If cryptography certificates are used in production environment and the production environment is replicated to disaster recovery, would the same certificates be valid for the disaster recovery environment?
closed as too broad by techraf, S.L. Barth, Stephane, Rory Alsop♦ Sep 26 '16 at 16:40
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As long as you have the certificate key pair (public and private), any computer can act as identified by the the certificate CN (common name). This is suppose to match the FQDN of your service, or else many browser will fail the authentication on the client side without even checking the signatures.
Provided that you use a reverse proxy (or DNS changes) to switch from production to recovery server, the transition can appear seamless to the client.