If you are used to using the "Default-Information Originate" command with OSPF or EIGRP to easily advertise a default route, you might be surprised to find that solely applying that command within BGP does not advertise a default route. You must also use
Redistribute Static in conjunction with
Default-Information Originate. Your BGP config would look something like this:
router bgp 65000 no synchronization bgp log-neighbor-changes redistribute static neighbor 10.10.10.10 remote-as 65010 default-information originate no auto-summary
Both commands are needed whether you are using eBGP or iBGP.