[Paper Review] Why the astrophysical Black Hole Candidates are not rotating black holes

Abhas Mitra|arXiv (Cornell University)|Jul 23, 2004

Pulsars and Gravitational Waves Research13 references3 citations

TL;DR

This paper argues that astrophysical black hole candidates (BHCs) cannot be rotating Kerr black holes due to a fundamental contradiction in the standard metric formulation: the condition $g_{\phi\phi} = \sin^2\theta \, g_{\theta\theta}$, required for axial symmetry and asymptotic flatness, forces the rotation parameter $a = 0$ if mass $m \geq 0$. Consequently, only non-rotating Schwarzschild black holes are mathematically consistent under these constraints, implying that observed BHCs are not true black holes but ultra-compact objects with physical surfaces and intrinsic magnetic fields.

ABSTRACT

It is believed that the basic component of the central engine of quasars, micro-quasars, and energetic Gamma Ray Bursts are the rotating or the Kerr Black Holes (BH)[1]. But by using a generic property[2-4] of the metric components of a stationary axisymmertic rotating metric in its standard form}, namely, g_phi ϕ= sin^2 theta g_theta theta, where phi is the azimuth angle and theta is the polar angle measured from the axis of symmetry, we have found the unexpected and surprising result that (i) in order to have a mass of a Kerr BH m ge 0, it is necessary that its rotation parameter a=0 and if one insists for an a ge 0, one must have m le 0! Thus if the suspected Black Hole candidates with m >0 are really rotating they cannot be BHs at all which is in agreement with some detailed analysis of recent observations[5-8]. However, if it is assumed that such objects are strictly non-rotating, they could be non-rotating Schwarzschild BHs (a=0) with m ge 0 if we ignore the physical difficulties associated with the existence of such objects. This result calls for new theoretical efforts to understand a vast range of astrophysical phenomenon. If one derives the Kerr Metric in a straightforward manner by using the Backlund transformation, it is seen that a=m sin phi. This relationship confirms that a=m=0 for Kerr BHs.

Motivation & Objective

• To resolve a long-standing inconsistency in the theoretical description of rotating black holes in general relativity.
• To challenge the widely held assumption that quasars, micro-quasars, and gamma-ray bursts are powered by Kerr black holes.
• To demonstrate that the standard form of the stationary, axisymmetric metric imposes a mathematical contradiction unless $a = 0$ for $m \geq 0$.
• To argue that observed astrophysical black hole candidates must instead be ultra-compact objects with physical surfaces and intrinsic magnetic fields, not event horizons.
• To call for new theoretical frameworks to describe spinning compact objects beyond the Kerr metric.

Proposed method

• Derives the standard form of the stationary, axisymmetric metric under the physical conditions of axial symmetry and asymptotic flatness, enforcing $g_{\phi\phi} = \sin^2\theta \, g_{\theta\theta}$.
• Applies a coordinate transformation $\theta \to \theta' = f(\theta)$ to test metric invariance, showing that Eq.(6) only holds if $\theta$ is uniquely measured from the symmetry axis.
• Uses the Backlund transformation to derive the Kerr metric, revealing the identity $a = m \sin\phi$, which forces $a = m = 0$ since $\phi$ is a variable and $\sin\phi \neq 0$ in general.
• Analyzes the Boyer-Lindquist form of the Kerr metric and confirms that the condition $g_{\phi\phi} = \sin^2\theta \, g_{\theta\theta}$ is only satisfied when $\theta$ is measured from the axis, fixing the coordinate system uniquely.
• Applies the requirement of invariance under $t \to -t$, $\phi \to -\phi$ to constrain metric components, leading to $g_{t\phi} = 0$ and $g_{\theta\phi} = 0$, simplifying the metric structure.
• Demonstrates that the Kerr metric cannot describe physical, spinning bodies with finite mass and pressure, as such objects would develop higher-order multipole moments ($l > 1$), violating the $l=1$ constraint of Kerr black holes.

Experimental results

Research questions

• RQ1 Can a rotating black hole with $m > 0$ and $a > 0$ exist under the standard form of the stationary, axisymmetric metric with $g_{\phi\phi} = \sin^2\theta \, g_{\theta\theta}$?
• RQ2 Does the requirement of axial symmetry and asymptotic flatness force the rotation parameter $a$ to vanish when mass $m \geq 0$?
• RQ3 Is the Kerr metric physically valid for describing real astrophysical compact objects with finite mass, pressure, and temperature?
• RQ4 Can the Backlund transformation derivation of the Kerr metric be used to prove that $a = 0$ for any non-zero mass?
• RQ5 Do observed astrophysical black hole candidates, such as those in quasars and gamma-ray bursts, actually possess event horizons or physical surfaces?

Key findings

• The condition $g_{\phi\phi} = \sin^2\theta \, g_{\theta\theta}$, required for axial symmetry and asymptotic flatness, implies that $a = 0$ if $m \geq 0$, making rotating black holes with positive mass impossible under this formulation.
• The Backlund transformation derivation of the Kerr metric yields $a = m \sin\phi$, which can only be satisfied if $a = m = 0$, confirming that only non-rotating black holes are mathematically consistent.
• The standard form of the Kerr metric in Boyer-Lindquist coordinates assumes $\theta$ is uniquely measured from the symmetry axis, and any deviation from this choice invalidates the metric's physical consistency.
• Astrophysical black hole candidates with $m > 0$ cannot be Kerr black holes, as they would violate the metric's geometric constraints unless $a = 0$, implying they are not true black holes.
• The observed central engines of quasars, micro-quasars, and gamma-ray bursts are likely powered by ultra-compact objects with physical surfaces and intrinsic magnetic fields, not event horizons.
• No known physical body other than a Kerr black hole can be described by the Kerr metric, and even for Kerr BHs, the metric only applies if $a = m = 0$, suggesting the metric is of limited physical relevance.