[Paper Review] Hawking radiation of black p-branes via gauge and gravitational anomalies

Zheng Ze|arXiv (Cornell University)|Sep 24, 2007

Black Holes and Theoretical Physics4 citations

TL;DR

This paper investigates Hawking radiation from black p-branes in superstring theory using the anomaly cancellation method, transforming non-Schwarzschild spherically symmetric metrics into Schwarzschild-like forms to simplify calculations. The resulting energy-momentum flux matches black body radiation with a temperature equal to the Hawking temperature, confirming consistency across both metric types.

ABSTRACT

We investigate the Hawking radiation of black $p$-branes of superstring theories using the method of anomaly cancelation, specially, we use the method of [S. Iso, H. Umetsu and F. Wilczek, {\sl Phys. Rev. Lett.} {\bf 96}, 151302 (2006); {\sl Phys. Rev. D} {\bf 74}, 044017 (2006)]. The metrics of black $p$-branes are spherically symmetric, but not the Schwarzschild type. In order to simplify the calculation, we first make a coordinate transformation to transform the metric to the Schwarzschild type. Then we calculate its energy-momentum flux from the method of anomaly cancelation of the above mentioned references. The obtained energy-momentum flux is equal to a black body radiation, the thermodynamic temperature of the radiation is equal to its Hawking temperature. And we find that the results are not changed for the original non-Schwarzschild type spherically symmetric metric.

Motivation & Objective

• To extend the anomaly cancellation method for deriving Hawking radiation to black p-branes in superstring theory.
• To address the challenge of non-Schwarzschild spherically symmetric metrics in p-brane spacetimes.
• To determine whether the Hawking radiation spectrum remains consistent when the metric is transformed to Schwarzschild-like form.
• To verify that the thermodynamic temperature of the radiation equals the Hawking temperature in this framework.

Proposed method

• Applying the anomaly cancellation method developed by Iso, Umetsu, and Wilczek to gauge and gravitational anomalies in p-brane backgrounds.
• Performing a coordinate transformation to convert the original spherically symmetric but non-Schwarzschild metric into a Schwarzschild-type form for analytical simplification.
• Calculating the energy-momentum flux from the anomaly cancellation condition in the transformed spacetime.
• Verifying that the derived flux corresponds to a thermal spectrum with temperature equal to the Hawking temperature.
• Confirming that the results remain invariant under the metric transformation, preserving physical consistency.

Experimental results

Research questions

• RQ1 Can the anomaly cancellation method reliably derive Hawking radiation for black p-branes with non-Schwarzschild metrics?
• RQ2 Does transforming a spherically symmetric p-brane metric into Schwarzschild form alter the resulting energy-momentum flux?
• RQ3 Is the thermodynamic temperature of the radiation equal to the Hawking temperature in this context?
• RQ4 Does the radiation spectrum match that of a black body in the derived framework?
• RQ5 Are the physical results independent of the choice of coordinate representation for the metric?

Key findings

• The energy-momentum flux derived via anomaly cancellation matches the spectrum of black body radiation.
• The thermodynamic temperature of the radiation is exactly equal to the Hawking temperature of the black p-brane.
• The radiation spectrum remains unchanged when the metric is transformed from its original spherically symmetric form to a Schwarzschild-like form.
• The consistency of the result across different metric representations confirms the robustness of the anomaly cancellation approach.
• The method successfully reproduces standard Hawking radiation features for p-branes despite the non-Schwarzschild geometry.