Horizon Entropy Research Articles

Covariant phase space with boundaries

The covariant phase space method of Iyer, Lee, Wald, and Zoupas gives an elegant way to understand the Hamiltonian dynamics of Lagrangian field theories without breaking covariance. The original literature however does not systematically treat total derivatives and boundary terms, which has led to some confusion about how exactly to apply the formalism in the presence of boundaries. In particular the original construction of the canonical Hamiltonian relies on the assumed existence of a certain boundary quantity “B”, whose physical interpretation has not been clear. We here give an algorithmic procedure for applying the covariant phase space formalism to field theories with spatial boundaries, from which the term in the Hamiltonian involving B emerges naturally. Our procedure also produces an additional boundary term, which was not present in the original literature and which so far has only appeared implicitly in specific examples, and which is already nonvanishing even in general relativity with sufficiently permissive boundary conditions. The only requirement we impose is that at solutions of the equations of motion the action is stationary modulo future/past boundary terms under arbitrary variations obeying the spatial boundary conditions; from this the symplectic structure and the Hamiltonian for any diffeomorphism that preserves the theory are unambiguously constructed. We show in examples that the Hamiltonian so constructed agrees with previous results. We also show that the Poisson bracket on covariant phase space directly coincides with the Peierls bracket, without any need for non-covariant intermediate steps, and we discuss possible implications for the entropy of dynamical black hole horizons.

Elementary Charge and Neutrino’s Mass from Planck Length

It is shown that the postulation of a minimum length for the horizons of a black hole leads to lower bounds for the electric charges and magnetic moments of elementary particles. If the minimum length has the order of the Planck scale, these bounds are given, respectively, by the electronic charge and by $\mu \sim 10^{-21} \mu_B$. The latter implies that the masses of fundamental particles are bounded above by the Planck mass, and that the smallest non-zero neutrino mass is $m_{\nu} \sim 10^{-2}$eV. A precise estimation in agreement to the area quantisation of Loop Quantum Gravity predicts a mass for the lightest massive state in concordance with flavor oscillation measurements, and a Barbero-Immirzi parameter in accordance to horizon entropy estimations.

Entropy production due to adiabatic particle creation in a holographic dissipative cosmology

Cosmological adiabatic particle creation results in the generation of irreversible entropy. The evolution of this entropy is examined in a flat Friedmann--Robertson--Walker universe at late times, using a dissipative model with a power-law term (proportional to the power of the Hubble parameter $H$). In a dissipative universe, the irreversible entropy included in the Hubble volume is found to be proportional to $H^{-1}$, unlike for the case of the Bekenstein--Hawking entropy on the horizon of the universe. In addition, the evolution of the horizon entropy is examined, extending the previous analysis of a non-dissipative universe [Phys.\ Rev.\ D \textbf{100}, 123545 (2019) (arXiv:1911.08306)]. In the present model, the generalized second law of thermodynamics is always satisfied, whereas the maximization of entropy is satisfied under specific conditions. The dissipative universe should be constrained by the entropy maximization as if the universe behaves as an ordinary, isolated macroscopic system. The thermodynamic constraints are likely to be consistent with constraints on a transition from a decelerating universe to an accelerating universe.

The Entropy of a Gravitating Body

This paper proposes a generalization of the dependence for the entropy of ‘‘ordinary’’ massive bodies with a relatively small entropy of the event horizon of the covering surface to the case of black holes (BH). By doing this, the nature of the famous Bekenstein bound, that is, the universal limit for entropy, is immediately explained and corrections to the values of the ‘‘gravitational’’ surface temperature are determined for the entire spectrum of astrophysical objects.

