2018/03/11 by Stefano Liberati, Giovanni Tricella, Matt Visser
Physics and Astronomy · #Astrophysical Phenomena and Observations #Kerr metric #Maxwell's equations in curved spacetime #Metric (unit) #Pulsars and Gravitational Waves Research #Relativity and Gravitational Theory #Spacetime #Spacetime symmetries #Spacetime topology #Spherically symmetric spacetime #Stationary spacetime #gr-qc
paper · pdf · doi:10.1088/1361-6382/aacb75
published as Classical and Quantum Gravity 35 (2018) 155004 · 20 pages
arxiv created 2018/03/11 · openalex created_date 2018/03/29 · openalex publication_date 2018/06/08 · arxiv updated 2018/08/16 · openalex updated_date 2026/08/05
Abstract It is not currently known how to put the Kerr spacetime metric into the so-called Gordon form, although the closely related Kerr–Schild form of the Kerr metric is well known. A Gordon form for the Kerr geometry, if it could be found, would be particularly useful in developing analogue models for the Kerr spacetime, since the Gordon form is explicitly given in terms of the 4-velocity and ‘refractive index’ of an effective medium. In the current article we report progress toward this goal. First we present the Gordon form for an approximation to Kerr spacetime in the slow-rotation limit, obtained by suitably modifying the well-known Lense–Thirring form of the slow-rotation metric. Second we present the Gordon form for the Kerr spacetime in the near-null limit, (the 4-velocity of the medium being close to null). That these two perturbative approximations to the Kerr spacetime in Gordon form exist gives us some confidence that ultimately one might be able to write the exact Kerr spacetime in this form.