Rotation in vacuum and scalar background: Are there alternatives to Newman–Janis algorithm?

Author:

Makukov Maxim1ORCID,Mychelkin Eduard1

Affiliation:

1. Fesenkov Astrophysical Institute, 050020 Almaty, Republic of Kazakhstan

Abstract

The Newman–Janis (NJ) algorithm is the standard approach to rotation in general relativity which, in vacuum, builds the Kerr metric from the Schwarzschild spacetime. Recently, we have shown that the same algorithm applied to the Papapetrou antiscalar spacetime produces a rotational metric devoid of horizons and ergospheres. Though exact in the scalar sector, this metric, however, satisfies the Einstein equations only asymptotically. We argue that this discrepancy between geometric and matter parts (essential only inside gravitational radius scale) is caused by the violation of the Hawking–Ellis energy conditions for the scalar energy–momentum tensor. The axial potential functions entering the metrics appear to be of the same form both in vacuum and scalar background, and they also coincide with the linearized Yang–Mills field, which might hint at their common nongravitational origin. As an alternative to the Kerr-type spacetimes produced by NJ algorithm we suggest the exact solution obtained by local rotational coordinate transformation from the Schwarzschild spacetime. Then, comparison with the Kerr-type metrics shows that the Lense–Thirring phenomenon might be treated as a coordinate effect, similar to the Coriolis force.

Funder

Ministry of Education and Science of the Republic of Kazakhstan

Publisher

World Scientific Pub Co Pte Ltd

Subject

Space and Planetary Science,Astronomy and Astrophysics,Mathematical Physics

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