Deforming charged black holes with dipolar differential rotation boundary

Motivated by the recent studies of the novel asymptotically global hbox {AdS}_4 black hole with deformed horizon, we consider the action of Einstein–Maxwell gravity in AdS spacetime and construct the charged deforming AdS black holes with differential boundary. In contrast to deforming black hole without charge, there exists at least one value of horizon for an arbitrary temperature. The extremum of temperature is determined by charge q and divides the range of temperature into several parts. Moreover, we use an isometric embedding in the three-dimensional space to investigate the horizon geometry. The entropy and quasinormal modes of deforming charged AdS black hole are also studied in this paper. Due to the existence of charge q, the phase diagram of entropy is more complicated. We consider two cases of solutions: (1) fixing the chemical potential mu ; (2) changing the value of mu according to the values of horizon radius and charge. In the first case, it is interesting to find there exist two families of black hole solutions with different horizon radii for a fixed temperature, but these two black holes have same horizon geometry and entropy. The second case ensures that deforming charged AdS black hole solutions can reduce to standard RN–AdS black holes.

Black hole and naked singularity geometries supported by three-form fields

We investigate static and spherically symmetric solutions in a gravity theory that extends the standard Hilbert–Einstein action with a Lagrangian constructed from a three-form field A_{alpha beta gamma }, which is related to the field strength and a potential term. The field equations are obtained explicitly for a static and spherically symmetric geometry in vacuum. For a vanishing three-form field potential the gravitational field equations can be solved exactly. For arbitrary potentials numerical approaches are adopted in studying the behavior of the metric functions and of the three-form field. To this effect, the field equations are reformulated in a dimensionless form and are solved numerically by introducing a suitable independent radial coordinate. We detect the formation of a black hole from the presence of a Killing horizon for the timelike Killing vector in the metric tensor components. Several models, corresponding to different functional forms of the three-field potential, namely, the Higgs and exponential type, are considered. In particular, naked singularity solutions are also obtained for the exponential potential case. Finally, the thermodynamic properties of these black hole solutions, such as the horizon temperature, specific heat, entropy and evaporation time due to the Hawking luminosity, are studied in detail.

Modified cosmology through spacetime thermodynamics and Barrow horizon entropy

We present modified cosmological scenarios that arise from the application of the “gravity-thermodynamics” conjecture, using the Barrow entropy instead of the usual Bekenstein-Hawking one. The former is a modification of the black hole entropy due to quantum-gravitational effects that deform the black-hole horizon by giving it an intricate, fractal structure. We extract modified cosmological equations which contain new extra terms that constitute an effective dark-energy sector, and which coincide with the usual Friedmann equations in the case where the new Barrow exponent acquires its Bekenstein-Hawking value. We present analytical expressions for the evolution of the effective dark energy density parameter, and we show that the universe undergoes through the usual matter and dark-energy epochs. Additionally, the dark-energy equation-of-state parameter is affected by the value of the Barrow deformation exponent and it can lie in the quintessence or phantom regime, or experience the phantom-divide crossing. Finally, at asymptotically large times the universe always results in the de-Sitter solution.

Mechanics of isolated horizons in scalar-tensor theories

Based on the first-order action for scalar-tensor theories with the Immirzi parameter, the symplectic form for the spacetimes admitting a weakly isolated horizon as internal boundary is derived by the covariant phase space approach. The first law of thermodynamics for the weakly isolated horizons with rotational symmetry is obtained. It turns out that the Immirzi parameter appears in the expression of the angular momentum of isolated horizon, and the scalar field contributes to the horizon entropy.

Entropy production from quasinormal modes

Horizons of black branes have an associated entropy current with non-negative divergence. We compute this divergence in a late-time transseries expansion for an inhomogeneous system evolving towards a maximally symmetric asymptotically anti-de Sitter black brane. The horizon area equilibrates on half the time-scale set by the dominant quasinormal mode and we find a simple analytic expression for this evolution purely in terms of the background and the quasinormal mode frequencies. This computation does not require a gradient expansion and is thus non-perturbative in momenta. We generalize this to include scalar and gauge field matter in any number of dimensions. Restricting to homogeneous evolution we match and prove earlier numerical work showing that the apparent horizon entropy saturates the area theorem, in that its time derivative periodically vanishes. The same is true for spherically symmetric evolution towards the Schwarzschild black hole.

