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Abstract
Starting from the differential equation describing the path of a photon in the Schwarzschild field of a spherically symmetric non‐rotating star in empty space we derive the condition for the light emitted from such a star to return to its surface, and describe some features of its orbit. The principal results are (a) only stars of radius < 1‐5 (in units of the Schwarzschild radius) can recapture their photons, (b) no photon which is ultimately recaptured goes further than 1 ‐5 units from the centre of the star, (c) provided the stellar radius is <l‐5 the angular diameter of the star as seen by a distant observer is independent of that radius.
Finally we determine an integral equation for the ‘ least gravitationally intense star’ with the property that its total surface is visible to a fixed distant observer.