Testing quantum gravity through dumb holes

Abstract

We propose a method to test the effects of quantum fluctuations on black holes by analyzing the effects of thermal fluctuations on dumb holes, the analogues for black holes. The proposal is based on the Jacobson formalism, where the Einstein field equations are viewed as thermodynamical relations, and so the quantum fluctuations are generated from the thermal fluctuations. It is well known that all approaches to quantum gravity generate logarithmic corrections to the entropy of a black hole and the coefficient of this term varies according to the different approaches to the quantum gravity. It is possible to demonstrate that such logarithmic terms are also generated from thermal fluctuations in dumb holes. In this paper, we claim that it is possible to experimentally test such corrections for dumb holes, and also obtain the correct coefficient for them. This fact can then be used to predict the effects of quantum fluctuations on realistic black holes, and so it can also be used, in principle, to experimentally test the different approaches to quantum gravity. The entropy of a black hole (s) scales with its area rather than its volume, s = A/4, where A is the area of its horizon [1,2]. This is true not only in general relativity but also in modified theories of gravity, and so even in modified theories of gravity the leading order entropy scales with the area [3][4][5][6][7]. This expression for the entropy of a black hole can be obtained using a semi-classical approximation. Since any approach to quantum gravity has to agree with the semi-classical approximation at a sufficiently low energy scale, it is expected that all the approaches to quantum gravity will produce this expression for the entropy of a black hole. In fact, it has been observed that even though there are various different approaches to quantum gravity, all of them predict that the entropy of a black hole would be related to the area of the horizon as s = A/4. However, all these different approaches to quantum gravity also predict corrections to this relation between the area and the entropy. Non-perturbative quantum general relativity has been used to obtain such a logarithmic correction to the area-entropy law [8]. It is known that a relation exists between the density of states of a black hole and the conformal blocks of a conformal field theory in non-perturbative quantum general relativity. This relation is used to obtain the logarithmic correction to the area-entropy law. It has also been demonstrated that such a logarithmic term can be obtained using the Cardy formula for the entropy of a black hole [9]. It is also possible to analyze the exact partition function for a Bañados-Teitelboim-Zanelli (BTZ) black hole [10], and calculate the correction to the area-entropy law for such a black hole. This calculation points out that the entropy of a BTZ black hole results corrected by a logarithmic term [11]. It has also been observed that the entropy of a dilatonic black holes is also corrected by a logarithmic term [12]. The string theory correc...

Quantum fluctuations from thermal fluctuations in Jacobson formalism

“…However, at the Planck scale, just as we expect a manifold description to spacetime to break down, we also expect the equilibrium discretion to the thermodynamics to break down. We would like to point out that such thermal fluctuations have been studied for various kinds of dynamical black objects [33][34][35][36][37][38][39][40][41][42]. It would be interesting to analyze the effects of such thermal fluctuations on the spacetime metric using the formalism developed in this paper.…”

“…In fact, this constant is usually proportional to some new constant in that theory. As this constant depends on the details of the model used, we will use an arbitrary constant α and define the corrected microcanonical entropy as [33][34][35][36][37][38][39][40][41][42] …”

The lower bound violation of shear viscosity to entropy ratio due to logarithmic correction in STU model

“…It would thus be interesting to analyze thermal fluctuations of such a STU black hole and discuss these corrections to the entropy using asymptotic charges. Testing quantum gravity using black objects [56] like the STU black hole is also an interesting research field.…”

Thermal fluctuations in a hyperscaling-violation background

“…As dumb holes are analogs of black hole like solutions, it is possible to study such effects for dumb holes. In fact, the effects of thermal fluctuations on the thermodynamics of dumb holes has been studied [34]. The thermal fluctuations can affect the critical behaviors of black holes.…”