The quantum states or Hilbert spaces for the quantum field theory in de Sitter space-time are studied on ambient space formalism. In this formalism, the quantum states are only depended $(1)$ on the topological character of the de Sitter space-time, {\it i.e.} $\R \times S^3$, and $(2)$ on the homogeneous spaces which are used for construction of the unitary irreducible representation of de Sitter group. A compact homogeneous space is chosen in this paper. The unique feature of this homogeneous space is that its total number of quantum states, ${\cal N}$, is finite although the Hilbert space has infinite dimensions. It is shown that ${\cal N}$ is a continuous function of the Hubble constant $H$ and the eigenvalue of the Casimir operators of de Sitter group. The entropy of the quantum fields on this Hilbert space have been calculated which is finite and invariant for all inertial observers on the de Sitter hyperboloid.
We revisit the Parikh-Wilczek tunneling through the de Sitter horizon and obtain the tunneling rate in Schwarzschild-de Sitter space, which is non-thermal and closely related to the change of entropy. We discuss the thermodynamics of Schwarzschild-de Sitter space and show existence of correlation which ensured the conservation of the total entropy in the transition process of Schwarzschild-de Sitter space to de Sitter space. The correlation and the conserved entropy enlighten a way to explain the entropy in empty de Sitter space.
From the partition function of canonical ensemble we derive the entropy of the de Sitter space by anti-Wick rotation. And then from the one-loop bubble $S^2\times S^2$ created from vacuum fluctuation in de Sitter background space, we obtain the one-loop quantum correction to the entropy of de Sitter space.
By introducing the generalized uncertainty principle (GUP) on the quantum state density, we calculate the statistical entropy of a scalar field on the background of (2+1)-dimensional de Sitter space without artificial cutoff. The desired entropy proportional to the horizon perimeter is obtained.
We calculate the statistical entropy of a scalar field on the background of (2+1)-dimensional de Sitter space without an artificial cutoff considering corrections to all orders in the Planck length from a generalized uncertainty principle (GUP) on the quantum state density. The desired entropy proportional to the horizon perimeter is obtained.
General geodesic equations of the motion of spinning systems around the (3+1)-dimensional and (2+1)-dimensional rotating anti-de Sitter black holes have been obtained. Based upon these equations, we derived the entropy bound for a rotating system from Kerr-Anti de Sitter black holes and BTZ black holes, respectively. Our result coincides with that of Hod's derived from Kerr black hole, which shows that the entropy bound of the rotating system is neither dependent on the black hole parameters, nor on spacetime dimensions. It is a universal entropy bound.
The paper deals with the calculation of the gravitational entropy in the context of teleparallel gravity for de Sitter space-time. In such a theory it is possible to define gravitational energy and pressure, thus we use those expressions to construct the gravitational entropy. We interpret the cosmological constant as the temperature and write the first law of thermodynamics. In the limit $Λ\ll 1$ we find that the entropy is proportional to volume and $ΔS\geq 0$.
By a simple physical consideration and uncertain principle, we derive that temperature is proportional to the surface gravity and entropy is proportional to the surface area of the black hole. We apply the same consideration to de Sitter space and estimate the temperature and entropy of the space, then we deduce that the entropy is proportional to the boundary surface area. By the same consideration, we estimate the temperature and entropy in the uniformly accelerated system (Rindler coordinate). The cases in higher dimensions are considered.
Using the analytic extension method, we study Hawking radiation of an $(n + 4)$-dimensional Schwarzschild-de Sitter black hole. Under the condition that the total energy is conserved, taking the reaction of the radiation of particles to the spacetime into consideration and considering the relation between the black hole event horizon and cosmological horizon, we obtain the radiation spectrum of de Sitter spacetime. This radiation spectrum is no longer a strictly pure thermal spectrum. It is related to the change of the Bekenstein-Hawking(B-H) entropy corresponding the black hole event horizon …
We calculate the intrinsic entropy of a Schwarzschild black hole in an asymptotically antide Sitter space. The statistical calculation of the entropy is based on a model for particle structure that leads to confinement. The constituents of the particle are distinguishable quasiparticles. The entropy (temperature) is less (greater) than the entropy of a Schwarzschild black hole in an asymptotically flat space. The equilibrium thermodynamic states are described by pure states, myriotic fields, and the distinguishability of the internal microstates may provide a solution to the black hole informa…
Based on the consideration that the black hole horizon and the cosmological horizon of Kerr-de Sitter black hole are not independent each other, we conjecture the total entropy of the system should have an extra term contributed from the correlations between the two horizons, except for the sum of the two horizon entropies. By employing globally effective first law and effective thermodynamic quantities, we obtain the corrected total entropy and find that the region of stable state for kerr-de Sitter is related to the angular velocity parameter $a$, i.e., the region of stable state becomes big…
The Newman-Penrose formalism is used to derive the Teukolsky master equations controlling massless scalar, neutrino, electromagnetic, gravitino, and gravitational field perturbations of the Kerr-de Sitter spacetime. Then the quantum entropy of a non-extreme Kerr-de Sitter black hole due to arbitrary spin fields is calculated by the improved thin-layer brick wall model. It is shown that the subleading order contribution to the entropy is dependent on the square of the spins of particles and that of the specific angular momentum of black holes as well as the cosmological constant. The logarithmi…
Based on the consideration that the black hole horizon and the cosmological horizon of Reissner-Nordström black hole in de Sitter space are not independent each other, we conjecture the total entropy of the system should have an extra term contributed from the entanglement between the two horizons, except for the sum of the two horizon entropies. Making use of the globally effective first law and the effective thermodynamic quantities, we derive the total entropy and find that it will diverge as the two horizons tends to coincide.
