I have a 'Page Viewer Web Part' in my SharePoint application, inside
which a .net application is hosted. The first page of the application
is a login page where I was passing the username of the users, having
access to the SharePoint site. It is working.

Now, I want to try something different.

As you all must be knowing, every application pool in IIS has a user
identity. I want to display that username and password (IIS
Application Pool user identity) in the embedded .aspx page(Login
Page) [Inside the 'Page Viewer Web Part' of the SharePoint site].
That is, the application pool user identity (username and password)
should sit inside the respective textboxes of the Login Page of
the .aspx page that is displayed inside the 'Page Viewer Web Part'.

Is this possible and if so, how? Kindly help me with good
articles/source code or relevant materials.

I will be eagerly waiting for your reply.