Gravitational Field of a Spherical Perfect Fluid
Merab Gogberashvili, Beka Modrekiladze

TL;DR
This paper investigates the gravitational field of a static spherical perfect fluid and finds that matching interior and exterior metrics is only feasible outside the photon sphere, impacting models of realistic astrophysical objects.
Contribution
It demonstrates the conditions under which interior and exterior metrics can be smoothly matched for a spherical perfect fluid, emphasizing the importance of the photon sphere radius.
Findings
Matching is only possible beyond the photon sphere
Interior and exterior metrics can be smoothly joined in realistic models
The photon sphere radius is critical for metric matching
Abstract
Analyzing the spacetime for a static spherically distributed perfect fluid we show that the smooth matching of the interior and exterior metrics for a realistic source is possible only for the distances from the origin that exceeds the photon sphere radius for this object.
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