Thermodynamic properties of higher-dimensional dS black holes in dRGT massive gravity

On the basis of the state parameter of de Sitter space-time satisfying the first law of thermodynamics, we can derive some effective thermodynamic quantities. When the temperature of the black hole horizon is equal to that of the cosmological horizon, we think that the effective temperature of the space-time should have the same value. Using this condition, we obtain a differential equation of the entropy of the de Sitter black hole in the higher-dimensional de Rham, Gabadadze and Tolley (dRGT) massive gravity. Solving the differential equation, we obtain the corrected entropy and effective thermodynamic quantities of the de Sitter black hole. The results show that for multi-parameter black holes, the entropy satisfied differential equation is invariable with different independent state parameters. Therefore, the entropy of higher-dimensional dS black holes in dRGT massive gravity is only a function of the position of the black hole horizon, and is independent of other state parameters. It is consistent with the corresponding entropy of the black hole horizon and the cosmological horizon. The thermodynamic quantities of self-consistent de Sitter space-time are given theoretically, and the equivalent thermodynamic quantities have the second-order phase transformation similar to AdS black hole, but unlike AdS black hole, the equivalent temperature of de Sitter space-time has a maximum value. By satisfying the requirement of thermodynamic equilibrium and stability of space-time, the conditions for the existence of dS black holes in the universe are obtained.

Generalized Misner–Sharp energy in generalized Rastall theory

Employing the unified first law of thermodynamics and the field equations of the generalized Rastall theory, we get the generalized Misner–Sharp mass of space–times for which gtt = –grr = –f(r). The obtained result differs from those of the Einstein and Rastall theories. Moreover, using the first law of thermodynamics, the obtained generalized Misner–Sharp mass, and the field equations, the entropy of static spherically symmetric horizons are also addressed in the framework of the generalized Rastall theory. In addition, by generalizing the study to a flat Friedmann–Robertson–Walker (FRW) universe, the apparent horizon entropy is also calculated. Considering the effects of applying the Newtonian limit to the field equations on the coupling coefficients of the generalized Rastall theory, our study indicates (i) the obtained entropy–area relation is the same as that of the Rastall theory, and (ii) the Bekenstein entropy is recovered when the generalized Rastall theory reduces to the Einstein theory. The validity of the second law of thermodynamics is also investigated in the flat FRW universe.

Energy density, temperature, and entropy dynamics in perturbative reheating

We discuss the perturbative decay of the energy density of a non standard inflaton field $\rho_{\phi}$ and the corresponding creation of the energy density of the relativistic fields $\rho_r$ at the end of inflation, in the perfect fluid description, refining some concepts and providing some new computations. In particular, the process is characterized by two fundamental time scales. The first one, $t_\text{max}$, occurs when the energy density $\rho_r$ reaches its largest value, slightly after the beginning of the reheating phase. The second one, $t_\text{reh}$, is the time in which the reheating is completely realized and the thermalization is attained. By assuming a non-instantaneous reheating phase, we are able to derive the energy densities and the temperatures of the produced relativistic bath at $t_\text{max}$ and $t_\text{reh}$, as well as the value of the corresponding horizon entropy $S_\text{hor}$, for an Equation-of-State (EoS) parameter $w\ne 0$.

