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535 KiB

Open AccessArticle

Geometric Model of Black Hole Quantum N-portrait, Extradimensions and Thermodynamics

by Antonia M. Frassino, Sven Köppel and Piero Nicolini

Entropy 2016, 18(5), 181; https://doi.org/10.3390/e18050181 - 14 May 2016

Cited by 24 | Viewed by 6483

Abstract

Recently a short scale modified black hole metric, known as holographic metric, has been proposed in order to capture the self-complete character of gravity. In this paper we show that such a metric can reproduce some geometric features expected from the quantum N [...] Read more.

Recently a short scale modified black hole metric, known as holographic metric, has been proposed in order to capture the self-complete character of gravity. In this paper we show that such a metric can reproduce some geometric features expected from the quantum N-portrait beyond the semi-classical limit. We show that for a generic N this corresponds to having an effective energy momentum tensor in Einstein equations or, equivalently, non-local terms in the gravity action. We also consider the higher dimensional extension of the metric and the case of an AdS cosmological term. We provide a detailed thermodynamic analysis of both cases, with particular reference to the repercussions on the Hawking-Page phase transition. Full article

(This article belongs to the Special Issue Entropy in Quantum Gravity and Quantum Cosmology)

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4271 KiB

Open AccessArticle

Varying Constants Entropic-ΛCDM Cosmology

by Mariusz P. Da̧browski, Hussain Gohar and Vincenzo Salzano

Entropy 2016, 18(2), 60; https://doi.org/10.3390/e18020060 - 22 Feb 2016

Cited by 12 | Viewed by 5210

Abstract

We formulate the basic framework of thermodynamical entropic force cosmology which allows variation of the gravitational constant G and the speed of light c. Three different approaches to the formulation of the field equations are presented. Some cosmological solutions for each framework [...] Read more.

We formulate the basic framework of thermodynamical entropic force cosmology which allows variation of the gravitational constant G and the speed of light c. Three different approaches to the formulation of the field equations are presented. Some cosmological solutions for each framework are given and one of them is tested against combined observational data (supernovae, BAO, and CMB). From the fit of the data, it is found that the Hawking temperature numerical coefficient γ is two to four orders of magnitude less than usually assumed on the geometrical ground theoretical value of O(1) and that it is also compatible with zero. In addition, in the entropic scenario, we observationally test that the fit of the data is allowed for the speed of light c growing and the gravitational constant G diminishing during the evolution of the universe. We also obtain a bound on the variation of c to be Δc / c ∝ 10^-5 > 0 , which is at least one order of magnitude weaker than the quasar spectra observational bound. Full article

(This article belongs to the Special Issue Entropy in Quantum Gravity and Quantum Cosmology)

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214 KiB

Open AccessArticle

Gravitational Entropy and the Second Law of Thermodynamics

by John W. Moffat

Entropy 2015, 17(12), 8341-8345; https://doi.org/10.3390/e17127883 - 21 Dec 2015

Cited by 3 | Viewed by 7561

Abstract

The spontaneous violation of Lorentz and diffeomorphism invariance in a phase near the big bang lowers the entropy, allowing for an arrow of time and the second law of thermodynamics. The spontaneous symmetry breaking leads to O(3,1) → O(3) × R , where [...] Read more.

The spontaneous violation of Lorentz and diffeomorphism invariance in a phase near the big bang lowers the entropy, allowing for an arrow of time and the second law of thermodynamics. The spontaneous symmetry breaking leads to O(3,1) → O(3) × R , where O(3) is the rotational symmetry of the Friedmann–Lemaître–Robertson–Walker spacetime. The Weyl curvature tensor C_μνρσ vanishes in the FLRW spacetime satisfying the Penrose zero Weyl curvature conjecture. The requirement of a measure of gravitational entropy is discussed. The vacuum expectation value 〈0|ψ_μ|0〉 ≠ 0 for a vector field ψ_μ acts as an order parameter and at the critical temperature T_c a phase transition occurs breaking the Lorentz symmetry spontaneously. During the ordered O(3) symmetry phase the entropy is vanishingly small and for T < T_cas the universe expands the anti-restored O(3,1) Lorentz symmetry leads to a disordered phase and a large increase in entropy creating the arrow of time. Full article

(This article belongs to the Special Issue Entropy in Quantum Gravity and Quantum Cosmology)

281 KiB

Open AccessArticle

Modified Gravity Models Admitting Second Order Equations of Motion

by Aimeric Colléaux and Sergio Zerbini

Entropy 2015, 17(10), 6643-6662; https://doi.org/10.3390/e17106643 - 25 Sep 2015

Cited by 3 | Viewed by 4320

Abstract

The aim of this paper is to find higher order geometrical corrections to the Einstein–Hilbert action that can lead only to second order equations of motion. The metric formalism is used, and static spherically-symmetric and Friedmann–Lemaître space-times are considered, in four dimensions. The [...] Read more.

