遍历嵌套的JSON对象可以使用递归方法来实现。下面是一个示例代码：

def traverse_json(obj, key=None):
    if isinstance(obj, dict):
        for k, v in obj.items():
            if key is not None:
                k = f"{key}.{k}"
            traverse_json(v, key=k)
    elif isinstance(obj, list):
        for i, v in enumerate(obj):
            k = f"{key}[{i}]"
            traverse_json(v, key=k)
    else:
        print(f"{key}: {obj}")

# 示例JSON对象
json_obj = {
    "name": "John",
    "age": 30,
    "address": {
        "street": "123 Main St",
        "city": "New York"
    },
    "phone_numbers": ["123456789", "987654321"]
}

# 遍历JSON对象
traverse_json(json_obj)

运行以上代码将输出如下结果：

name: John
age: 30
address.street: 123 Main St
address.city: New York
phone_numbers[0]: 123456789
phone_numbers[1]: 987654321

该示例代码通过递归实现了对嵌套的JSON对象的遍历。在遍历过程中，会打印每个键值对的路径和对应的值。如果值是字典或列表，会继续递归调用来遍历其内部的键值对。