The following th eorem is proven: axisymmetric\, stationary solutions of the Einstein field equations formed from classical gravitational collapse of matter obeying the null energy condition\, that are everywhere smooth and ultracompact (i .e.\, they have a \; light ring\, a.k.a. circular photon orbit) must h ave at least two light rings\, and one of them is stable. It has been argu ed that stable light rings generally lead to nonlinear spacetime instabili ties. Thus this result implies that smooth\, physically and dynamically re asonable ultracompact objects are not viable as observational alternatives to black holes whenever these instabilities occur on astrophysically shor t time scales. The proof of the theorem has two parts: (i) We show that li ght rings always come in pairs\, one being a saddle point and the other a local extremum of an effective potential. This result follows from a topol ogical argument based on the Brouwer degree of a continuous map\, with no assumptions on the spacetime dynamics\, and hence it is applicable to any metric gravity theory where photons follow null geodesics. (ii) Assuming E instein&rsquo\;s equations\, we show that the extremum is a local minimum of the potential (i.e.\, a stable light ring) if the energy-momentum tenso r satisfies the null energy condition.

\n DTSTART:20190424T193000Z LOCATION:Physics Building\, Room 204 SUMMARY:Light ring stability in ultra-compact objects END:VEVENT END:VCALENDAR