[Paper Review] On the question of trapped surfaces and black holes

Abhas Mitra|arXiv (Cornell University)|May 30, 2001

Relativity and Gravitational Theory3 references3 citations

TL;DR

This paper argues that black holes (BHs) cannot exist in general relativity due to a fundamental conflict with the timelike nature of material particle worldlines; instead, it proposes that observed black hole candidates (BHCs) are 'eternal' compact objects (ECOs) with hard surfaces that avoid singularities. These ECOs can explain hard X-ray tails via relativistic plasma flows with Lorentz factors γ ~ few, unlike standard neutron stars, and avoid the infinite proper length paradox of BHs by requiring M(r) → 0 as R → 0.

ABSTRACT

There are many observational evidences for the detection of compact objects with masses significantly larger (in galactic cases) or much larger (in extragalactic cases) than the upper limits of masses of em cold Neutron Stars. Such compact objects are commonly interpreted as Black Holes (BHs). However, we point out that while such Black Hole Candidates (BHCs) must be similar to BHs in many respects they, actually, can not be BHs because existence of Black Holes would violate the basic tenet of the General Theory of Relativity that the worldline of a material particle must be TIMELIKE at any regular region of spacetime. We arrive at this unique conclusion by approaching the problem from various directions. We feel that such ``operational'' Black Holes could be able to explain hard X-ray tail found in the galactic BHCs because Lorentz factor of the plasma accreting on such objects should be considerably higher than the corresponding NS case.

Motivation & Objective

• To resolve the contradiction between general relativity’s requirement that particle worldlines be timelike and the existence of black holes with event horizons.
• To explain the observed hard X-ray tails in galactic black hole candidates without invoking standard black hole accretion physics.
• To demonstrate that trapped surfaces cannot form in spherically symmetric gravitational collapse under general relativity.
• To propose that observed BHCs are not true black holes but compact objects with hard surfaces, avoiding singularities.
• To reconcile observational data—such as X-ray luminosities and polarization—with non-BH models like ECOs or self-gravitating fermion balls.

Proposed method

• Uses spherically symmetric spacetime metrics with invariant circumference coordinate R to analyze radial worldlines.
• Applies the condition ds² ≥ 0 for timelike geodesics to derive constraints on g₀₀ and g₁₁, showing V ≤ 1 implies g₀₀ ≥ 0.
• Analyzes spherical gravitational collapse using comoving coordinates (r,t), deriving the constraint Γ² = 1 + U² - 2GM(r)/R.
• Reinterprets Γ and U as dR/dl and dR/dτ, respectively, to express the constraint as Γ²(1 - V²) = 1 - 2GM(r)/R.
• Shows that the right-hand side must be ≥ 0, so 2GM(r)/R ≤ 1, proving trapped surfaces cannot form in spherical collapse.
• Concludes that a true black hole singularity would require M(r) → 0 as R → 0, implying zero gravitational mass at the center.

Experimental results

Research questions

• RQ1 Can trapped surfaces form in spherically symmetric gravitational collapse under general relativity?
• RQ2 Does the existence of a black hole event horizon violate the timelike nature of material particle worldlines?
• RQ3 Can observed black hole candidates (BHCs) be explained by objects other than true black holes?
• RQ4 What is the maximum Lorentz factor achievable in accretion flows onto compact objects, and can it explain hard X-ray tails?
• RQ5 Is the observed X-ray emission from BHCs like Sgr A* consistent with accretion or more plausibly with synchrotron radiation from ECOs?

Key findings

• Trapped surfaces cannot form in spherically symmetric gravitational collapse because 2GM(r)/R ≤ 1 is required by the timelike worldline condition.
• True black holes would require the central singularity to have zero gravitational mass, contradicting the existence of finite-mass black holes.
• The final singularity in collapse must have M(r) → 0 as R → 0, implying that the central object is not a massive singularity.
• Accretion flows onto ECOs can achieve Lorentz factors γ ~ few, sufficient to explain hard X-ray tails, unlike neutron stars with γ ~ 1.1.
• Synchrotron radiation, not ADAF accretion, better explains low-luminosity X-ray emissions in AGNs and BHCs like Sgr A*, especially given observed polarization and luminosity constraints.
• The supermassive BHC Sgr A* may be better explained by a self-gravitating ball of weakly interacting fermions with mass mf ~ 15.9 keV, consistent with observed mass and dynamics.