[Paper Review] Microscopic entropy of rotating black holes with planar horizon

Moisés Bravo‐Gaete, Luis Guajardo+1 more|arXiv (Cornell University)|Feb 8, 2017

Black Holes and Theoretical Physics23 references3 citations

TL;DR

This paper proposes a Cardy-like formula to compute the semiclassical entropy of D-dimensional rotating black holes with planar horizons by relating the microcanonical degeneracy of states to a gravitational bulk soliton, obtained via double analytic continuation from the non-rotating solution. The method successfully reproduces entropy without relying on central charges, demonstrating robustness across diverse black hole types including AdS, Lifshitz, and hyperscaling-violating solutions.

ABSTRACT

We show that the semiclassical entropy of $D$-dimensional rotating (an)isotropic black holes with planar horizon can be successfully computed from the microcanonical degeneracy of states according to a Cardy-like formula. This formula does not refer to any central charges but instead involves the vacuum energy which is identified with a gravitational bulk soliton. The soliton is obtained from the non-rotating black hole solution by means of a double analytic continuation. The robustness of the Cardy-like formula is tested with numerous and varied examples, including AdS, Lifshitz and hyperscaling violation planar black holes.

Motivation & Objective

• To derive a universal method for computing the semiclassical entropy of rotating planar-horizon black holes in D dimensions.
• To eliminate reliance on central charges in entropy calculations by introducing a vacuum energy identified with a gravitational bulk soliton.
• To test the robustness of the proposed formula across diverse black hole solutions, including those with Lifshitz and hyperscaling-violating scaling.
• To establish a microscopic statistical origin for the entropy of rotating black holes using a soliton-based approach.

Proposed method

• The method employs a double analytic continuation of the non-rotating black hole solution to obtain a gravitational bulk soliton that represents the vacuum energy.
• The microcanonical degeneracy of states is computed using a Cardy-like formula that depends on the soliton's energy rather than central charges.
• The entropy is derived from the logarithm of the state degeneracy, with the soliton energy serving as the effective Hamiltonian in the Cardy formula.
• The approach is applied to various black hole solutions, including asymptotically AdS, Lifshitz, and hyperscaling-violating planar black holes, to test consistency and generality.
• The formula is validated by comparing its predictions with known entropy results in multiple cases, confirming its robustness.

Experimental results

Research questions

• RQ1 Can the semiclassical entropy of rotating planar-horizon black holes be computed without reference to central charges?
• RQ2 How does the vacuum energy of a gravitational bulk soliton relate to the entropy of rotating black holes?
• RQ3 Does the proposed Cardy-like formula remain valid across different spacetime geometries such as AdS, Lifshitz, and hyperscaling-violating black holes?
• RQ4 What is the role of double analytic continuation in connecting non-rotating and rotating black hole solutions for entropy computation?
• RQ5 Can the microcanonical degeneracy of states be consistently linked to a soliton solution in the bulk?

Key findings

• The proposed Cardy-like formula successfully computes the semiclassical entropy of rotating planar-horizon black holes without requiring knowledge of central charges.
• The vacuum energy in the formula is identified with a gravitational bulk soliton obtained via double analytic continuation from the non-rotating black hole solution.
• The method demonstrates robustness across diverse black hole types, including AdS, Lifshitz, and hyperscaling-violating solutions, confirming its generality.
• The entropy calculation is consistent with known results in multiple cases, validating the soliton-based approach.
• The microcanonical degeneracy of states is accurately captured by the formula, providing a statistical mechanical interpretation of black hole entropy.