Exploring the shear viscosity in four-dimensional planar black holes beyond General Relativity

Abstract

The well known shear viscosity to entropy density ratio ($\eta /s$) cannot be computed when the black hole space-time has zero thermodynamic entropy. This is the case, for example, when General Relativity in four dimensions is complemented with Critical Gravity, or in particular scenarios within the Four-dimensional-scalar-Gauss-Bonnet theories. Recently, it has been shown that the zero entropy situation can be overcome in these examples by introducing suitable matter fields. With this at hand, in this paper we analyze each case and the impact of these extra sources in the ratio, in terms of their new parameters. We find that, while the $\eta /s$ ratio remains constant and insensitive in the former, this is not the case for the latter. To perform the calculations, we construct a Noether charge using a space-like Killing vector. The accuracy of the aforementioned findings is supported by the Kubo formalism.

Version 3, references modified. Accepted version to Physical Review D

References in corpus (25)

• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way
• First M87 Event Horizon Telescope Results. VI. The Shadow and Mass of the Central Black Hole
• First M87 Event Horizon Telescope Results. IV. Imaging the Central Supermassive Black Hole
• First M87 Event Horizon Telescope Results. V. Physical Origin of the Asymmetric Ring
• Minkowski-space correlators in AdS/CFT correspondence: recipe and applications
• First M87 Event Horizon Telescope Results. II. Array and Instrumentation
• First M87 Event Horizon Telescope Results. III. Data Processing and Calibration
• First Sagittarius A* Event Horizon Telescope Results. VI: Testing the Black Hole Metric
• First Sagittarius A* Event Horizon Telescope Results. V. Testing Astrophysical Models of the Galactic Center Black Hole
• 200 A GeV Au+Au collisions serve a nearly perfect quark-gluon liquid
• Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm
• First Sagittarius A* Event Horizon Telescope Results. III: Imaging of the Galactic Center Supermassive Black Hole
• First Sagittarius A* Event Horizon Telescope Results. II. EHT and Multi-wavelength Observations, Data Processing, and Calibration
• First Sagittarius A* Event Horizon Telescope Results. IV. Variability, Morphology, and Black Hole Mass
• Critical Gravity in Four Dimensions
• On Taking the $D\to 4$ limit of Gauss-Bonnet Gravity: Theory and Solutions
• The 4D Einstein-Gauss-Bonnet Theory of Gravity: A Review
• Shear Viscosity from Effective Couplings of Gravitons
• Shear Viscosity from Gauss-Bonnet Gravity with a Dilaton Coupling
• Anisotropic shear viscosity of a strongly coupled non-Abelian plasma from magnetic branes
• Shear viscosity of a superfluid Fermi gas in the unitarity limit
• A Strongly Coupled Anisotropic Fluid From Dilaton Driven Holography
• Lower-dimensional Gauss-Bonnet Gravity and BTZ Black Holes