Google Sitemap for multiple domains of same site

Question

I have a website and its domain has been used for several years. Now I want to use an additional new name for the site, so I got a new domain. There are four valid addresses now: http://old.com, http://www.old.com, http://new.com, http://www.new.com, and they all show the same site; they are synonyms (no re-direction).

I am using Google Webmaster Service. So far my sitemap contained lines for http://www.old.com (and I always wondered whether I should have http://old.com in there, too, thus listing each page twice). <- This would be my first question: should I or not? Would it be good or bad or wouldn't it matter at all?

Now the same site can also be called via http://new.com and http://www.new.com. What to do now? Add this as a new website in Google Webmaster Service? This seems ridiculous, as it is the same site (with another name). And I would even fear that Google might feel betrayed and punish my site with a low rank for the duplicate post.

However, the new addresses do exist. So where to tell Google that this is the case? How to make Google know that http://old.com = http://www.old.com = http://new.com = http://www.new.com?

And: How to write the sitemap that I submit to Google? Shall it contain one domain only or both? The Website is registered with Google as www.old.com. Would I even be allowed to have www.new.com in the same sitemap? Would it do good or bad?

I already read on https://support.google.com/webmasters, but didn't find answers to my (rather basic?) questions. I don't use Google Analytics.

Answer 1

There are four valid addresses...and they all show the same site; they are synonyms (no re-direction).

Prior to considering your sitemap, which is not essential for Google to index your site, you should deal with all the duplicate content issues you have going on here. As covered in this Google Webmaster Tools help doc:

Duplicate content generally refers to substantive blocks of content within or across domains that either completely match other content or are appreciably similar. 

You should therefore pick one domain, and one URL version of that domain (e.g., www.new.com if preferred), and 301 redirect all the others to this so that Google doesn't crawl and find the same content on each of these URLs.

That also includes doing a 301 redirect from one URL version of new.com to the other (e.g., http://new.com -> http://www.new.com). You should also indicate to Google that this is the preferred version of your site using Google Webmaster Tools.

Last but not least, it's a good idea to let Google know that your site moved to the new address using the change of address tool.

With that completed, you can then list all the URLs that correspond to one version (e.g., http://www.new.com) in your sitemap without concern for duplicate content penalties from all the others.