Do Black Holes Exist? — The Crothers Case

The black hole is one of modern physics' most confident claims: a region where matter has collapsed so completely that not even light escapes. It also has a determined dissenter. Stephen J. Crothers argues that the black hole is not merely unobserved but mathematically impossible — that the solution everyone points to was misread, and that black-hole theory violates the very logic of the equations meant to predict it. This page lays out his case as precisely as he makes it, with the mathematics he actually disputes, and adds the Electric Universe's own answer to what sits at the hearts of galaxies.

Who Stephen Crothers is

Stephen John Crothers (b. 1957, Queensland) is an independent researcher in general relativity and astrophysics. He began a PhD candidature in physics at the University of New South Wales around 2003 and was later removed from the program — an episode he recounts at length on his own site. He works outside conventional peer review, posting most of his papers at viXra and on his website, and has been closely associated with the Thunderbolts Project, speaking at several Electric Universe conferences. He frames his work as exposing what he calls the deliberate suppression of scientific truth.

The argument that black holes cannot exist

Crothers' case is not observational ("we haven't found one") but logical-mathematical ("the theory forbids one"). Its main pillars:

1. The "Schwarzschild solution" isn't Schwarzschild's. Every black hole begins with one line element, the metric universally taught as the Schwarzschild solution:

The event horizon appears where the first coefficient vanishes — at the Schwarzschild radius $r_{s} = \dfrac{2Gm}{c^{2}}$ — and the central singularity at $r = 0$. Crothers' first claim is historical: this form is David Hilbert's (1916), not the solution Karl Schwarzschild actually derived. His deeper claim is about what $r$ means. In the metric a sphere of symmetry has surface area

so $r$ is an areal (curvature) coordinate — fixed by the area of a sphere, not a measured distance out from a center; he identifies it with the inverse square root of the Gaussian curvature of the geodesic surface, $r = 1/\sqrt{K}$. Its smallest physical value is $r = r_{s}$, not zero. On that reading, letting $r$ run from $r_{s}$ down to $0$ — the move that manufactures the interior, the horizon, and the singularity — is illegitimate from the start.

2. Black holes violate the Principle of Superposition. A black hole is a solution of the vacuum field equations,

which describe a spacetime containing exactly one mass and nothing else. But the full equations $G_{\mu\nu} = \dfrac{8\pi G}{c^{4}}\,T_{\mu\nu}$ are nonlinear in the metric, so — unlike Newtonian gravity — their solutions cannot be added together. You cannot superpose two one-mass universes, drop a black hole into a cosmos that also holds stars and galaxies, or write down an exact solution for two black holes (none exists). On this argument, binary black-hole mergers and whole populations of black holes are mathematically incoherent.

3. The singularity structure is backwards. Standard general relativity treats $r = r_{s}$ (the horizon) as a removable coordinate artifact and $r = 0$ as the true singularity. Crothers argues that Schwarzschild's original solution has only one boundary, and that once $r$ is understood as an areal coordinate, "$r = 0$" cannot denote a spatial center at all — so the manifold simply cannot be "extended" through the horizon down to a central point.

4. Escape velocity is self-contradictory. The black hole is often introduced as an object whose escape velocity reaches the speed of light. But escape velocity comes from Newton's two-body gravity,

a relation between two masses — one body escaping another. Setting $v_{e} = c$ returns $r = 2GM/c^{2} = r_{s}$, the very radius used to define the horizon. Crothers' objection is twofold: a black hole is a one-mass construct, so there is no second body for which an escape velocity is even defined; and the definition is self-cancelling — an object cannot at once have an escape velocity (something can leave if it moves faster than $v_{e}$) and forbid anything from leaving at all.

5. General Relativity violates energy conservation. In general relativity the energy of the gravitational field itself is carried not by a tensor but by Einstein's pseudotensor $t^{\nu}_{\;\mu}$ — a coordinate-dependent object that can be transformed away to zero by a suitable choice of coordinates. A quantity that vanishes in one frame and not another, Crothers argues, cannot represent a real, localizable energy, so the theory has no proper energy-conservation law — and anything defined through it, gravitational waves included, inherits the problem.

His papers stating these arguments appeared in Progress in Physics (several, 2005–2010) and other venues; his own paper-and-talk index collects them, and "Geometric and Physical Defects in the Theory of Black Holes" gathers the core case.

Crothers in his own words (talks)

• Stephen Crothers: Black Holes & Relativity, Part One and Part Two (EU2013) — the full conference case.

• Stephen Crothers: General Relativity – a Case Study in Numerology | EU2015 — where he calls black holes and the Big Bang "numerology."

• Stephen Crothers: LIGO — Its Claims for Black Holes and Gravitational Waves | EU2017 and The Logical Inconsistency of the Special Theory of Relativity | EU2017.

• Stephen Crothers on the Synthetic Imaging of EHT's "First Image of a Black Hole" in M87 — his Event Horizon Telescope critique.

The Electric Universe alternative: plasmoids, not singularities

Where Crothers argues the black hole away, the Electric Universe offers a replacement. In Wal Thornhill's model the dense object at a galactic core is a plasmoid — a magnetically self-confined knot of plasma produced by a z-pinch in galactic Birkeland currents, storing electromagnetic energy and periodically ejecting it. Stars and galaxies form in plasma z-pinches, not by gravitational collapse, so no singularity is needed anywhere. After the 2019 Event Horizon Telescope image of M87*, Thornhill argued the bright ring is exactly what a luminous plasmoid would show — not proof of an event horizon (Black Hole or Plasmoid?). Crothers supplies the mathematical "impossibility"; the EU supplies the plasma alternative — the two are presented as complementary.

On the EHT images specifically, the objection is technical: the telescope is a sparse array that samples only limited data, so the final picture is reconstructed using algorithms and assumed priors — which, the argument goes, can bias the result toward the very ring it expects to find.

Related pages

The Electric Galaxy — Birkeland Currents, No Dark Matter

Electric Gravity — Thornhill's Dipole Theory

Did the Big Bang Happen? — The Plasma-Cosmology Dissent

The Electric Universe — An Introduction

Sources & Method

Sources & further reading

• Stephen J. Crothers, papers & talks index; "Geometric and Physical Defects in the Theory of Black Holes"; "On the General Solution to Einstein's Vacuum Field…" (Progress in Physics, 2005)

• Stephen J. Crothers — Thunderbolts author page

• Wal Thornhill, "On the Black Hole's Non-existence" — the plasmoid alternative