How much longer? If he just not reply, what time frame we are talking about?

Him not signing complicates things. While you can file in Georgia, service must be under Indian law, and they require a great deal just to serve the case.

As of August 1, 2007, the Hague Convention on the Service Abroad of Judicial and Extra Judicial Documents in Civil and Commercial Matters is in force between the United States and India. Requests for service of process on persons or entities located in India, utilizing the USM-94 form should be sent to the Indian Central Authority for that Convention. Contact and practical information regarding requests for service of process in India may be found on the Hague Conference website. India has made a reservation to the Convention objecting to service of process by mail, or directly through judicial officers in India without the involvement of the Central Authority. Service in India is very expensive. Many process servers there charge over $1000 for a service that would cost $50 in Georgia.

Ok, thank you. If he will agree to sign - how much would service cost?

Then it's free. The form would be part of what your lawyer would draft.