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Register a new userA microscopic model for the black-hole horizon-fluid
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Added by
S. Shankaranarayanan
Publication date
2019
fields
Physics
and research's language is
English
Authors
Swastik Bhattacharya
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There is a compelling connection between equations of gravity near the black-hole horizon and fluid-equations. The correspondence suggests a novel way to unearth microscopic degrees of freedom of the event horizons. In this work, we construct a microscopic model of the horizon-fluid of a 4-D asymptotically flat, quasi-stationary, Einstein black-holes. We demand that the microscopic model satisfies two requirements: First, the model should incorporate the near-horizon symmetries (S1 diffeomorphism) of a stationary black-hole. Second, the model possesses a mass gap. We show that the Eight-vertex Baxter model satisfies both the requirements. In the continuum limit, the Eight-vertex Baxter model is a massive free Fermion theory that is integrable with an infinite number of conserved charges. We show that this microscopic model explains the origin of the macroscopic properties of the horizon-fluid like bulk viscosity. Finally, we connect this model with Damours analysis and determine the mass-gap in the microscopic model.
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Einstein equations projected on to a black hole horizon gives rise to Navier-Stokes equations. Horizon-fluids typically possess unusual features like negative bulk viscosity and it is not clear whether a statistical mechanical description exists for such fluids. In this work, we provide an explicit derivation of the Bulk viscosity of the horizon-fluid based on the theory of fluctuations a la Kubo. The main advantage of our approach is that our analysis remains for the most part independent of the details of the underlying microscopic theory and hence the conclusions reached here are model independent. We show that the coefficient of bulk viscosity for the horizon-fluid matches exactly with the value found from the equations of motion for the horizon-fluid.
For the Schwarzschild black hole the Bekenstein-Hawking entropy is proportional to the area of the event horizon. For the black holes with two horizons the thermodynamics is not very clear, since the role of the inner horizons is not well established. Here we calculate the entropy of the Reissner-Nordstrom black hole and of the Kerr black hole, which have two horizons. For the spherically symmetric Reissner-Nordstrom black hole we used several different approaches. All of them give the same result for the entropy and for the corresponding temperature of the thermal Hawking radiation. The entropy is not determined by the area of the outer horizon, and it is not equal to the sum of the entropies of two horizons. It is determined by the correlations between the two horizons, due to which the total entropy of the black hole and the temperature of Hawking radiation depend only on mass $M$ of the black hole and do not depend on the black hole charge $Q$. For the Kerr and Kerr-Newman black holes it is shown that their entropy has the similar property: it depends only on mass $M$ of the black hole and does not depend on the angular momentum $J$ and charge $Q$.
In this paper, the new formalism of thermodynamic geometry proposed in [1] is employed in investigating phase transition points and the critical behavior of a Gauss Bonnet-AdS black hole in four dimensional spacetime. In this regard, extrinsic and intrinsic curvatures of a certain kind of hypersurface immersed in the thermodynamic manifold contain information about stability/instability of heat capacities. We, therefore, calculate the intrinsic curvature of the $Q$-zero hypersurface for a four-dimensional neutral Gauss Bonnet black hole case in the extended phase space. Interestingly, intrinsic curvature can be positive for small black holes at low temperature, which indicates a repulsive interaction among black hole microstructures. This finding is in contrast with the five-dimensional neutral Gauss Bonnet black hole with only dominant attractive interaction between its microstructures.
We establish a one-to-one mapping between entanglement entropy, energy, and temperature (quantum entanglement mechanics) with black hole entropy, Komar energy, and Hawking temperature, respectively. We show this explicitly for 4-D spherically symmetric asymptotically flat and non-flat space-times with single and multiple horizons. We exploit an inherent scaling symmetry of entanglement entropy and identify scaling transformations that generate an infinite number of systems with the same entanglement entropy, distinguished only by their respective energies and temperatures. We show that this scaling symmetry is present in most well-known systems starting from the two-coupled harmonic oscillator to quantum scalar fields in spherically symmetric space-time. The scaling symmetry allows us to identify the cause of divergence of entanglement entropy to the generation of (near) zero-modes in the systems. We systematically isolate the zero-mode contributions using suitable boundary conditions. We show that the entanglement entropy and energy of quantum scalar field scale differently in space-times with horizons and flat space-time. The relation $E=2TS$, in analogy with the horizons thermodynamic structure, is also found to be universally satisfied in the entanglement picture. We then show that there exists a one-to-one correspondence leading to the Smarr-formula of black hole thermodynamics for asymptotically flat and non-flat space-times.
In this work we derive some general features of the redshift measured by radially moving observers in the black hole background. Let observer 1 cross the black hole horizon emitting of a photon while observer 2 crossing the same horizon later receives it. We show that if (i) the horizon is the outer one (event horizon) and (ii) it is nonextremal, received frequency is redshifted. This generalizes previous recent results in literature. For the inner horizon (like in the Reissner-Nordstr{o}m metric) the frequency is blueshifted. If the horizon is extremal, the frequency does not change. We derive explicit formulas describing the frequency shift in generalized Kruskal- and Lemaitre-like coordinates.
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