To create a RabbitMQ cluster within my kubernetes cluster, I use kubernetes objects definition from the following source: https://wesmorgan.svbtle.com/rabbitmq-cluster-on-kubernetes-with-statefulsets

which are:

---
apiVersion: v1
kind: Service
metadata:
  # Expose the management HTTP port on each node
  name: rabbitmq-management
  labels:
    app: rabbitmq
spec:
  ports:
  - port: 15672
    name: http
  selector:
    app: rabbitmq
  type: NodePort # Or LoadBalancer in production w/ proper security
---
apiVersion: v1
kind: Service
metadata:
  # The required headless service for StatefulSets
  name: rabbitmq
  labels:
    app: rabbitmq
spec:
  ports:
  - port: 5672
    name: amqp
  - port: 4369
    name: epmd
  - port: 25672
    name: rabbitmq-dist
  clusterIP: None
  selector:
    app: rabbitmq
---
apiVersion: apps/v1beta1
kind: StatefulSet
metadata:
  name: rabbitmq
spec:
  serviceName: "rabbitmq"
  replicas: 5
  template:
    metadata:
      labels:
        app: rabbitmq
    spec:
      containers:
      - name: rabbitmq
        image: rabbitmq:3.6.6-management-alpine
        lifecycle:
          postStart:
            exec:
              command:
              - /bin/sh
              - -c
              - >
                if [ -z "$(grep rabbitmq /etc/resolv.conf)" ]; then
                  sed "s/^search \([^ ]\+\)/search rabbitmq.\1 \1/" /etc/resolv.conf > /etc/resolv.conf.new;
                  cat /etc/resolv.conf.new > /etc/resolv.conf;
                  rm /etc/resolv.conf.new;
                fi;
                until rabbitmqctl node_health_check; do sleep 1; done;
                if [[ "$HOSTNAME" != "rabbitmq-0" && -z "$(rabbitmqctl cluster_status | grep rabbitmq-0)" ]]; then
                  rabbitmqctl stop_app;
                  rabbitmqctl join_cluster rabbit@rabbitmq-0;
                  rabbitmqctl start_app;
                fi;
                rabbitmqctl set_policy ha-all "." '{"ha-mode":"exactly","ha-params":3,"ha-sync-mode":"automatic"}'
        env:
        - name: RABBITMQ_ERLANG_COOKIE
          valueFrom:
            secretKeyRef:
              name: rabbitmq-config
              key: erlang-cookie
        ports:
        - containerPort: 5672
          name: amqp
        volumeMounts:
        - name: rabbitmq
          mountPath: /var/lib/rabbitmq
  volumeClaimTemplates:
  - metadata:
      name: rabbitmq
      annotations:
        volume.alpha.kubernetes.io/storage-class: anything
    spec:
      accessModes: [ "ReadWriteOnce" ]
      resources:
        requests:
          storage: 1Gi # make this bigger in production

With this configuration, pods cannot find each other on the network with the following error:

unable to connect to epmd (port 4369) on rabbitmq-1: nxdomain (non-existing domain)