Higher spin de Sitter Hilbert space

We propose a complete microscopic definition of the Hilbert space of minimal higher spin de Sitter quantum gravity and its Hartle-Hawking vacuum state. The funda- mental degrees of freedom are 2N bosonic fields living on the future conformal boundary, where N is proportional to the de Sitter horizon entropy. The vacuum state is normalizable. The model agrees in perturbation theory with expectations from a previously proposed dS- CFT description in terms of a fermionic Sp(N) model, but it goes beyond this, both in its conceptual scope and in its computational power. In particular it resolves the apparent pathologies affecting the Sp(N) model, and it provides an exact formula for late time vac- uum correlation functions. We illustrate this by computing probabilities for arbitrarily large field excursions, and by giving fully explicit examples of vacuum 3- and 4-point functions. We discuss bulk reconstruction and show the perturbative bulk QFT canonical commuta- tions relations can be reproduced from the fundamental operator algebra, but only up to a minimal error term ∼ e−O(N ), and only if the operators are coarse grained in such a way that the number of accessible “pixels” is less than O(N ). Independent of this, we show that upon gauging the higher spin symmetry group, one is left with 2N physical degrees of freedom, and that all gauge invariant quantities can be computed by a 2N × 2N matrix model. This suggests a concrete realization of the idea of cosmological complementarity.

Cosmological consequences and thermodynamics of modified gravity with extended nonminimal derivative couplings

We consider the newly proposed gravitational modifications that go beyond Horndeski’s theory, named as theories with extended nonminimal derivative couplings. By these modifications, the coefficient functions depend on the scalar field and its kinetic energy. These theories become ghost-free in cosmological background. We consider the flat FRW universe and explore the equation-of-state parameter, [Formula: see text]–[Formula: see text] plane and the squared speed of sound. The equation-of-state parameter exhibits phantom behavior of the universe, [Formula: see text]–[Formula: see text] plane represents the freezing region of the universe while the squared speed of sound denotes the stability of the model for the specific choice of constant parameters. Also, we investigate the validity of generalized second law of thermodynamics on the Hubble horizon taking into account the Bekenstein, power-law, Renyi and logarithmic corrections to the horizon entropy.

Cosmological horizons, Noether charges and entropy

It has recently been shown that, in the vicinity of their event horizons, black holes exhibit an infinite-dimensional symmetry. This symmetry captures relevant physical information about the black hole, and in particular about its thermodynamics. Here, we show that the same holds in a cosmological setup. More precisely, we show that around the de Sitter cosmological horizon, an infinite set of diffeomorphisms preserving a sensible set of boundary conditions emerges. These boundary conditions are similar to those considered by Price and Thorne in the context of the membrane paradigm, and permit to accommodate interesting gravity solutions. As for other boundary conditions considered previously, they are preserved by an infinite-dimensional asymptotic isometry algebra that includes supertranslations and two copies of the Virasoro algebra. This symmetry has associated a set of Noether charges that turn out to be conserved, finite, and integrable. We derive these charges explicitly using the covariant formalism and analyze their physical meaning by evaluating them to the case of de Sitter space. In this case, the zero-mode of the charge is found to account for the Gibbons–Hawking entropy of the cosmological horizon. We then consider a much more general set of solutions, including asymptotically de-Sitter black holes and asymptotically Taub–NUT–de Sitter black holes.

Quantum Hubble horizon

The article addresses the possibility of obtaining cosmologically relevant effects from the quantum nature of the Hubble horizon. Following the observation made by Bianchi and Rovelli (Phys Rev D 84:027502, 2011) we explore the relationship between the Planck scale discreteness of the Hubble horizon and deformations of the symmetry of rotations. We show that the so-called q-deformations in a natural way lead to a mechanism of condensation in the very early Universe. We argue that this provides a possible resolution of the problem of the initial homogeneity at the onset of inflation. Furthermore, we perform an analysis in terms of entropy of the quantum Hubble horizon and show that the Lambda CDM model may arise from a linearly corrected Bekenstein–Hawking entropy (that is, linearly in area of the horizon). Based on this, we show that the current accelerating expansion can be associated with the entropy decrease in the Hubble volume. The results presented open new ways to explore the relation between the Planck scale effects and observationally relevant features of our Universe.

