What are the documents needed to visit a relative in Germany?
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If you are from a country with visa-free entry (EU, EEA, many "Western" nations"), you need a valid passport and enough funds on hand to pay for your immediate expenses.
If you are from a country that requires a visa, your application will have to show ties to your home nation and a stable financial situation which make it credible that you are a tourist. There is no need for a formal invitation if you can pay your own food and lodging. You would still mention your sister in your description of the itinerary and the premise of the trip.
If your financial situation is such that you cannot afford the trip on your own, it may help your chances if your sister signs a VerpflichtungserklΓ€rung, which is a promise to reimburse the German state for any costs if you should overstay your visa.