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The Modified Schwarzschild Radius with Hubble Field and its Connection to Dark Matter

The classical Schwarzschild radius defines the boundary at which an object becomes a black hole. In an expanding universe governed by the Hubble flow, this concept must be generalized. We derive the modified Schwarzschild radius by including the repulsive Hubble potential into the escape velocity condition v=c.
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Using of the Correction Schwarzschild radius Equation and Its Application of the Black Holes

Ibn Al-Haitham Journal for Pure and Applied Sciences, 2017
This study is a try to compare between the traditional Schwarzschildâ€™s radius and the equation of Schwarzschildâ€™s radius including the photonâ€™s wavelength that is suggested by Kanarev for black holes to correct the error in the calculation of the gravitational radius where the wavelengths of the electromagnetic radiation will be in our ...
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Strict Gravitational-Radius Cosmology Linear Expansion, Frozen Structure Growth, and the Empirical Status of the Schwarzschild Radius

We present a cosmological framework based on a strict gravitational-radius postulate, ( R_g = GM/c^2 ), applied globally to the Universe as a whole. In this approach, cosmology is formulated as a boundary-value problem defined by the causal horizon rather than as a superposition of independently evolving components.
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Timelike Thin-Shell Evolution in Gravitational Collapse: Classical Dynamics and Thermodynamic Interpretation. [PDF]

Entropy (Basel)
Schubert AG.
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Reversible Evaporation and the Entropy of Black Holes. [PDF]

Entropy (Basel)
Herrmann F, Pohlig M.
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Design and Demonstration of Compact and Lightweight Imaging Spectrometer Based on Schwarzschild Reflector Systems Using Commercial Off-the-Shelf Optics. [PDF]