3-arm Study of Abiraterone Acetate Alone, Abiraterone Acetate Plus Degarelix, a GnRH Antagonist, and Degarelix Alone for Patients With Prostate Cancer With a Rising PSA or a Rising PSA and Nodal Disease Following Definitive Radical Prostatectomy

Inclusion Criteria: * Willing and able to provide written informed consent and Authorization for Use and Release of Health and Research Study Information (HIPAA authorization) NOTE: HIPAA authorization may be either included in the informed consent or obtained separately. * Male aged 18 years and above * Patients must have undergone local treatment via radical prostatectomy * Patients who have received primary radiation therapy followed by a salvage radical prostatectomy are eligible. * Patients who have had post-operative radiation therapy for presumed locally recurrent disease are eligible * Histologically confirmed prostate cancer (per standards at Institution of participant registration) currently with progressive disease, defined as: * Rising PSA (50% or more increase to a level of 1 ng/mL or more, based on at least 3 PSA determinations obtained at least 1 week apart). The 50% rise in PSA is across the 3 determinations, and these determinations do not need to be sequential AND * PSADT ≤ 9 months as calculated according to the Memorial Sloan-Kettering Cancer Center nomogram (http://www.mskcc.org/mskcc/html/10088.cfm) OR * Rising PSA as defined above AND * Metastatic disease limited to the presence of pelvic and/or retroperitoneal nodes \< 2 cm in short axis. * Patients must have a serum testosterone of 150 ng/dL or greater * ECOG performance status of ≤ 2 (Appendix A) * Adequate bone marrow, hepatic, and renal function, as evidenced within 14 days prior to treatment initiation by: * Absolute neutrophil count (ANC) ≥ 1500/mm3 * Platelet count ≥ 100,000/mm3 * Hemoglobin ≥ 9 g/dL without need for hematopoietic growth factor or transfusion support within 30 days prior to treatment initiation * Aspartate aminotransferase (AST) ≤ 1.5 times the upper limit of the normal range (x ULN) * Alanine aminotransferase (ALT) ≤ 1.5 x ULN * Total bilirubin ≤ 1.5 x ULN * Serum creatinine of ≤ 1.5 mg/dl or Calculated creatinine clearance of ≥ 60 mL/min * Serum albumin ≥ 3.0 g/dL * Serum potassium ≥ 3.5 mEq/L * Prothrombin time (PT) ≤ 1.5 x ULN (or international normalized ratio \[INR\] ≤ 1.3) unless the patient is receiving anticoagulant therapy * Partial thromboplastin time (PTT) ≤ 1.5 x ULN unless the patient is receiving anticoagulant therapy At least 4 weeks and recovery to Grade 0-1 from reversible effects of prior surgery (i.e., incisional pain, wound drainage) * Able to swallow the study drug whole as a tablet * Willing to take abiraterone acetate on an empty stomach; no food should be consumed at least two hours before and for at least one hour after the dose of abiraterone acetate is taken * Patients who have partners of childbearing potential must be willing to use a method of birth control with adequate barrier protection as determined to be acceptable by the principal investigator during the study and for 1 week after last dose of abiraterone acetate. Exclusion Criteria: * Prior cytotoxic chemotherapy or biologic therapy for prostate cancer * More than 8 months of prior hormonal therapy (e.g., gonadotropin-releasing hormone analogs, megestrol acetate, or Casodex) Note: Patients who have been on prior hormonal therapy must wait at least 1 year after the drug is fully metabolized to start treatment on protocol. * Prior ketoconazole, abiraterone acetate, or enzalutamide for the treatment of prostate cancer. * Known brain metastasis or evidence of metastatic disease by CT scan, physical exam, or bone scan within 4 weeks of registration * Patients with equivocal uptake on a bone scan that in the clinician's opinion do not definitively constitute metastatic disease are eligible * Currently active second malignancy Significant medical condition other than cancer, that would prevent consistent and compliant participation in the study that would, in the opinion of the investigator, make this protocol unreasonably hazardous including but not limited to: * Active infection or other medical condition that would make prednisone/prednisolone (corticosteroid) use contraindicated * Severe hepatic impairment (Child-Pugh Class C) * History of gastrointestinal disorders (medical disorders or extensive surgery) that may interfere with the absorption of the study agents * Uncontrolled hypertension (systolic BP ≥ 160 mmHg or diastolic BP ≥ 95 mmHg); patients with a history of hypertension are allowed provided blood pressure is controlled by anti-hypertensive treatment * Active or symptomatic viral hepatitis or chronic liver disease * History of pituitary or adrenal dysfunction * Clinically significant heart disease as evidenced by myocardial infarction, or arterial thrombotic events in the past 6 months, severe or unstable angina, or New York Heart Association (NYHA) Class III or IV heart disease or cardiac ejection fraction measurement of \< 50 % at baseline * Atrial fibrillation, or other cardiac arrhythmia requiring medical therapy * Uncontrolled diabetes mellitus * Active psychiatric condition Use of any prohibited concomitant medications (Section 5.5) within 30 days prior to Cycle 1, Day 1 * Pre-existing condition that warrants long-term corticosteroid use in excess of study dose * Grade \> 2 treatment-related toxicity from prior therapy * Known allergies, hypersensitivity or intolerance to abiraterone acetate, prednisone or degarelix * Administration of an investigational therapeutic within 30 days of Cycle 1, Day1 * Any condition which, in the opinion of the investigator, would preclude participation in this trial