Someone drove by and saw a door open at my house, called the police and the police came and entered the house with no search warrant... are they allowed to enter with no search warrant without probable cause?

They are not searching, they are doing a welfare check, an open door when reported would be the probable cause.

Was the "probable cause" already not established? The open door may be the "cause". What if someone saw smoke coming from your house, should the police or the fire department not try to find the "cause"? Or let your house burn to the ground! If the police had ignored the alert about the open door and someone robbed you blind, would you not be upset? --- Ace

I will also add that you also have to remember that the police can search without a valid warrant, but all that happens is that what is found in that search can't be used in court.

But as a police officer in Atlanta we used to get calls several times a week about a door open, or window open, and we would go and search the area to see if someone had broken in the home or not.

Normally most would be someone just leaving a door open but about 1 in 10 would be someone had broken in.

The police would not normally just stop if they see a door open ( unless it is a business after business hours) but when a neighbor calls, there is an assumption that this is not the norm, since if this normally happened, why would the neighbor call.