I can't find toByteArray() as @atrioom said, so I use StringWriter, please try:

public void writeListToJsonArray() throws IOException {  

    //your list
    final List<Event> list = new ArrayList<Event>(2);
    list.add(new Event("a1","a2"));
    list.add(new Event("b1","b2"));


    final StringWriter sw =new StringWriter();
    final ObjectMapper mapper = new ObjectMapper();
    mapper.writeValue(sw, list);
    System.out.println(sw.toString());//use toString() to convert to JSON

    sw.close(); 
}

Or just use ObjectMapper#writeValueAsString:

    final ObjectMapper mapper = new ObjectMapper();
    System.out.println(mapper.writeValueAsString(list));

comment : is request to return in server.

headers : type of comment json or xml ,html,Image ,multipart ... etc.

see this example :

RestTemplate restTemplate = new RestTemplate();
ObjectMapper mapper = new ObjectMapper();
String requestJson = null;
try {
    requestJson = mapper.writeValueAsString(Yourrequest);HttpHeaders headers = new HttpHeaders();
    headers.setContentType(MediaType.APPLICATION_JSON);
    HttpEntity<Object> entity = new HttpEntity<Object>(requestJson, headers);
    LOGGER.info("send request to  url {} ", getUrl());
    YourTypeOfResponse response = restTemplate.postForObject(URL_LOCAL,
            entity, YourTypeOfResponse.class);
} catch (JsonGenerationException e) {
    LOGGER.error("JsonGenerationException occurred ", e);
} catch (JsonMappingException e) {
    LOGGER.error("JsonMappingException occurred ", e);
} catch (IOException e) {
    LOGGER.error("IOException occurred ", e);
}