[Paper Review] Charged Vector Particles Tunneling From 5D Black Hole and Black Ring

Wajiha Javed, Riasat Ali+1 more|arXiv (Cornell University)|May 4, 2017

Black Holes and Theoretical Physics1 references3 citations

TL;DR

This paper investigates the semiclassical quantum tunneling of charged vector particles (W± bosons) from 5D charged black rings and Myers-Perry black holes using the Proca equation and WKB approximation. It derives the tunneling probability and Hawking temperature, showing that the temperature is independent of particle type or electromagnetic fields, consistent with established results, while the tunneling rate depends on particle charge, energy, and vector potential components.

ABSTRACT

In this paper, we investigate the Hawking radiation process as a semiclassical quantum tunneling phenomenon from black ring and Myers-Perry black holes in 5-dimensional (5D) spaces. Using Lagrangian of Glashow-Weinberg-Salam model with background electromagnetic field (for charged W-bosons) and the WKB approximation, we will evaluate the tunneling rate/probability of charged vector particles through horizons by taking into account the electromagnetic vector potential. Moreover, we investigate the corresponding Hawking temperature values by considering Boltzmann factor for both cases and analyze the whole spectrum generally.

Motivation & Objective

• To extend the study of Hawking radiation beyond scalar and fermionic particles to charged vector bosons (W±) in 5D black hole spacetimes.
• To analyze the tunneling process of charged vector particles through the event horizon of 5D black rings and Myers-Perry black holes.
• To compute the Hawking temperature using the Boltzmann factor and assess its dependence on black hole parameters and particle species.
• To investigate whether electromagnetic interactions affect the Hawking temperature or only the tunneling probability.
• To verify consistency of the derived temperature with known results across different particle types and geometries.

Proposed method

• Formulates the Lagrangian of the Glashow-Weinberg-Salam model with background electromagnetic fields to describe charged W-bosons.
• Applies the WKB approximation to the Proca equation for massive vector particles in curved 5D spacetime.
• Uses the Hamilton-Jacobi ansatz to solve the action integral and extract the imaginary part of the action, related to tunneling probability.
• Derives the tunneling probability as an exponential of the negative imaginary action, with dependence on energy, charge, vector potential, and surface gravity.
• Computes the Hawking temperature via the Boltzmann factor, relating it to the surface gravity of the black hole.
• Evaluates the results in both Boyer-Lindquist-like and corotating coordinate systems to test coordinate independence.

Experimental results

Research questions

• RQ1 What is the tunneling probability of charged vector particles from a 5D charged black ring?
• RQ2 How does the presence of an electromagnetic vector potential affect the tunneling rate of charged vector bosons?
• RQ3 Does the Hawking temperature for charged vector particles depend on the black hole's charge or the particle's electromagnetic coupling?
• RQ4 Is the derived Hawking temperature consistent with known values for scalar and fermionic particles?
• RQ5 How do the results compare across different coordinate systems (e.g., Painlevé-like, corotating) for Myers-Perry black holes?

Key findings

• The tunneling probability for charged vector particles depends on the particle's energy, charge, angular momentum, and the electromagnetic vector potential components $A_0$ and $A_3$.
• The Hawking temperature for the 5D black ring is derived as $T_H = \frac{\sqrt{\tilde{M}_r(r,\theta)\tilde{N}_r(r,\theta)}}{4\pi}$, which depends on parameters $r_0$, $a$, and $b$, but not on the particle's charge or electromagnetic coupling.
• For Myers-Perry black holes, the tunneling probability is given by $\tilde{\Gamma} = \exp\left[-4\pi \frac{(E - eA_0 - \Omega_1 eA_3 - \sum j_i \hat{\Omega}_i)}{\sqrt{\tilde{M}_r \tilde{N}_r}}\right]$, showing dependence on electromagnetic potentials.
• The Hawking temperature for Myers-Perry black holes is $T_H = \frac{\sqrt{2r^2[r^2_0 r^3 - b^2 - rb^2 \sin^2\theta (b^2 + 2a^2 - 2r^2 - 1)]}}{4\pi(r^2 + a^2\cos^2\theta + b^2\sin^2\theta)(r^4 + b^2 r^2 + a^2 r^2 - r^2_0 r^2)}$, matching known literature values.
• The study confirms that the Hawking temperature is independent of particle species (scalar, fermion, vector boson) and electromagnetic interactions, consistent across different methods and geometries.
• Electromagnetic effects influence only the tunneling probability, not the final Hawking temperature, which remains universal across particle types and spacetime backgrounds.