Antiandrogen Therapy and SBRT in Treating Patients With Recurrent, Metastatic Prostate Cancer

Inclusion Criteria: * Confirmed diagnosis of prostate adenocarcinoma after radical prostatectomy (primary small cell carcinoma of the prostate is not allowed, however adenocarcinoma with neuroendocrine differentiation is allowed) * Presence of 1-5 visible metastases (by PSMA PET-CT) * At least one metastasis must be M1a-b * Visceral metastases are not allowed * Patients may have any number of pelvic nodal metastases (but largest must be \< 2 cm) * Metastases must be amenable to treatment with SBRT * Biopsy of one metastasis must be attempted, unless unsafe to perform * Patient must be fit to undergo SBRT to all visible sites of metastases, ADT * Total testosterone \> 150 ng/dL prior to ADT (optimal time to measure total testosterone is between 8 and 9 am) * Adequate performance status (Eastern Cooperative Oncology Group \[ECOG\] 0-1) * Hemoglobin \>= 9.0 g/dL, independent of transfusion and/or growth factors within 3 months prior to randomization * Platelet count \>= 100,000 x 10\^9/uL independent of transfusion and/or growth factors within 3 months prior to randomization * Serum albumin \>= 3.0 g/dL * Glomerular filtration rate (GFR) \>= 45 mL/min * Serum potassium \>= 3.5 mmol/L * Serum total bilirubin =\< 1.5 x upper limits of normal (ULN) * Note: In subjects with Gilbert?s syndrome, if total bilirubin is \> 1.5 x ULN, measure direct and indirect bilirubin and if direct bilirubin is =\< 1.5 x ULN, subject may be eligible * Aspartate aminotransferase (AST) or…