Photon Regions and Shadows of Kerr-Newman-NUT Black Holes with a Cosmological Constant (1403.5234v2)

Abstract: We consider the Pleba\'nski class of electrovacuum solutions to the Einstein equations with a cosmological constant. These space-times, which are also known as the Kerr-Newman-NUT-(anti-)de Sitter space-times, are characterized by a mass $m$, a spin $a$, a parameter $\beta$ that comprises electric and magnetic charge, a NUT parameter $\ell$ and a cosmological constant $\Lambda$. Based on a detailed discussion of the photon regions in these space-times (i.e., of the regions in which spherical lightlike geodesics exist), we derive an analytical formula for the shadow of a Kerr-Newman-NUT-(anti-)de Sitter black hole, for an observer at given Boyer-Lindquist coordinates $(r_O, \vartheta_O)$ in the domain of outer communication. We visualize the photon regions and the shadows for various values of the parameters.

• The paper introduces an analytical framework to compute photon regions and shadow boundaries for Kerr-Newman-NUT-(anti)-de Sitter black holes.
• It finds that spin induces asymmetry in the shadow while charge, the NUT parameter, and the cosmological constant predominantly affect shadow size.
• The study lays a foundation for extracting black hole parameters from shadow observations and testing general relativity under extreme conditions.

An Analytical Study of Photon Regions and Shadows in Kerr-Newman-NUT Black Holes with a Cosmological Constant

This paper investigates the photon regions and the shadows cast by Kerr-Newman-NUT-(anti)-de Sitter black holes, a specific class of solutions to the Einstein equations incorporating a cosmological constant. The fundamental aim of the paper is to extend the theoretical groundwork essential for interpreting the anticipated observational data of black hole shadows by the Event Horizon Telescope and similar instruments.

Analytical Framework

The space-time considered in this paper is characterized by a complex interplay of parameters: mass $m$, spin $a$, a parameter $\beta$ (encompassing electric and magnetic charge), the NUT parameter $\ell$, and the cosmological constant $\Lambda$. These parameters define the Kerr-Newman-NUT-(anti)-de Sitter space-times, which are part of the Plebański class of electrovacuum solutions.

The authors develop an analytical formalism needed to compute the shadows of these black holes as observed from any given set of Boyer-Lindquist coordinates, ensuring that the analysis includes non-asymptotically flat scenarios (i.e., where $\Lambda \neq 0$ and a cosmological horizon may be present). The paper emphasizes the role of photon regions, key areas where light can orbit the black hole, which influence the characteristics of the shadows. The photon region's configuration allows for the determination of the shadow boundaries through analytical methods rather than reliance on computational ray tracing.

Numerical Results and Visualizations

Through the derivation of photon regions, the research presents detailed visualizations under varying black hole parameters. A crucial part of the paper is the influence of the additional NUT parameter and cosmological constant on the shape and size of the shadow. The paper provides comprehensive plots to depict these parameters' effects across various rotations ($a$) and charges ($\beta$).

The analysis finds that while the black hole's spin significantly alters the shadow's asymmetrical shape—attributable to frame dragging effects—the other parameters, including $\beta$, $\ell$, and $\Lambda$, primarily influence shadow size but have negligible effects on its shape. A key insight is that the presence of the NUT parameter ($\ell$) and non-zero cosmological constant maintains symmetry about a horizontal axis, even when the observer is situated off the equatorial plane.

Implications and Future Work

The analytical formula derived for the shadow's boundary represents a foundation for potential applications in extracting black hole parameters from observed shadows. This approach could enhance our capacity to utilize shadow observations as a diagnostic tool for testing general relativity's predictions under extreme gravitational conditions. Furthermore, the paper suggests further computational follow-ups may include Fourier analysis of the boundary to extract physical parameters.

Overall, this research extends shadow theory by providing a solid analytical basis necessary when observers are located at finite distances, counteracting previous limitations confined to observing from infinity. This theoretical work lays a critical groundwork for interpreting future empirical observations of black hole shadows, striving to bridge observational astrophysics with established theoretical predictions in general relativity.