SEVERE: Servlet.service() for servlet springapp threw exception
java.lang.NullPointerException at com.mashup.dao.UserDAOImpl.findById(UserDAOImpl.java:42)

@Stateless
public class UserDAOImpl {
   private EntityManager entityManager;   

   @PersistenceContext(unitName = "example")
   public void setEntityManager(EntityManager entityManager) {
      this.entityManager = entityManager;
   }

   public EntityManager getEntityManager() {
      return entityManager;
   }
   public User findById(String i) {
// /!\ Ici se trouve le nullPointerException /!\
// /!\ Ici se trouve le nullPointerException /!\
// /!\ Ici se trouve le nullPointerException /!\
      System.out.println(entityManager.toString());
// /!\ Ici se trouvait le nullPointerException /!\
// /!\ Ici se trouvait le nullPointerException /!\
// /!\ Ici se trouvait le nullPointerException /!\
      
      log.debug("getting Users instance with id: " + i);
      try {
         User instance = entityManager.find(User.class, i);
         return instance;
      } catch (RuntimeException re) {
         throw re;
      }
   }
}

@Entity
public class User {
   @Id
   @GeneratedValue
   private Long id;
   private String name;
   private String login;
   private String password;

   // Avec les getters et les setters en dessous

public class HelloController implements Controller {
   private UserDAOImpl userDAOImpl;

   public ModelAndView handleRequest(HttpServletRequest request,
         HttpServletResponse response) throws ServletException, IOException {

      // Ce bloc fonctionne bien, la connexion est etablie
      // ----
      EntityManagerFactory emf = Persistence.createEntityManagerFactory("example");
      EntityManager em = emf.createEntityManager();

      em.close();
      emf.close();
      // ----

      this.userDAOImpl.findById("0");

      return new ModelAndView("hello", "now", now);
   }

   public UserDAOImpl getUserDAOImpl() {
      return userDAOImpl;
   }

   public void setUserDAOImpl(UserDAOImpl userDAOImpl) {
      this.userDAOImpl = userDAOImpl;
   }
}

<?xml version="1.0" encoding="UTF-8"?>
<persistence xmlns="http://java.sun.com/xml/ns/persistence"
   xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
   xsi:schemaLocation="http://java.sun.com/xml/ns/persistence
    http://java.sun.com/xml/ns/persistence/persistence_1_0.xsd"
   version="1.0">
   <persistence-unit name="example" transaction-type="RESOURCE_LOCAL">
      <properties>
         <property name="hibernate.ejb.cfgfile" value="META-INF/hibernate.cfg.xml" />
         <property name="hibernate.c3p0.min_size" value="5" />
         <property name="hibernate.c3p0.max_size" value="20" />
         <property name="hibernate.c3p0.timeout" value="300" />
         <property name="hibernate.c3p0.max_statements" value="50" />
         <property name="hibernate.c3p0.idle_test_period" value="3000" />
      </properties>
   </persistence-unit>
</persistence>

<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE beans PUBLIC "-//SPRING//DTD BEAN//EN" "http://www.springframework.org/dtd/spring-beans.dtd">
<beans>
   <bean id="userDAOImpl" class="com.mashup.dao.UserDAOImpl">
   </bean>

   <bean name="/hello.htm" class="com.mashup.controllers.HelloController">
      <property name="userDAOImpl" ref="userDAOImpl"/>
   </bean>

   <bean id="viewResolver"
      class="org.springframework.web.servlet.view.InternalResourceViewResolver">
      <property name="viewClass"
         value="org.springframework.web.servlet.view.JstlView"></property>
      <property name="prefix" value="/WEB-INF/jsp/"></property>
      <property name="suffix" value=".jsp"></property>
   </bean>
</beans>

<?xml version="1.0" encoding="UTF-8"?>
<beans xmlns="http://www.springframework.org/schema/beans"
   xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:context="http://www.springframework.org/schema/context"
   xmlns:tx="http://www.springframework.org/schema/tx"
   xsi:schemaLocation="
                http://www.springframework.org/schema/beans http://www.springframework.org/schema/beans/spring-beans-2.5.xsd
                http://www.springframework.org/schema/context http://www.springframework.org/schema/context/spring-context-2.5.xsd
                http://www.springframework.org/schema/tx http://www.springframework.org/schema/tx/spring-tx.xsd">

   <bean id="entityManagerFactory" class="org.springframework.orm.jpa.LocalEntityManagerFactoryBean" />

   <bean id="transactionManager" class="org.springframework.orm.jpa.JpaTransactionManager">
      <property name="entityManagerFactory" ref="entityManagerFactory" />
   </bean>

   <tx:annotation-driven />

   <bean
      class="org.springframework.orm.jpa.support.PersistenceAnnotationBeanPostProcesser" />

   <context:annotation-config />
   <!--   <context:spring-configured />-->
</beans>