and the Quevedo–Mashhoon metrics might be suitable ones for the description of the exterior gravitational field of some real non-collapsed body. A new proposal to represent such exterior field is the stationary q-metric. In this contribution, we computed by means of the Fodor–Hoenselaers–Perjés formalism the lowest 10 relativistic multipole moments of these metrics. Corresponding moments were derived for the static vacuum solutions of Gutsunayev–Manko and Hernández–Martín. A direct comparison between the multipole moments of these non-isometric space–times is given.
Highlights
In 1968, Ernst [1,2] developed a complex procedure to simplify the Einstein field equations (EFE) for a stationary Weyl–Lewis– Papapetrou (WLP) type metric by means of two complex potentials
The HKX method was employed by Quevedo and Mashhoon (QM) to find new stationary solutions from the Erez– Rosen space–time as seed metric [6,7,8]
The Erez–Rosen metric is an exact vacuum solution of EFE representing a static metric with a mass and a quadrupole parameter (M and Q) [9]
Summary
In 1968, Ernst [1,2] developed a complex procedure to simplify the Einstein field equations (EFE) for a stationary Weyl–Lewis– Papapetrou (WLP) type metric by means of two complex potentials. The Manko–Novikov (MN) metric was derived by solving the Ernst equations using the techniques developed by Yamazaki [11, 12], Cosgrove [13] and Dietz & Hoenselaers [14] This metric has parameters k, α (representing mass and rotation parameter, respectively) and αn (α2 representing the quadrupole) [15]. From the Ernst formalism, Fodor, Hoenselaers and Perjés (FHP) [26] found an elegant method to derive explicit expressions for the multipole moments of a given stationary (axially symmetric) space–time with asymptotic flatness. Later, this method was generalized by Hoenselaers & Perjés [27].
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