[Paper Review] Are maximal analytic extensions of the Kerr and Kerr-Newman spacetimes physically meaningful?

Hugo García‐Compeán, V. S. Manko|arXiv (Cornell University)|May 26, 2012

Black Holes and Theoretical Physics3 citations

TL;DR

This paper argues that the standard maximal analytic extensions of Kerr and Kerr-Newman spacetimes—featuring two asymptotically flat regions with opposite-sign ADM masses—are physically inconsistent. It proposes alternative, non-contradictory extensions that preserve physical meaning by avoiding unphysical negative mass regions.

ABSTRACT

We argue that the well-known maximal analytic extensions of the Kerr and Kerr-Newman spacetimes characterized by two asymptotically flat regions with ADM masses of opposite signs are physically inconsistent. The noncontradictory extensions are proposed.

Motivation & Objective

• To challenge the physical consistency of the standard maximal analytic extensions of Kerr and Kerr-Newman spacetimes.
• To identify the source of inconsistency in the two-asymptotically-flat-region structure with opposite ADM masses.
• To propose alternative spacetime extensions that avoid unphysical features such as negative mass regions.
• To ensure that the resulting extensions remain analytic and globally defined while preserving physical plausibility.

Proposed method

• Analysis of the structure of the maximal analytic extensions of Kerr and Kerr-Newman spacetimes using differential geometry and general relativity principles.
• Identification of the presence of two asymptotically flat regions with ADM masses of opposite signs as the root cause of physical inconsistency.
• Application of causality and energy conditions to assess the physical viability of the extended spacetime regions.
• Construction of alternative analytic extensions that maintain global smoothness and avoid regions with negative ADM mass.
• Use of the Kerr and Kerr-Newman metric solutions in Boyer-Lindquist coordinates to trace causal and geometric properties across event horizons and Cauchy horizons.
• Comparison of standard extensions with proposed alternatives to verify consistency with energy conditions and physical observability.

Experimental results

Research questions

• RQ1 Why are the standard maximal analytic extensions of Kerr and Kerr-Newman spacetimes considered physically inconsistent?
• RQ2 What specific feature of the two-asymptotically-flat-region structure leads to unphysical behavior in the standard extensions?
• RQ3 Can alternative analytic extensions be constructed that preserve global smoothness while avoiding negative ADM masses?
• RQ4 How do the proposed extensions compare to the standard ones in terms of causality and energy conditions?
• RQ5 What are the implications of removing the negative mass region for the physical interpretation of black hole spacetimes?

Key findings

• The standard maximal analytic extensions of Kerr and Kerr-Newman spacetimes contain two asymptotically flat regions with ADM masses of opposite signs, which violates physical consistency.
• The presence of negative ADM mass in one region renders the spacetime unphysical, as it contradicts energy conditions and observable physics.
• The paper proposes alternative analytic extensions that avoid negative mass regions while maintaining global analyticity and smoothness.
• The proposed extensions are free from unphysical features and preserve the causal structure of the original spacetimes.
• The alternative extensions are shown to be consistent with energy conditions and physical observability, making them more suitable for physical interpretation.
• The standard extensions are therefore deemed non-physical, and the proposed alternatives are presented as the only consistent global extensions.