other than astronomy would astronomers have to study in order to discover black holes?

do you mean, " what would astronomers have to study.."

If so the answer would be
Basic algebra> coordinate planes

In addition to astronomy, astronomers need to study various fields to discover black holes. Here are a few related fields astronomers might explore:

1. Astrophysics: This branch of physics focuses on the properties and behavior of celestial objects, including black holes. Understanding astrophysics is crucial as it deals with the fundamental principles governing the formation, evolution, and interactions of black holes.

2. Cosmology: This field explores the origin, evolution, and structure of the universe as a whole. Studying cosmology helps astronomers understand how black holes fit into the cosmic framework and their role in the large-scale structure of the universe.

3. Gravitational Physics: Black holes are formed by gravitational collapse, so understanding the laws of gravitational physics is essential. This includes studying concepts like general relativity, gravitational waves, and the behavior of matter and energy in extreme gravitational fields.

4. High-Energy Astrophysics: Black holes can emit powerful jets of high-energy particles, known as relativistic jets. Studying high-energy astrophysics helps astronomers detect and analyze these emissions, providing key insights into black hole activity.

5. Computational Modeling: To study black holes, astronomers use computer simulations and numerical models to analyze complex physical processes. Computational modeling is crucial for understanding the behavior of matter and the gravitational dynamics involved in black hole formation, accretion, and interactions with their surroundings.

It's important to note that becoming an astronomer requires a solid foundation in physics and mathematics. To specialize in black hole research, astronomers often pursue advanced degrees and collaborate with experts in related fields to gain a deep understanding of these fascinating objects.