Weak Gravity Conjecture and extremal black holes

Motivated by the desire to improve our understanding of the Weak Gravity Conjecture, we compute the one-loop correction of charged particles to the geometry and entropy of extremal black holes in 4D. We use the entropy function formalism to extend previous analysis that dealt with neutral particles, and obtain the corrections to the horizon entropy for different regimes of black hole masses. These corrections are small in general. They are furthermore reduced when supersymmetry is present, and disappear in N = 4 supergravity. We provide some speculative arguments that in a theory with only sub-extremal particles, classical Reissner-Nordstrom black holes actually possess an infinite microcanonical entropy, though only a finite amount is visible to an external observer, as shown by the horizon entropy computation.

Thermodynamics in loop quantum cosmology with non-canonical scalar field model

The cosmological scenario is built up within the framework of scalar field model possessing a noncanonical kinetic term in loop quantum gravity. The noncanonical scalar field is permitted to interact with dark matter field by assuming a specific form of coupling term. The equation of state parameter is set to be constant as well as variable (Chevallier–Polarski–Linder parametrization) and evaluated the behavior of universe through deceleration parameter and weak energy condition. These parameters favor the accelerated expansion of the universe for three values of equation of state parameter in both cases allowed by observational data. The squared speed of sound leads to the stability of the underlying models in both forms of equation of state parameter. Moreover, the validity of generalized second law of thermodynamics is analyzed by using first law of thermodynamics and assume the universe to be enclosed by apparent horizon. The Bekenstein, logarithmic and power-law entropy is being considered as entropy of horizon. The thermodynamic equilibrium condition is also discussed for all three cases of entropies. The generalized second law of thermodynamics and thermal equilibrium condition is satisfied for all the three types of entropies.

More on spacetime thermodynamics in the light of Weyl transformations

It was recently found that, after performing a Weyl conformal transformation, the familiar analogy between black hole mechanics and black hole thermodynamics becomes ambiguous. It was argued that this fact can be traced back to the fundamental dichotomy between matter and geometry, which is at the heart of Einstein's field equations. As a further study of this issue, we investigate here the general link between spacetime thermodynamics and Weyl transformations from two other angles. We first examine the conformal behaviour of the horizon entropy within Wald's approach based on the fundamental diffeomorphism symmetry of $pure$ geometry. We then revisit $-$ using Weyl transformations $-$ Jacobson's derivation of Einstein's field equations, the starting point of which is precisely built on the fundamental dichotomy between matter and geometry. As a result, we show that in order for Jacobson's approach to be able to yield the right Einstein field equations in the conformal frame, a specific conformal behavior of the horizon temperature and its entropy $-$ different from what Wald's approach implies $-$ is required. The two approaches to spacetime thermodynamics become thus incompatible in the conformal frame. In addition, we show $-$ in greater detail in the conformal frame $-$ that in the presence of a null dust the thermodynamics approach for extracting Einstein's field equations necessarily fails. An extensive discussion of the whole issue is given.

Spherically symmetric static vacuum solutions in hybrid metric-Palatini gravity

We consider vacuum static spherically symmetric solutions in the hybrid metric-Palatini gravity theory, which is a combination of the metric and Palatini $f(R)$ formalisms unifying local constraints at the Solar System level and the late-time cosmic acceleration. We adopt the scalar-tensor representation of the hybrid metric-Palatini theory, in which the scalar-tensor definition of the potential can be represented as a Clairaut differential equation. Due to their mathematical complexity, it is difficult to find exact solutions of the vacuum field equations, and therefore we adopt a numerical approach in studying the behavior of the metric functions and of the scalar field. After reformulating the field equations in a dimensionless form, and by introducing a suitable independent radial coordinate, the field equations are solved numerically. We detect the formation of a black hole from the presence of a singularity in the metric tensor components. Several models, corresponding to different functional forms of the scalar field potential are considered. The thermodynamic properties of these black hole solutions (horizon temperature, specific heat, entropy and evaporation time due to Hawking luminosity) are also investigated in detail.