Yes, you can use a standard Oyster card (or Contactless payment) for travel on Thameslink and Southern trains between Central London and Gatwick Airport. Gatwick is one of the few major airports outside of London's traditional zones where "Pay As You Go" (PAYG) technology has been extended. When using Oyster, you simply "touch in" at your starting station (e.g., London Blackfriars or St Pancras) and "touch out" at the Gatwick Airport station. However, there are two important caveats. First, Gatwick is not in a London Travel Zone, so your journey will be charged a special airport fare which is higher than a standard zone-to-zone trip. Second, while Oyster is accepted, it is often not the cheapest option for families or those with Railcards; sometimes a paper ticket or a "Contactless" mobile payment is more cost-effective due to capping rules. Also, note that Oyster is not valid on the Gatwick Express service—you must use Contactless or a specific ticket for that premium train.