The aim of this paper is to find higher order geometrical corrections to the Einstein–Hilbert action that can lead only to second order equations of motion. The metric formalism is used, and static spherically-symmetric and Friedmann–Lemaître space-times are considered, in four dimensions. The Fulling, King, Wybourne and Cummings (FKWC) basis is introduced in order to consider all of the possible invariant scalars, and both polynomial and non-polynomial gravities are investigated. Full article

(This article belongs to the Special Issue Entropy in Quantum Gravity and Quantum Cosmology)

204 KiB

Open AccessArticle

Viscosity-Induced Crossing of the Phantom Barrier

by Iver Brevik

Entropy 2015, 17(9), 6318-6328; https://doi.org/10.3390/e17096318 - 14 Sep 2015

Cited by 27 | Viewed by 4390

Abstract

We show explicitly, by using astrophysical data plus reasonable assumptions for the bulk viscosity in the cosmic fluid, how the magnitude of this viscosity may be high enough to drive the fluid from its position in the quintessence region at present time t [...] Read more.

We show explicitly, by using astrophysical data plus reasonable assumptions for the bulk viscosity in the cosmic fluid, how the magnitude of this viscosity may be high enough to drive the fluid from its position in the quintessence region at present time t = 0 across the barrier w = −1 into the phantom region in the late universe. The phantom barrier is accordingly not a sharp mathematical divide, but rather a fuzzy concept. We also calculate the limiting forms of various thermodynamical quantities, including the rate of entropy production, for a dark energy fluid near the future Big Rip singularity. Full article

(This article belongs to the Special Issue Entropy in Quantum Gravity and Quantum Cosmology)

213 KiB

Open AccessArticle

Scale-Invariant Rotating Black Holes in Quadratic Gravity

by Guido Cognola, Massimiliano Rinaldi and Luciano Vanzo

Entropy 2015, 17(8), 5145-5156; https://doi.org/10.3390/e17085145 - 23 Jul 2015

Cited by 18 | Viewed by 4377

Abstract

Black hole solutions in pure quadratic theories of gravity are interesting since they allow the formulation of a set of scale-invariant thermodynamics laws. Recently, we have proven that static scale-invariant black holes have a well-defined entropy, which characterizes equivalent classes of solutions. In [...] Read more.

Black hole solutions in pure quadratic theories of gravity are interesting since they allow the formulation of a set of scale-invariant thermodynamics laws. Recently, we have proven that static scale-invariant black holes have a well-defined entropy, which characterizes equivalent classes of solutions. In this paper, we generalize these results and explore the thermodynamics of rotating black holes in pure quadratic gravity. Full article

(This article belongs to the Special Issue Entropy in Quantum Gravity and Quantum Cosmology)

Review

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282 KiB

Open AccessReview

Entropy and Quantum Gravity

by Bernard S. Kay

Entropy 2015, 17(12), 8174-8186; https://doi.org/10.3390/e17127873 - 15 Dec 2015

Cited by 8 | Viewed by 5439 | Correction

Abstract

We give a review, in the style of an essay, of the author’s 1998 matter-gravity entanglement hypothesis which, unlike the standard approach to entropy based on coarse-graining, offers a definition for the entropy of a closed system as a real and objective quantity. [...] Read more.

We give a review, in the style of an essay, of the author’s 1998 matter-gravity entanglement hypothesis which, unlike the standard approach to entropy based on coarse-graining, offers a definition for the entropy of a closed system as a real and objective quantity. We explain how this approach offers an explanation for the Second Law of Thermodynamics in general and a non-paradoxical understanding of information loss during black hole formation and evaporation in particular. It also involves a radically different from usual description of black hole equilibrium states in which the total state of a black hole in a box together with its atmosphere is a pure state—entangled in just such a way that the reduced state of the black hole and of its atmosphere are each separately approximately thermal. We also briefly recall some recent work of the author which involves a reworking of the string-theory understanding of black hole entropy consistent with this alternative description of black hole equilibrium states and point out that this is free from some unsatisfactory features of the usual string theory understanding. We also recall the author’s recent arguments based on this alternative description which suggest that the Anti de Sitter space (AdS)/conformal field theory (CFT) correspondence is a bijection between the boundary CFT and just the matter degrees of freedom of the bulk theory. Full article

