Do frozars exist? Coordinate time, proper time and the formation of black-hole horizons
Bobir Toshmatov
1,*
,
Nozima Isamadinova
2
,
Azamjon Boydedayev
2
1 Department of Physics, New Uzbekistan University , Movarounnahr str. 1, Tashkent 100000, Uzbekistan
2 Ulugh Beg Astronomical Institute , Astronomy street 33, Tashkent 100052, Uzbekistan
Abstract
General relativity does not forbid horizon formation; the “frozar” theory of Zahid Zakir reaches that conclusion only by promoting the Schwarzschild time coordinate t to a physically privileged “world time”. In this paper, we first review the etymology and history of the terms frozen star and frozar, and show that the latter revives a 1960s label while reversing its meaning. We then show, with explicit calculations, that (i) Z. Zakir's infall formulas are correct but describe a coordinate whose range ends at the horizon, not the end of the infaller's history; (ii) the Painlevé–Gullstrand time T satisfies every criterion Z. Zakir uses to define world time, yet in T the collapsing surface crosses r = 2M at finite time; (iii) the identical “freezing” appears for an inertial particle in flat spacetime seen by a uniformly accelerated observer; (iv) in the Oppenheimer–Snyder solution the event horizon forms at the centre while the stellar surface is still at r ≃ 4.5M, and trapped surfaces form at finite comoving proper time; (v) the “metrics with independent parameters” for charged and rotating sources are the Reissner–Nordström and Kerr(–Newman) metrics re-expressed through the Christodoulou–Ruffini irreducible mass; and (vi) the claims that do differ from standard general relativity (frozars do not merge, have no ergosphere, carry asymmetric “hair”) conflict with gravitational-wave ringdown and area-theorem tests, including GW150914 and GW250114, and with Event Horizon Telescope images. We also identify errors in the cosmological and quantum-gravity claims of the founding 2006 paper.
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Toshmatov, B., Isamadinova, N. and Boydedayev, A., Do frozars exist? Coordinate time, proper time and the formation of black-hole horizons, Turanian J. Vol. 2, No. 2 (020206), 2026.