[Paper Review] Gravitational waves versus black holes

Trevor W. Marshall|ArXiv.org|Jul 2, 2007

Relativity and Gravitational Theory6 references3 citations

TL;DR

This paper argues that gravitational waves require a preferred global inertial frame to satisfy Einstein's Principle of Locality, rejecting the standard general relativistic treatment of black holes. By introducing additional field equations that preserve causality and locality, the model shows gravitational collapse halts before reaching the Schwarzschild radius, preventing singularities and excluding black holes as physical solutions.

ABSTRACT

It is argued that, in order for the gravitational field to be propagated as a wave, it is necessary for it to satisfy a further set of field equations, in addition to those of Einstein and Hilbert, and these equations mean there is a preferred coordinate frame, called the Global Inertial Frame, giving rise to a unique metric . The implication is that a true gravitational field is not compatible with Einstein's Principle of Equivalence, which is in contradiction with his other fundamental concept of locality. The additional field equations ensure that gravitational collapse does not go below the Schwarzschild radius, thereby excluding the possibility of singular solutions (black holes) of the Einstein-Hilbert equations. Such solutions would also violate Einstein's locality principle.

Motivation & Objective

• To resolve the incompatibility between Einstein's Principle of Locality and the existence of gravitational waves in standard general relativity.
• To show that the standard formulation of Einstein-Hilbert equations permits solutions violating causality and locality, particularly at the event horizon.
• To propose a modified gravitational theory (RTG) with a preferred global inertial frame to restore consistency with Einstein’s locality principle.
• To demonstrate that gravitational collapse does not proceed beyond the Schwarzschild radius, thus excluding black hole formation.
• To establish that infinite redshift and finite time in the global frame prevent the formation of singularities or event horizons.

Proposed method

• Introduces an additional set of field equations beyond Einstein-Hilbert, enforcing a global inertial frame to ensure wave propagation at speed c without violating locality.
• Applies a harmonic gauge condition (de Donder-Fock) to ensure the d’Alembertian operator remains well-defined and causal.
• Uses a comoving coordinate system with variable X and Y to model the interior of a collapsing dust cloud, avoiding coordinate singularities.
• Imposes a boundary condition at r = r∞ where the metric coefficient grr diverges, matching the exterior Schwarzschild solution.
• Solves the resulting partial differential equations numerically by transforming them into ordinary differential equations along characteristic curves Y = constant.
• Imposes the Correspondence Principle to ensure the interior solution matches the exterior Schwarzschild metric at the boundary.

Experimental results

Research questions

• RQ1 Can gravitational waves be consistently described in general relativity without violating Einstein’s Principle of Locality?
• RQ2 Is the standard prediction of black hole formation via gravitational collapse compatible with the Principle of Locality and causality?
• RQ3 Does the existence of an event horizon, where time and space coordinates swap, violate the locality principle in general relativity?
• RQ4 Can a stationary solution of the Einstein-Hilbert equations be found that avoids singularities and preserves causality?
• RQ5 What happens to the density and metric during gravitational collapse when infinite redshift is taken into account?

Key findings

• The model shows that gravitational collapse ceases at a finite radius r∞ = 0.5 in dimensionless units, preventing the formation of a black hole.
• The function r∞(X) reaches a minimum at X = 1.0, where r∞ = 0, indicating the collapse stops at the Schwarzschild radius.
• The cumulative particle density P∞(r) increases sharply near r = 0.5, with P∞ giving over 61% of particles in the range 0.481 < r < 0.5, compared to only 11% for a uniform distribution.
• The metric determinant g approaches zero at r = 0.5, and grr becomes infinite, consistent with the exterior Schwarzschild solution.
• The time coordinate t becomes infinite as Y approaches Y0, indicating infinite gravitational redshift and effective freezing of physical processes at the event horizon.
• The solution remains finite and causal in the global inertial frame, with no coordinate singularity or topology change, preserving Einstein’s locality principle.