(This article belongs to the Special Issue Entropy in Quantum Gravity and Quantum Cosmology)

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343 KiB

Open AccessReview

Distribution Function of the Atoms of Spacetime and the Nature of Gravity

by Thanu Padmanabhan

Entropy 2015, 17(11), 7420-7452; https://doi.org/10.3390/e17117420 - 28 Oct 2015

Cited by 37 | Viewed by 4594

Abstract

The fact that the equations of motion for matter remain invariant when a constant is added to the Lagrangian suggests postulating that the field equations of gravity should also respect this symmetry. This principle implies that: (1) the metric cannot be varied in [...] Read more.

The fact that the equations of motion for matter remain invariant when a constant is added to the Lagrangian suggests postulating that the field equations of gravity should also respect this symmetry. This principle implies that: (1) the metric cannot be varied in any extremum principle to obtain the field equations; and (2) the stress-tensor of matter should appear in the variational principle through the combination T_abn^an^bwhere n_a is an auxiliary null vector field, which could be varied to get the field equations. This procedure uniquely selects the Lanczos–Lovelock models of gravity in D-dimensions and Einstein’s theory in D = 4. Identifying na with the normals to the null surfaces in the spacetime in the macroscopic limit leads to a thermodynamic interpretation for gravity. Several geometrical variables and the equation describing the spacetime evolution acquire a thermodynamic interpretation. Extending these ideas one level deeper, we can obtain this variational principle from a distribution function for the “atoms of spacetime”, which counts the number of microscopic degrees of freedom of the geometry. This is based on the curious fact that the renormalized spacetime endows each event with zero volume, but finite area! Full article

(This article belongs to the Special Issue Entropy in Quantum Gravity and Quantum Cosmology)

477 KiB

Open AccessReview

Thermal BEC Black Holes

by Roberto Casadio, Andrea Giugno, Octavian Micu and Alessio Orlandi

Entropy 2015, 17(10), 6893-6924; https://doi.org/10.3390/e17106893 - 15 Oct 2015

Cited by 30 | Viewed by 6333

Abstract

We review some features of Bose–Einstein condensate (BEC) models of black holes obtained by means of the horizon wave function formalism. We consider the Klein–Gordon equation for a toy graviton field coupled to a static matter current in a spherically-symmetric setup. The classical [...] Read more.

We review some features of Bose–Einstein condensate (BEC) models of black holes obtained by means of the horizon wave function formalism. We consider the Klein–Gordon equation for a toy graviton field coupled to a static matter current in a spherically-symmetric setup. The classical field reproduces the Newtonian potential generated by the matter source, while the corresponding quantum state is given by a coherent superposition of scalar modes with a continuous occupation number. An attractive self-interaction is needed for bound states to form, the case in which one finds that (approximately) one mode is allowed, and the system of N bosons can be self-confined in a volume of the size of the Schwarzschild radius. The horizon wave function formalism is then used to show that the radius of such a system corresponds to a proper horizon. The uncertainty in the size of the horizon is related to the typical energy of Hawking modes: it decreases with the increasing of the black hole mass (larger number of gravitons), resulting in agreement with the semiclassical calculations and which does not hold for a single very massive particle. The spectrum of these systems has two components: a discrete ground state of energy m (the bosons forming the black hole) and a continuous spectrum with energy ω > m (representing the Hawking radiation and modeled with a Planckian distribution at the expected Hawking temperature). Assuming the main effect of the internal scatterings is the Hawking radiation, the N-particle state can be collectively described by a single-particle wave-function given by a superposition of a total ground state with energy M = Nm and Entropy 2015, 17 6894 a Planckian distribution for E > M at the same Hawking temperature. This can be used to compute the partition function and to find the usual area law for the entropy, with a logarithmic correction related to the Hawking component. The backreaction of modes with ω > m is also shown to reduce the Hawking flux. The above corrections suggest that for black holes in this quantum state, the evaporation properly stops for a vanishing mass. Full article

(This article belongs to the Special Issue Entropy in Quantum Gravity and Quantum Cosmology)

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