onehourago=$(date --date='1 hours ago' +"%b%e %H:%M:%S")
echo $onehourago | cat /var/log/auth.log - | sort | sed "1,/$onehourago/d"
Intermediate output without the sed-command:
Aug 7 00:00:03 thinkpux CRON[25475]: pam_unix(cron:session): session closed for user stefan
Aug 7 00:17:01 thinkpux CRON[25504]: pam_unix(cron:session): session closed for user root
Aug 7 00:17:01 thinkpux CRON[25504]: pam_unix(cron:session): session opened for user root by (uid=0)
Aug 7 00:19:33
Aug 7 01:00:02 thinkpux CRON[25652]: pam_unix(cron:session): session opened for user stefan by (uid=0)
Aug 7 01:00:03 thinkpux CRON[25652]: pam_unix(cron:session): session closed for user stefan
Aug 7 01:17:01 thinkpux CRON[25885]: pam_unix(cron:session): session closed for user root
Aug 7 01:17:01 thinkpux CRON[25885]: pam_unix(cron:session): session opened for user root by (uid=0)
Output:
Aug 7 01:00:02 thinkpux CRON[25652]: pam_unix(cron:session): session opened for user stefan by (uid=0)
Aug 7 01:00:03 thinkpux CRON[25652]: pam_unix(cron:session): session closed for user stefan
Aug 7 01:17:01 thinkpux CRON[25885]: pam_unix(cron:session): session closed for user root
Aug 7 01:17:01 thinkpux CRON[25885]: pam_unix(cron:session): session opened for user root by (uid=0)
Note: First I had build the date with +"%b %e %H:%M:%S" (note the blank between %b and %e, but echo compresses two blanks into one. Searching by sed seems to look for two blanks and doesn't find the expression, so it is somehow complicated to distinguish whether the day of month has two or one digit. However, sort seems agnostic about the superflous/missing blank. Maybe there is a bash-switch to prevent compression? However - your dateformat is different and so you will not be affected, but I had to test this approach somehow, and learners might step into the same trap.
So the overall Idea is, to get the date/time of 1 hour ago, format it as in the logfile, add the pure date to the logfile and sort that mix, then delete with sed anything up to the pure date.
Not funny to remember and type, but you may put it into a script and/or function.