A Fluid-Membrane Description of Static and Rotating BTZ Black Holes

Core Concepts

This paper presents a classical fluid-membrane description of both static and rotating Bañados-Teitelboim-Zanelli (BTZ) black holes, demonstrating that these geometries can be mimicked by a dynamical viscous Newtonian fluid with specific transport coefficients.

Abstract

Agca, C.U., & Tekin, B. (2024). A Fluid-Membrane Description of the BTZ Black Hole. arXiv:2411.06164v1 [gr-qc].

This paper aims to provide a classical fluid-membrane description of the 2+1 dimensional BTZ black hole, in both its static and rotating forms, and to determine the transport coefficients of the corresponding fluid.

Key Insights Distilled From

A Fluid-Membrane Description of the BTZ Black Hole

by Cagdas Ulus ... at arxiv.org 11-12-2024

https://arxiv.org/pdf/2411.06164.pdf

Deeper Inquiries

How does the fluid-membrane description of BTZ black holes contribute to the understanding of the AdS/CFT correspondence, particularly in the context of fluid/gravity duality?

The fluid-membrane description of BTZ black holes provides a compelling example of the AdS/CFT correspondence and, more specifically, fluid/gravity duality. This duality proposes a remarkable connection between strongly coupled conformal field theories (CFTs) in d-dimensions and gravitational theories in (d+1)-dimensional anti-de Sitter (AdS) spacetimes.
Here's how the fluid-membrane paradigm contributes to our understanding:

Holographic Principle: The membrane paradigm embodies the holographic principle by encoding the information of the 3D black hole on a 2D surface, the stretched horizon. This aligns with the AdS/CFT idea that a higher-dimensional gravitational system can be fully described by a lower-dimensional CFT living on its boundary.
Fluid/Gravity Duality: The fluid-membrane description demonstrates that the dynamics of the stretched horizon, a timelike surface just outside the event horizon, can be described by the Navier-Stokes equations of a viscous fluid. This fluid's transport coefficients, such as shear viscosity and entropy density, can be directly related to the properties of the BTZ black hole. This realization is a prime example of fluid/gravity duality, where the long-wavelength behavior of a strongly coupled CFT (represented by the fluid) is dual to the dynamics of a black hole spacetime (represented by the membrane).
Testing Ground for AdS/CFT: The BTZ black hole, being a simpler solution in 3D gravity, offers a valuable testing ground for exploring the AdS/CFT correspondence. The fluid-membrane description allows for explicit calculations of transport coefficients and other thermodynamic quantities, which can then be compared to predictions from the dual CFT. This provides a concrete way to test and refine our understanding of the duality.
Quantum Behavior of Gravity: The fluid/gravity duality, exemplified by the BTZ membrane, hints at a deeper connection between the hydrodynamic behavior of strongly coupled quantum systems and the dynamics of spacetime near black holes. This connection could potentially shed light on the quantum nature of gravity and the emergence of spacetime from microscopic degrees of freedom.
In summary, the fluid-membrane description of BTZ black holes provides a tangible and computationally tractable framework for investigating the AdS/CFT correspondence. It offers a concrete realization of fluid/gravity duality, allowing us to probe the connections between black hole physics, fluid dynamics, and strongly coupled quantum field theories.

Could the presence of exotic matter or modified gravity theories within the BTZ black hole spacetime lead to non-zero bulk viscosity in the fluid-membrane description, and if so, what would be the implications for the stability and evolution of such systems?

Yes, the presence of exotic matter or modifications to Einstein's theory of gravity within the BTZ black hole spacetime could indeed lead to a non-zero bulk viscosity in the fluid-membrane description. This has significant implications for the stability and evolution of such systems.
Here's a breakdown:

Einstein Gravity and Zero Bulk Viscosity: In standard (2+1)-dimensional Einstein gravity, the BTZ black hole exhibits zero bulk viscosity. This is a direct consequence of the dimensionality of the spacetime and the absence of propagating gravitons in 3D.
Exotic Matter and Modified Gravity: Introducing exotic matter fields with non-trivial couplings or modifying gravity itself (e.g., through higher-derivative corrections, scalar-tensor theories, or Horndeski gravity) can alter the dynamics of the gravitational field. These modifications can induce a non-zero bulk viscosity in the dual fluid description.
Implications of Non-Zero Bulk Viscosity:

Stability: A non-zero bulk viscosity implies that the fluid-membrane is no longer perfectly fluid but exhibits a resistance to expansion or contraction. This can have significant consequences for the stability of the black hole. Depending on the sign and magnitude of the bulk viscosity, it could either stabilize the black hole against perturbations or drive it towards a different equilibrium state.
Dissipation and Entropy Production: Bulk viscosity is inherently related to dissipative processes in the fluid. A non-zero bulk viscosity would lead to entropy production during processes involving changes in volume, such as black hole formation or evaporation. This has implications for the thermodynamics of the black hole and its evolution over time.
Observational Signatures: The presence of non-zero bulk viscosity could potentially lead to observable signatures in astrophysical systems. For example, it could affect the gravitational wave emission from merging black holes or the dynamics of accretion disks around black holes.
In conclusion, deviations from standard Einstein gravity, either through exotic matter or modified gravity theories, can induce a non-zero bulk viscosity in the fluid-membrane description of BTZ black holes. This has profound implications for the stability, thermodynamic evolution, and potential observational signatures of these systems, offering a window into the nature of gravity beyond Einstein's theory.

If we consider the fluid membrane as a representation of information encoded on the event horizon, what insights can we gain about the quantum nature of information and its relationship to gravity from this analogy?

The analogy of the fluid membrane representing information encoded on the event horizon of a BTZ black hole offers intriguing insights into the quantum nature of information and its relationship to gravity. Here's an exploration of these insights:

Holographic Encoding of Information: The membrane paradigm aligns with the holographic principle, suggesting that information about the black hole's interior is encoded on its boundary, the event horizon. The fluid membrane, as a proxy for the event horizon, embodies this idea by capturing the black hole's properties through its fluid degrees of freedom. This supports the notion that information in a quantum theory of gravity might be holographically stored on lower-dimensional surfaces.
Quantum Information and Black Hole Entropy: The entropy of a black hole, a measure of its information content, is proportional to its horizon area. The fluid membrane, with its own entropy density and temperature, provides a framework for understanding this relationship. The microscopic degrees of freedom of the fluid could potentially represent the underlying quantum states that contribute to the black hole's entropy.
Information Conservation and Black Hole Evaporation: The black hole information paradox arises from the apparent conflict between quantum unitarity (information conservation) and black hole evaporation. The fluid membrane, being a dissipative system with viscosity, could play a role in resolving this paradox. The information might not be lost but rather encoded in subtle correlations within the fluid, which are then carried away by Hawking radiation as the black hole evaporates.
Emergent Spacetime and Quantum Entanglement: The fluid/gravity duality suggests a deep connection between the dynamics of spacetime and the entanglement structure of the underlying quantum degrees of freedom. The fluid membrane, with its collective behavior arising from the interactions of its constituent particles, could provide a glimpse into how spacetime might emerge from a more fundamental quantum theory. The entanglement entropy of the fluid could be related to the geometry of the emergent spacetime.
In summary, the fluid membrane analogy for information on the event horizon offers a valuable tool for exploring the profound connections between gravity, quantum information, and the emergence of spacetime. While many questions remain unanswered, this framework provides a path for investigating the quantum nature of black holes and the fundamental nature of information in a theory of quantum gravity.