[Paper Review] Gravitational collapses to bodies of a finite volume

Tiziana Marsico, A. Loinger|ArXiv.org|Dec 16, 2006

Cosmology and Gravitation Theories7 references5 citations

TL;DR

This paper presents an exact relativistic computation showing that spherically symmetric gravitational collapses with time-dependent pressure do not form black holes, but instead result in compact bodies of finite, non-zero volume. Using a relativistic hydrodynamic model with time-varying pressure and density, the authors demonstrate that the collapse terminates in a finite-sized object, challenging the widespread belief that pressure cannot prevent infinite density singularities in general relativity.

ABSTRACT

We prove with an exact relativistic computation that the spherosymmetric gravitational collapses with a time-dependent pressure end in bodies with a small, but finite volume. Against a diffuse, wrong conviction.

Motivation & Objective

• To challenge the widespread belief that relativistic gravitational collapse inevitably leads to black hole formation.
• To demonstrate through exact relativistic computation that pressure—especially time-dependent pressure—can prevent infinite density singularities.
• To show that the final state of collapse is a compact body of finite, non-zero volume, not a point mass or black hole.
• To correct a foundational error in Chandrasekhar's interpretation of general relativity regarding collapse outcomes.
• To provide a physically consistent model of gravitational collapse that avoids fictitious singularities and event horizons.

Proposed method

• Adopts a spherically symmetric, time-dependent relativistic hydrodynamic model with pressure and density functions of time only.
• Uses the relativistic Euler equations in the form derived from the energy-momentum tensor and four-velocity dynamics.
• Applies the internal solution framework from McVittie (1964), extended to include time-dependent pressure.
• Employs Eddington's coordinate system and the function $ f(r) $ to describe the spacetime geometry without event horizons.
• Analyzes the absence of event horizons by ensuring $ f(r) $ does not lead to $ r = 2m $ singularities.
• Compares the Schwarzschild solution in its original form (regular everywhere except $ r=0 $) with the standard form, highlighting the physical inadmissibility of $ r \leq 2m $.

Experimental results

Research questions

• RQ1 Can a relativistic gravitational collapse with time-dependent pressure result in a finite-volume compact object rather than a black hole?
• RQ2 What is the role of time-varying pressure in preventing the formation of an event horizon and infinite density?
• RQ3 Why does Chandrasekhar’s conclusion that pressure cannot prevent black hole formation represent a fundamental error?
• RQ4 How does the choice of coordinate function $ f(r) $ affect the physical interpretation of the spacetime geometry in collapse models?
• RQ5 To what extent do the standard assumptions about the Schwarzschild solution's validity for $ r \leq 2m $ misrepresent general relativity?

Key findings

• Gravitational collapse with time-dependent pressure ends in a body of finite, non-zero volume, not a black hole.
• The final state is a compact object with a regular spacetime geometry, free from event horizons and singularities beyond $ r=0 $.
• The computation confirms that accelerated motion of particles in the collapsing body does not generate gravitational waves, as they follow geodesics.
• The standard form of the Schwarzschild solution is physically valid only for $ r > 2m $, and its extension to $ r \leq 2m $ is a mathematical fiction.
• Chandrasekhar’s assertion that pressure cannot prevent collapse into a black hole is based on a double error: misinterpreting the solution's domain and assuming physical meaning for $ r \leq 2m $.
• The concept of gravitational potential energy in general relativity is not tensorial and thus not fundamental, though it remains practically useful in astrophysical estimates.