Optical properties of null geodesics emerging from dynamical systems

Batic, Davide; Chanda, Sumanto; Guha, Partha

doi:10.1140/epjc/s10052-022-10392-z

Cited by 3 publications

(3 citation statements)

References 68 publications

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“…The second reason behind our work is related to the claims made in [29], where the authors, besides presenting the derivation of a weak lensing formula recently corrected by [30], analyse the motion of a massive test particle starting at space-like infinity with zero total angular momentum. It was found by [29] that for q = 0 and q = 1, the corresponding trajectories emerging from the geodesic equations exhibit a perihelion.…”

Section: Discussionmentioning

confidence: 99%

“…We draw the attention of the reader to the fact that there is a typo in Equation (3.3a) in [20] where the term ∂ z u should appear squared. The Ernst equation [23] emerges from (30) and ( 31) by introducing some complex-valued function E = f + iu and realizing that the aforementioned equations are the real and imaginary parts of the complex PDE…”

Section: Derivation Of the Tomimatsu-sato Metric With Deformation Par...mentioning

confidence: 99%

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The Tomimatsu–Sato Metric Reloaded

Batic

2023

Universe

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In this work, we derive exact analytic formulae for the inner and outer surfaces representing the boundary of the ergoregion appearing in the Tomimatsu–Sato (TS) metric. Exact expressions for the radii of the ergoregion in prolate spheroidal coordinates and in Boyer-Lindquist coordinates are obtained. We also found that in addition to the ring-shaped naked singularity, there is an event horizon placed in the inner region inside the aforementioned curvature singularity. In comparing our results with previous studies, we also uncovered and corrected several errors in the literature. Finally, we provide tables of numerical values for the inner and outer boundaries of the ergoregion for different values of the rotational parameter. We hope this study will be a useful resource for all researchers interested in the Tomimatsu–Sato metric.

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Section: Discussionmentioning

confidence: 99%

Section: Derivation Of the Tomimatsu-sato Metric With Deformation Par...mentioning

confidence: 99%

The Tomimatsu–Sato Metric Reloaded

Batic

2023

Universe

Self Cite

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show abstract

“…The second reason behind our work is related to the claims made in [31] where the authors, beside presenting the derivation of a weak lensing formula recently corrected by [32], analyse the motion of a massive test particle starting at space-like infinity with zero total angular momentum. It was found by [31] that for q = 0 and q = 1 the corresponding trajectories emerging from the geodesic equations exhibit a perihelion.…”

Section: Discussionmentioning

confidence: 99%

The Tomimatsu-Sato metric reloaded

Batic

2023

Preprint

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In this work, we derive exact analytic formulae for the inner and outer surfaces representing the boundary of the ergoregion appearing in the Tomimatsu-Sato (TS) metric. Exact expressions for the radii of the ergoregion in prolate spheroidal coordinates and in Boyer-Lindquist coordinates are obtained. We also found that in addition to the ring-shaped naked singularity there is an event horizon placed in the inner region inside the aforementioned curvature singularity. In comparing our results with previous studies, we also uncovered and corrected several errors in the literature. Finally, we provide tables of numerical values for the inner and outer boundaries of the ergoregion for different values of the rotational parameter. We hope this study will be a useful resource for all researchers interested in the Tomimatsu-Sato metric.

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Purely spatial frame-dragging and oblate spherodial refractive index as an optical analog to Kerr spacetime

Marquez

2024

Class. Quantum Grav.

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This paper presents an optical analogy to the lightlike geodesics in spacetime with frame-dragging effects, particularly in Kerr spacetime. This was done by correspondingly equating parts of the deflection angle expression of the lightlike geodesics to that of the optical analog with gradient refractive index (GRIN). The resulting conditions of analogy separates the GRIN from the frame-dragging effects, yielding an oblate spheroidally symmetric GRIN expression and a new optical Lagrangian which situates such medium in a non-Euclidean background space. Such space is demostrated to possess a purely spatial frame-dragging effect. This analogy might suggest a generalized notion of analog magnetism or provide additional insights to studies on gravitational lensing and construction of optical analogs in the laboratory setting.

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Optical properties of null geodesics emerging from dynamical systems

Cited by 3 publications

References 68 publications

The Tomimatsu–Sato Metric Reloaded

The Tomimatsu–Sato Metric Reloaded

The Tomimatsu-Sato metric reloaded

Purely spatial frame-dragging and oblate spherodial refractive index as an optical analog to Kerr spacetime

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