- #1
princeton118
- 33
- 0
Please recommend some good books of differential geometry for a physics student.
Thanks!
Thanks!
robphy said:If the goal is to understand relativity, I would first seek out treatments of differential geometry by a mathematically-oriented relativist... then to others when needed.
Some names (in no particular order... some found in the URL I pasted above):
Schutz, Faber, and Frankel (as named above)
Burke, Isham, Sachs&Wu, O'Neill, Crampin, Marsden, Choquet-Bruhat, Hawking&Ellis, ...
http://www.math.harvard.edu/~shlomo/docs/semi_riemannian_geometry.pdf
edit:
add Szekeres
see also https://www.physicsforums.com/showthread.php?t=168568
princeton118 said:I am reading Frankel's book. But it is the first edition. Is the change between the first edition and the second edition very big and significant?
Differential geometry is a branch of mathematics that studies the properties of curves and surfaces in higher dimensions. It uses the tools of calculus to understand the geometric properties of these objects.
Differential geometry is used in general relativity to describe the curvature of spacetime caused by the presence of massive objects. It provides a mathematical framework for understanding how gravity works and how objects move in the presence of massive bodies.
Euclidean geometry deals with flat spaces, while differential geometry deals with curved spaces. In Euclidean geometry, the rules of geometry are based on the properties of straight lines and parallel lines. In differential geometry, the rules of geometry are based on the curvature of the space.
Differential geometry is used in general relativity to understand the behavior of black holes, gravitational waves, and the expansion of the universe. It also has applications in cosmology, astrophysics, and the study of the large-scale structure of the universe.
Yes, differential geometry is essential for understanding general relativity. It provides the mathematical tools and concepts needed to describe the curvature of spacetime and how it is affected by the presence of matter and energy. Without differential geometry, it would be impossible to fully understand the theory of general relativity.