Why is add timestamp column with default not null so slow in Oracle 11g?
This is actually improved in Oracle 12c.

From Oracle Magazine's Ask Tom column:
http://www.oracle.com/technetwork/issue-archive/2013/13-sep/o53asktom-1999186.html


  In Oracle Database 11g you were able to perform a fast add of a column
  to a table if it had a default value and was defined as NOT NULL.
  (Arup Nanda has written about this at bit.ly/16tQNCh.) However, if you
  attempted to add a column with a default value and that column
  permitted null values, the ADD COLUMN operation could take a
  significant amount of time, generate a large amount of undo and redo,
  and lock the entire table for the duration of the operation. In Oracle
  Database 12c, that time, volume, and locking are no longer part of the
  process.


I know this doesn't help if you're stuck on 11gR2, since you probably want to get that column added before taking an outage to upgrade the DB.

As to why it takes so long only when the data type is TIMESTAMP, I'm at a loss.  Maybe since the TIMESTAMP data type is a few more bytes to store than DATE, or than VARCHAR2 for empty strings, and those extra bytes are causing a cascade of row migrations.  To test that theory, try adding a fixed length CHAR column (in a non-Prod environment): alter table my_table add my_char_col CHAR(200) default 'hello' not null; I expect this would not be instantaneous due to row migrations.

Your best bet on 11gR2 might be either to 


Take an outage at an appropriate time that is ok with your stakeholders to add this column


or


Use DBMS_REDEFINITION to add the column as part of an online redefinition.  This should be non-blocking, and even though it may take hours, the users will not even notice it happening (no locking).  If you have a lot of indexes, this becomes a little more difficult.  If you have foreign keys, this becomes even more difficult.  If you have stored procs or views that reference this table, be sure to recompile them after you FINISH the redef. This will have a side-benefit that your table will be reorganized (i.e. defragmented).


or 


Maybe add the column without the NOT NULL constraint.  When that finishes, then alter the column to add the NOT NULL constraint. My intuition is that you'll still get locking somewhere in the process, so no promises. Maybe just a crazy idea.


If you want to try the Online Redefinition, then you might find these links helpful:


http://www.oracle-base.com/articles/11g/online-table-redefinition-enhancements-11gr1.php
http://docs.oracle.com/cd/E18283_01/server.112/e17120/tables007.htm