# Works of Riemann related to Astronomy that I can understand?

• benorin
In summary, there is a connection between Riemannian geometry and astronomy through the use of general relativity. This was developed by Bernhard Riemann and is used to explain phenomena that Newton's laws could not. However, the use of tensors in this context may be too complex for the person asking the question. There may also be a connection between Riemann geometry and special relativity, specifically through the concept of Lorentz contraction. This can be further explored by reading the section on relativity and geometry on a recommended website.

#### benorin

Homework Helper
Looking for a connection to astronomy for a history of mathematics report on 19th century mathematicians. I don't do astronomy. Would like to know of any mathematical developments of Riemann that are used in astronomy that I can understand (which expressly excludes any thing with the word tensor in it.) Don't work to hard on it (I have google too,) just thought you guys would know.

TIA,

Benorin

Bernhard Riemann developed Riemannian geometry. This is used through out general relativity. Newton’s laws didn't work at very large (astronomical distances), that is why we use GR. Einstein wouldn't of been able to develop his theories in Euclidean geometry.

Is there any connection between Riemann geometry and special relativity, that subject is within my mental grasp. Perhaps the Lorentz contraction?

http://www.superstringtheory.com/basics/basic2a.html, read the section on relativity and geometry.

## 1. What is Riemann's contribution to astronomy?

Riemann's main contribution to astronomy is his theory of non-Euclidean geometry, which is the foundation for our understanding of curved space and the theory of relativity.

## 2. How did Riemann's work impact our understanding of the universe?

Riemann's theories helped to revolutionize our understanding of space and time, and paved the way for the development of Einstein's theory of general relativity. His work also had a major influence on modern cosmology and our understanding of the structure and evolution of the universe.

## 3. What is the significance of Riemannian geometry in astronomy?

Riemannian geometry is a type of non-Euclidean geometry that allows for the possibility of curved space. This is crucial in understanding the behavior of objects in the universe, such as planets orbiting around a star or galaxies moving through space.

## 4. How did Riemann's work impact the study of black holes?

Riemann's theories, particularly his work on the curvature of space, played a key role in the development of black hole theory. His concepts of non-Euclidean geometry allowed scientists to understand the extreme gravitational effects of black holes and their impact on the fabric of space.

## 5. Is Riemann's work still relevant in modern astronomy?

Absolutely. Riemann's theories are still used in modern cosmology and continue to be an important foundation for our understanding of the universe. His work on non-Euclidean geometry is also essential in the study of gravitational waves and the behavior of objects in the presence of strong gravitational fields.