Spinning black holes with a separable Hamilton–Jacobi equation from a modified Newman–Janis algorithm
Abstract Obtaining solutions of the Einstein field equations describing spinning compact bodies is typically challenging. The Newman–Janis algorithm provides a procedure to obtain rotating spacetimes from a static, spherically symmetric, seed metric. It is not guaranteed, however, that the resulting...
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2020-11-01
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doaj-bf0c003d0df54e1c819c2361616ed17c2020-11-25T03:58:35ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60441434-60522020-11-01801111210.1140/epjc/s10052-020-08572-wSpinning black holes with a separable Hamilton–Jacobi equation from a modified Newman–Janis algorithmHaroldo C. D. Lima Junior0Luís C. B. Crispino1Pedro V. P. Cunha2Carlos A. R. Herdeiro3Faculdade de Física, Universidade Federal do ParáFaculdade de Física, Universidade Federal do ParáMax Planck for Gravitational Physics, Albert Einstein InstituteDepartamento de Matemática da Universidade de Aveiro and Centre for Research and Development in Mathematics and Applications (CIDMA)Abstract Obtaining solutions of the Einstein field equations describing spinning compact bodies is typically challenging. The Newman–Janis algorithm provides a procedure to obtain rotating spacetimes from a static, spherically symmetric, seed metric. It is not guaranteed, however, that the resulting rotating spacetime solves the same field equations as the seed. Moreover, the former may not be circular, and thus expressible in Boyer–Lindquist-like coordinates. Amongst the variations of the original procedure, a modified Newman–Janis algorithm (MNJA) has been proposed that, by construction, originates a circular, spinning spacetime, expressible in Boyer–Lindquist-like coordinates. As a down side, the procedure introduces an ambiguity, that requires extra assumptions on the matter content of the model. In this paper we observe that the rotating spacetimes obtained through the MNJA always admit separability of the Hamilton–Jacobi equation for the case of null geodesics, in which case, moreover, the aforementioned ambiguity has no impact, since it amounts to an overall metric conformal factor. We also show that the Hamilton–Jacobi equation for light rays propagating in a plasma admits separability if the plasma frequency obeys a certain constraint. As an illustration, we compute the shadow and lensing of some spinning black holes obtained by the MNJA.http://link.springer.com/article/10.1140/epjc/s10052-020-08572-w |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Haroldo C. D. Lima Junior Luís C. B. Crispino Pedro V. P. Cunha Carlos A. R. Herdeiro |
spellingShingle |
Haroldo C. D. Lima Junior Luís C. B. Crispino Pedro V. P. Cunha Carlos A. R. Herdeiro Spinning black holes with a separable Hamilton–Jacobi equation from a modified Newman–Janis algorithm European Physical Journal C: Particles and Fields |
author_facet |
Haroldo C. D. Lima Junior Luís C. B. Crispino Pedro V. P. Cunha Carlos A. R. Herdeiro |
author_sort |
Haroldo C. D. Lima Junior |
title |
Spinning black holes with a separable Hamilton–Jacobi equation from a modified Newman–Janis algorithm |
title_short |
Spinning black holes with a separable Hamilton–Jacobi equation from a modified Newman–Janis algorithm |
title_full |
Spinning black holes with a separable Hamilton–Jacobi equation from a modified Newman–Janis algorithm |
title_fullStr |
Spinning black holes with a separable Hamilton–Jacobi equation from a modified Newman–Janis algorithm |
title_full_unstemmed |
Spinning black holes with a separable Hamilton–Jacobi equation from a modified Newman–Janis algorithm |
title_sort |
spinning black holes with a separable hamilton–jacobi equation from a modified newman–janis algorithm |
publisher |
SpringerOpen |
series |
European Physical Journal C: Particles and Fields |
issn |
1434-6044 1434-6052 |
publishDate |
2020-11-01 |
description |
Abstract Obtaining solutions of the Einstein field equations describing spinning compact bodies is typically challenging. The Newman–Janis algorithm provides a procedure to obtain rotating spacetimes from a static, spherically symmetric, seed metric. It is not guaranteed, however, that the resulting rotating spacetime solves the same field equations as the seed. Moreover, the former may not be circular, and thus expressible in Boyer–Lindquist-like coordinates. Amongst the variations of the original procedure, a modified Newman–Janis algorithm (MNJA) has been proposed that, by construction, originates a circular, spinning spacetime, expressible in Boyer–Lindquist-like coordinates. As a down side, the procedure introduces an ambiguity, that requires extra assumptions on the matter content of the model. In this paper we observe that the rotating spacetimes obtained through the MNJA always admit separability of the Hamilton–Jacobi equation for the case of null geodesics, in which case, moreover, the aforementioned ambiguity has no impact, since it amounts to an overall metric conformal factor. We also show that the Hamilton–Jacobi equation for light rays propagating in a plasma admits separability if the plasma frequency obeys a certain constraint. As an illustration, we compute the shadow and lensing of some spinning black holes obtained by the MNJA. |
url |
http://link.springer.com/article/10.1140/epjc/s10052-020-08572-w |
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