Exterior field of slowly and rapidly rotating neutron stars: Rehabilitating spacetime metrics involving hyperextreme objects

Abstract

The 4-parameter exact solution presumably describing the exterior gravitational field of a generic neutron star is presented in a concise explicit form defined by only three potentials. In the equatorial plane, the metric functions of the solution are found to be given by particularly simple expressions that make them very suitable for the use in concrete applications. Following Pappas and Apostolatos, we perform a comparison of the multipole structure of the solution with the multipole moments of the known physically realistic Berti-Stergioulas numerical models of neutron stars to argue that the hyperextreme sectors of the solution are not less (but possibly even more) important for the correct description of rapidly rotating neutron stars than the subextreme sector involving exclusively the black-hole constituents. We have also worked out in explicit form an exact analog of the well-known Hartle-Thorne approximate metric.

Approximate universal relations for neutron stars and quark stars

“…In fact, one can approximately represent the full metric tensor outside a stationary compact star entirely in terms of only these three quantities [56][57][58]. In particular, Pappas [56,57] use the two-soliton solution found by Manko et al [59] (see also Manko and Ruiz [60] for a simpler representation of the solution).…”

Simplest static and stationary vacuum quadrupolar metrics

“…For this purpose, one has first to pass in (19) We note that in the paper [26] a physical representation of the general 4-parameter metric for the exterior field of a neutron star was obtained in terms of multipole moments. So, taking into account that the static solution (11) is a 2-parameter specialization of that metric, it would be logic to search for its simplest stationary generalization within the same generic metric too.…”

“…which have been worked out with the aid of the general formulas of the paper [26]. Note that the Kerr metric [27] is contained in the above formulas as the q = −j 2 particular case.…”

Testing exterior spacetime of the neuron star via x-ray reflection spectroscopy

“…Their approach was based on expansion up to second order in rotation. Also there have been attempts to describe spacetime around NSs by analytic solutions of stationary, axially symmetric and also vacuum spacetime, see, for example, [6][7][8][9][10][11]. These solutions are not constrained to a slow rotation and the numbers of parameters that construct their geometries.…”