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This clinical trial evaluates whether positron emission tomography-magnetic resonance imaging (PET-MRI) using the radioactive drug radiohybrid prostate-specific membrane antigen (rhPSMA)-7.3 may help in detecting higher grade or stage disease in men with low and favorable intermediate risk prostate cancer who are candidates for active surveillance. A PET scan is a test that uses a radioactive drug and a computer to create images of how organs and tissues in the body are functioning. The radioactive drug used in this study, rhPSMA-7.3, attaches to the abnormal cells in the body at a different rate than normal cells which allows the scanner to create a detailed picture of how the body is working. An MRI scan uses strong magnets and computers to create detailed images of the soft tissue in your body. A multiparametric (mp)MRI is a type of MRI scan that creates a more detailed picture of the prostate gland. Using rhPSMA-73 with PET-MRI and mpMRI may be more effective in detecting higher grade or stage disease in men with low and favorable intermediate risk prostate cancer.

This phase II trial compares the effect of relugolix to leuprolide on cardiac function and performance in patients with prostate cancer. Androgen deprivation therapy (ADT) has been a key component for the treatment of advanced prostate cancer for decades. The term androgen deprivation therapy means lowering a man's testosterone. Long-term studies show that ADT may contribute to a detriment to cardiac health and predisposes men to developing cardiac diseases. Recent studies suggest that men taking relugolix for treatment of prostate cancer may have a lower risk of developing cardiovascular problems, but more studies are needed to understand this observation, and there are currently no studies reporting the direct impact of ADT (relugolix, versus the more-commonly used leuprolide) on cardiac function and outcomes. Participants will receive definitive radiotherapy for unfavorable intermediate risk prostate cancer and 6-month ADT (either relugolix or leuprolide). In addition, participants will undergo the following: 1. Comprehensive cardiac and exercise testing before and after starting ADT 2. Completion of quality-of-life questionnaires at specific intervals during the study period 3. Provide blood samples at specific intervals during the study period to test for changes in steroid levels and certain biomarkers

This phase III trial tests the side effects of stereotactic body radiation therapy (SBRT) compared to hypofractionated radiotherapy for treating patients with prostate adenocarcinoma that has come back after a period of improvement (recurrent) or that has spread from where it first started (primary site) to a limited number of sites (oligometastatic). SBRT is a type of external radiation therapy that uses special equipment to position a patient and precisely deliver radiation to tumors in the body (except the brain). The total dose of radiation is divided into smaller doses given over several days. This type of radiation therapy helps spare normal tissue. Hypofractionated radiation therapy delivers higher doses of radiation therapy over a shorter period of time and may kill more tumors cells and have fewer side effects. SBRT may work just as well as hypofractionated radiation therapy at treating patients with biochemically recurrent or oligometastatic prostate cancer, but with a shorter treatment time and possibly fewer side effects.