[Paper Review] Penrose process in charged axion-dilaton coupled black hole

Chandrima Ganguly, Soumitra SenGupta|arXiv (Cornell University)|Jan 27, 2014

Relativity and Gravitational Theory5 references4 citations

TL;DR

This paper applies the Newman-Janis algorithm to construct a charged axion-dilaton black hole, demonstrating that energy extraction via the Penrose process originates from the axion/Kalb-Ramond field energy, which contributes to the black hole's angular momentum. Upon complete energy extraction, the spacetime becomes torsion-free and evolves into a static, spherically symmetric dilaton black hole remnant with no rotational energy or axion field strength.

ABSTRACT

Using the Newman-Janis method to construct the axion-dilaton coupled charged rotating black holes, we show that the energy extraction from such black holes via Penrose process takes place from the axion/Kalb-Ramond field energy responsible for rendering the angular momentum to the black hole. Determining the explicit form for the Kalb-Ramond field strength, which is argued to be equivalent to spacetime torsion, we demonstrate that at the end of the energy extraction process, the spacetime becomes torsion free with a spherically symmetric non-rotating black hole remnant.

Motivation & Objective

• To investigate energy extraction from charged axion-dilaton black holes using the Penrose process in a string-theory-motivated framework.
• To clarify the role of the axion field and its dual Kalb-Ramond field strength in providing rotational energy to the black hole.
• To determine how the dilaton field influences the geometry and energy extraction efficiency in such black holes.
• To analyze the final state of the black hole after complete energy extraction, particularly whether it becomes torsion-free and spherically symmetric.

Proposed method

• The Newman-Janis complexification method is applied to a spherically symmetric, charged dilaton-coupled black hole solution to generate an axisymmetric, rotating black hole solution with axion and dilaton fields.
• The axion field is identified as dual to the third-rank antisymmetric field strength of the Kalb-Ramond field, which is interpreted as spacetime torsion in the Einstein-Cartan formalism.
• The metric is derived in Eddington-Finkelstein coordinates and transformed via complex coordinate shifts (r → r + ia cosθ, u → u - ia cosθ) to obtain the rotating solution.
• The energy extraction process is modeled using the Penrose process, with the maximum extractable energy computed as the difference between initial and irreducible mass of the black hole.
• The irreducible mass is defined via the area of the outer event horizon, and the change in this quantity is shown to be positive, confirming energy extraction feasibility.
• The dependence of energy extraction on the dilaton parameter r₂ and axion strength is numerically analyzed and plotted.

Experimental results

Research questions

• RQ1 How does the axion field contribute to the rotational energy of a black hole in a string-inspired axion-dilaton gravity model?
• RQ2 Can the Penrose process extract energy from the axion/Kalb-Ramond field energy, and if so, how is this energy quantified?
• RQ3 What is the final geometric state of the black hole after complete energy extraction via the Penrose process?
• RQ4 How does the dilaton field strength influence the maximum extractable energy and the rate of energy extraction?
• RQ5 Is the spacetime geometry after energy extraction torsion-free, and does it reduce to a spherically symmetric, non-rotating dilaton black hole?

Key findings

• The maximum extractable energy via the Penrose process is derived as ΔM = √[M(M - r₂/2)] - √[(M/2){(M - r₂/2) + √[(M - r₂/2)² - a²]}], showing dependence on mass, dilaton parameter r₂, and angular momentum a.
• As the axion field strength decreases, the amount of extractable energy and the rate of extraction both diminish, vanishing entirely when the axion field becomes zero.
• When the axion field is fully extracted, the resulting black hole remnant is a static, spherically symmetric, charged dilaton black hole with no rotation and no torsion.
• The final spacetime geometry is torsion-free and Riemannian, confirming that the axion/Kalb-Ramond field energy was the source of the initial rotational energy.
• The irreducible mass of the final dilaton black hole is proportional to the area of its event horizon, and the difference between initial and final irreducible masses quantifies the total extractable energy.
• The energy extraction process is shown to be consistent with thermodynamic principles, as the change in irreducible mass is always positive, confirming the process is physically viable.