I needed a minimally-configured Real Time kernel, I compiled a new kernel with menuconfig. Firstly I added the rt patch to the new kernel directory using patch, and then ran make menuconfig. Then I added the bzImage find inside arch/x86/boot/bzImage and the System.map files to /boot.
After that I ran update-grub.
Here are the contents of my grub.cfg
The problem is the the new kernel cannot be loaded when grub prompts.