Empirical constraints on the general relativistic electric field associated with PSR J0437-4715

We simulate the magnetosphere of the nearby millisecond pulsar PSR J0437 - 4715, which is expected to have an unscreened electric potential due to the lack of magnetic pair production. We incorporate general relativistic (GR) effects and study curvature radiation (CR) by primary electrons but neglect inverse Compton scattering of thermal X-ray photons by these electrons. We find that the CR spectrum cuts off at energies below similar to 17 GeV, well below the threshold of the High Energy Stereoscopic System (H. E. S. S.) telescope (less than or similar to 100 GeV), while other models predict a much higher cutoff of greater than or similar to 100 GeV. GR theory also predicts a relatively narrow pulse (betadegrees similar to 0.2 phase width) centered on the magnetic axis. EGRET observations above 100 MeV significantly constrain 0.2 the application of the Muslimov & Harding model for gamma-ray production as a result of GR frame dragging and ultimately its polar cap ( PC) current and accelerating potential. Whereas the standard prediction of this pulsar's gamma-ray luminosity due to GR frame dragging is similar to 10% of the spin-down power, a nondetection by forthcoming H. E. S. S. observations will constrain it to less than or similar to 0.3%, enforcing an even more severe revision of the accelerating electric field and PC current.