A320
Flight Crew Air Transport Pilot (ATP)
Aircraft Equipment Problem Less Severe
General None Reported / Taken
Aircraft
We were departing SJC on runway 30R. Conditions were clear skies and 10 miles or greater visibility. My duties were the pilot monitoring and the F/O (First Officer) was the pilot flying. Upon reaching thrust reduction altitude; we received a TCAS RA to descend at a rate of at least 2000 fpm. The target aircraft was at our 12 o'clock less than a mile and 500 ft above us. There was no way we were able to comply with the TCAS command [because] as soon as the TCAS alert had happened; it disappeared. Further; our initial climb rate was over 4000 fpm because were very light. We never saw an aircraft and shortly after; SJC Tower instructed us to contact departure control. Tower and NorCal TRACON never reported any aircraft in our vicinity. I don't know if this was a phantom RA or not. Needless to say; this was a very disconcerting event. I truly thought we were going to have a midair collision. We both were very shaken by this event and I even failed to report it to SJC Tower or any controlling ATC authorities. This event only lasted about 3-5 seconds. We didn't even have time to comply with procedures. The FO elected to continue the climb to avoid the RA and we did so by 200 ft.It is unknown if there was or wasn't an aircraft directly in our departure path; but we never saw one. I just don't know.After reflecting on this event for several days; I have come to the reasoning; that with the surrounding airspace protections at SJC; the possibility of an aircraft intrusion in the departure corridor is possible; but not likely. My failure to recognize that it was a possible phantom RA; I didn't realize that the TCAS system on this aircraft may be failing as well. I did not write up the TCAS system on this aircraft and it probably should be.
A320 Captain reported receiving an RA on climb out from SJC that was likely a false target generated by a malfunctioning TCAS.