Radial acceleration for spherically symmetric systems in GR

[FluteGuy]

Hello, I was reading few papers discussing modified gravity theories and their use in understanding galaxies with no dark matter by checking for anomalous velocity dispersion. Now, the author was using 4 gravity theories MOND, Weyl, MOG and Emergent gravity. The thing is he had provided the radial acceleration relation that he had used for all of them. After finding the result, he had plotted it along with GR (for no dark matter) as well. Now, I have been looking for resources to get a single radial acceleration relation in GR for spherically symmetric system. All I could find was a set of equations in different book. If you know some literature with that, do tell me. I am trying to reproduce the results of that paper myself. Thank you.

Paper: [1908.07160] Modified Gravity Theories in Light of the Anomalous Velocity Dispersion of NGC1052-DF2 (arxiv.org)

 

[lippyka]

I recommend looking into the book "Gravitation" by Charles W. Misner, Kip S. Thorne, and John A. Wheeler for an equation for the acceleration in GR for a spherically symmetric system. This book is widely regarded as the classic text on general relativity. It provides a comprehensive treatment of the subject and includes equations for the acceleration in GR for a spherically symmetric system. Additionally, the book "Gravity: An Introduction to Einstein's General Relativity" by James B. Hartle also features a section on GR and its application to spherically symmetric systems. Finally, the website Hyperphysics (http://hyperphysics.phy-astr.gsu.edu/hbase/gr.html) provides a discussion of the equations of motion in GR and includes an equation for the radial acceleration in a spherically symmetric system.