Courts in Georgia have held that when a landlord fails to respond to repair requests after a reasonable time, tenants can hire a competent repair person to perform the needed repairs. The cost must be reasonable, and the tenant may deduct the cost from the rent. It's a good idea to put your request in writing, keep all receipts and invoices, hire licensed workers if possible, and perform only needed repairs, not upgrades.
After the Tenant has given reasonable notice of a defect to the Landlord, and the Landlord has failed to make the repair within a reasonable time, the Tenant may make reasonable repairs and deduct the reasonable cost from the rent, or the Tenant may file a lawsuit against the Landlord for damages arising from the failure to repair.