Learjet 70 pilot reported a loud noise from the passenger cabin during climb. Pilot felt door seal was compromised even though pressurization was normal and diverted.

Narrative

We departed from ZZZ with a planned flight to ZZZ1. I was the PIC and pilot flying on this leg. We had been cleared to climb to our filed altitude of FL430 and were climbing through FL350 when the failure took place. There was a sudden and very loud howling noise coming from the passenger cabin. I turned to check on the welfare of the two passengers and found that the noise appeared to be coming from the main cabin door. However; there was no visual evidence that the cabin was depressurizing. I then looked to the cabin altitude controller and noticed that the cabin was maintaining altitude. Despite this; it was evident that a door seal was compromised. I instructed my SIC to notify Center that we were beginning an immediate descent and request FL180. Simultaneously I began an emergency descent. Center immediately cleared to 10;000 feet and asked if we were [requesting priority]. I again checked the status of our cabin altitude and found that it was decreasing normally. Upon my instructions the SIC advised Center of the nature of our situation and that the cabin pressure was still normal and as long as we could keep descending we did not believe [requesting priority] was necessary. As we descended through FL180 the howling noise stopped. We continued our descent to 10;000 and diverted to ZZZ2. We did require delayed vectoring in order to burn fuel in order to land at/below maximum landing weight. This portion of the flight and the landing at ZZZ2 was uneventful. I believe that the actions of the crew and air traffic controllers went well and communication was excellent. However; after considerable debrief there are two areas that I would do differently. First; [request priority] and squawk. Secondly; it was not until a much lower altitude that the seat belt sign was turned on. In the noise; emergency descent; ATC communications etc; that myself and my SIC neglected to turn this on.