Analytical determination of the shadow of the schwarzschild black hole

Fulgencio Villegas Silva ¹, Miguel Castillo Corzo ², Marco A. Merma Jara ^3*

^1,2,3Facultad de Ciencias Físicas, Universidad Nacional Mayor de San Marcos, Lima, Perú.

^3*Corresponding Author: Marco A. Merma Jara, Facultad de Ciencias Físicas, Universidad Nacional Mayor de San Marcos, Lima, Perú.
Email: aulaslivres@gmail.com

Received: 12th Dec, 2025; Revised: 6th Feb 2026; Accepted: 12th Feb, 2026; Available Online: 28th Feb, 2026

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ABSTRACT

Objective: This paper undertakes an analytical study of the shadow of the Schwarzschild black hole.

Method: In order to accomplish this objective, it is necessary to emphasize the definition of a black hole, its primary characteristics, and its significance in the field of cosmology. In this case, the shadow of an object is defined as the shape that the object possesses in space, as perceived by an observer when considering solely the properties of spacetime.

Results: The analytical solution is derived using the Hamilton-Jacobi equation, the method of separation of variables, and the introduction of a Carter-type conserved quantity.

Conclusions: The determination of constant-radius orbits is achieved through the utilization of impact parameters and celestial coordinates.

Keywords: Black holes, shadow, null geodesics.

How to cite this article: Villegas Silva F, Castillo Corzo M, Merma Jara MA. Analytical determination of the shadow of the schwarzschild black hole. Int J Drug Deliv Technol. 2026;16(5s): 473-478; DOI: 10.25258/ijddt.16.5s.64

Source of support: Nil.

Conflict of interest: None