How to switch between the black and light themes authomatically?

It will depend on the DE.

kde or gnome or what DE/WM you using?

if yiu want them timed, you can just put the respective settings command in your crontab

https://hannes.hauswedell.net/post/2023/12/10/darkmode/ mught help with the commands

I never used them since I'm a dark theme kinda lad, but I swore I've encountered a few that change from dark to light dependent on time.

With Gnome this extension works really well: https://extensions.gnome.org/extension/2236/night-theme-switcher/