Electromagnetic wave propagation in static black hole spacetimes: an effective refractive index description in Schwarzschild geometry
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2026
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| author | Guvendi, Abdullah Dogan, Omar Mustafa Semra Gurtas Hassanabadi, Hassan |
| author_facet | Guvendi, Abdullah Dogan, Omar Mustafa Semra Gurtas Hassanabadi, Hassan |
| contents | We present a fully covariant and gauge-invariant formulation of electromagnetic wave propagation in static, spherically symmetric black hole spacetimes, developed entirely within Schwarzschild-like coordinates. Start ing from the source-free Maxwell equations on a curved background, electromagnetic perturbations are de composed according to parity and systematically reduced to gauge-invariant dynamical variables without introducing auxiliary coordinate transformations or horizon-regular variables. Both axial and polar sectors are shown to obey the same parity-independent master equation, and their exact isospectrality emerges nat urally as a direct consequence of Maxwell theory in four dimensions. By eliminating first-derivative terms through an appropriate field redefinition, the radial dynamics is cast into a Helmholtz-type equation, which motivates the introduction of an effective, position- and frequency-dependent refractive index encoding grav itational redshift, curvature effects, and angular momentum within a unified optical framework. Specializing to the Schwarzschild geometry, we obtain the refractive index in closed analytical form and analyze its behavior in the near-horizon, intermediate, and asymptotic regimes. The resulting description provides a transparent and physically intuitive interpretation of electromagnetic evanescence, and propagation in black hole spacetimes, and establishes a robust foundation for wave-optical, semiclassical, and numerical studies in more general static gravitational backgrounds. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_07371 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Electromagnetic wave propagation in static black hole spacetimes: an effective refractive index description in Schwarzschild geometry Guvendi, Abdullah Dogan, Omar Mustafa Semra Gurtas Hassanabadi, Hassan General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics We present a fully covariant and gauge-invariant formulation of electromagnetic wave propagation in static, spherically symmetric black hole spacetimes, developed entirely within Schwarzschild-like coordinates. Start ing from the source-free Maxwell equations on a curved background, electromagnetic perturbations are de composed according to parity and systematically reduced to gauge-invariant dynamical variables without introducing auxiliary coordinate transformations or horizon-regular variables. Both axial and polar sectors are shown to obey the same parity-independent master equation, and their exact isospectrality emerges nat urally as a direct consequence of Maxwell theory in four dimensions. By eliminating first-derivative terms through an appropriate field redefinition, the radial dynamics is cast into a Helmholtz-type equation, which motivates the introduction of an effective, position- and frequency-dependent refractive index encoding grav itational redshift, curvature effects, and angular momentum within a unified optical framework. Specializing to the Schwarzschild geometry, we obtain the refractive index in closed analytical form and analyze its behavior in the near-horizon, intermediate, and asymptotic regimes. The resulting description provides a transparent and physically intuitive interpretation of electromagnetic evanescence, and propagation in black hole spacetimes, and establishes a robust foundation for wave-optical, semiclassical, and numerical studies in more general static gravitational backgrounds. |
| title | Electromagnetic wave propagation in static black hole spacetimes: an effective refractive index description in Schwarzschild geometry |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2604.07371 |