To add absolute paths to an archive, there is "-P" option, and man says it works only for creating archives: "Don't strip leading slashes from filenames when creating archives".
To extract absolute paths from the archive, you need to add the "-C /" option, and although the tool says "tar: Strip leading `/' from member names", it will still extract it in the right place because the paths become relative and -C puts them in the root.
However, if you add "-P" during the extraction (which is not mentioned in man), the "strip leading slashes" information disappears.
So if this message bothers someone, "tar -C / -xPf file.tar" will cleanly extract absolute paths from the archive ;)
char name[100];
(See https://man.archlinux.org/man/tar.5.en )So anything that will write an absolute path there, including literally opening it in a text editor and replacing the path by hand because that whole header is just fixed length ASCII with null terminated strings.
(I mean I assume the tar(1) command can do it too but you don't need that, the format is dead simple, if weird.)