Apple Watch not able to measure your heart rate? Relax, you're not dead
To obtain a user's heart rate, the Apple Watch sensors on the back of the watch flash green and UV lights at your skin. The lights are absorbed and are reflected back by your red blood. More blood can be found in your wrists when your heart beats. There is less blood there between beats. By computing the time between heart beats, your heart rate can be computed. But a tattoo, especially a red one, can also absorb the lights sent from the sensors and reflect back red light. Black tattoos can absorb green and red lights and also play havoc with the watch. One tattooed Reddit user was able to turn off wrist detection and could receive notifications, but could not make calls or use Apple Pay.
The Apple Watch works on dark-colored skin and with scars and abrasions. But those are translucent and allow light to go through them. The ink used for tattoos is opaque and light does not penetrate it. And that could be the reason why your Apple Watch shows that you have no heart rate. Unless you have tattoos on both wrists, the simple solution is to move your watch to the other arm.