Based on the perspective that continuum gravitational physics is an emergent quantum gravitational phenomenon, and that spacetime thermodynamic is the natural langauge in which it can be described, we derive a modified Schwarzschild-de Sitter geometry in static coordinates from quantum gravity inspired logarithmic corrections to the entropy-area law. The resulting quantum corrections to classical geometry can be encoded in explicitly radius dependent black hole and cosmological constant parameters. By considering the pure black hole case we study linear perturbations on this modified backgroun…
From a new perspective, we discuss the thermodynamic entropy of $n+2$-dimensional Reissner-Nordström-de Sitter(RNdS) black hole and analyze the phase transition of the effective thermodynamic system. Considering the correlations between the black hole event horizon and the cosmological horizon, we conjecture that the total entropy of the RNdS black hole should contain an extra term besides the sum of the entropies of the two horizons. In the lukewarm case, the effective temperature of the RNdS black hole is the same as that of the black hole horizon and the cosmological horizon. Under this con…
The fundamental equation of the thermodynamic system gives the relation between internal energy, entropy and volume of two adjacent equilibrium states. Taking higher dimensional charged Gauss-Bonnet black hole in de Sitter space as a thermodynamic system, the state parameters have to meet the fundamental equation of thermodynamics. We introduce the effective thermodynamic quantities to describe the black hole in de Sitter space. Considering that in the lukewarm case the temperature of the black hole horizon is equal to that of the cosmological horizon, the effective temperature of spacetime is…
We calculate Sorkin's manifestly covariant entanglement entropy $\mathcal{S}$ for a massive and massless minimally coupled free Gaussian scalar field for the de Sitter horizon and Schwarzschild de Sitter horizons respectively in $d > 2$. In de Sitter spacetime we restrict the Bunch-Davies vacuum in the conformal patch to the static patch to obtain a mixed state. The finiteness of the spatial $\mathcal{L}^2$ norm in the static patch implies that $\mathcal{S}$ is well defined for each mode. We find that $\mathcal{S}$ for this mixed state is independent of the effective mass of the scalar field, …
An alternative method to compute the entropy of de Sitter spacetime for dimensions higher than or equal to five is presented. It is shown that de Sitter entropy may be obtained from the Bekenstein-Hawking entropy of a lower-dimensional black hole. This result follows from the existence of a one-to-one correspondence between de Sitter and a spacetime containing a black hole localized on a p-brane. Under this correspondence and due to the holographic principle, the entropy of a five-dimensional de Sitter space may be obtained from that of a BTZ black hole localized on a 2-brane. For dimensions h…
We consider the thermodynamics of minimally coupled massive scalar field in 3+1 dimensional constant curvature black hole background. The brick wall model of 't Hooft is used. When Schwarzschild like coordinates are used it is found that two radial brick wall cut-off parameters are required to regularize the solution. Free energy of the scalar field is obtained through counting of states using the WKB approximation. It is found that the free energy and the entropy are divergent in both the cut-off parameters.
We investigate nature of asymptotically de Sitter space-times containing a black hole. We show that if the matter fields satisfy the dominant energy condition and the cosmic censorship holds in the considering space-time, the area of the cosmological event horizon for an observer approaching a future timelike infinity does not decrease, i.e. the second law is satisfied. We also show under the same conditions that the total area of the black hole and the cosmological event horizon, a quarter of which is the total Bekenstein-Hawking entropy, is less than $12π/Λ$, where $Λ$ is a cosmological cons…
We first briefly discuss the relation between black hole thermodynamics and the entropy function formalism. We find that an equation which governs the relationship between Sen's entropy function and black hole entropy, can quickly give higher order corrections to entropy of pure (anti-) de Sitter space without knowing the corrected metric. We also show that near horizon geometry and the entropy function extremization is no longer required for pure (anti-)de Sitter space. The entropy of (anti-)de Sitter space and Schwarzschild-(anti-) de Sitter black holes together with Gauss-Bonnet terms, $R^2…
This brief report studies the behavior of entropy in two recent models of cosmic evolution by J.A.S. Lima, S. Basilakos, and F.E.M. Costa [Phys. Rev. D \underline{86}, 103534 (2012)], and J. A. S. Lima, S. Basilakos, and J. Solá [arXiv:1209.2802]. Both start with an initial de Sitter expansion, go through the conventional radiation and matter dominated eras to be followed by a final and everlasting de Sitter expansion. In spite of their outward similarities (from the observational viewpoint they are arbitrary close to the conventional $Λ$CDM model), they deeply differ in the physics behind the…
Using the adiabatic invariant action and applying Bohr-Sommerfeld quantization rule and first law of black hole thermodynamics a study of quantization of entropy and horizon area of Kerr-Newman-de Sitter black hole is carried out. The same entropy spectrum is obtained in two different coordinate systems. It is also observed that the spacing of the entropy spectrum is independent of the black hole parameters and also the corresponding quantum of horizon area is in agreement with the results of Bekenstein.
A de Sitter black hole or a black hole spacetime endowed with a positive cosmological constant has two Killing horizons -- a black hole and a cosmological event horizon surrounding it. It is natural to expect that the total Bekenstein-Hawking entropy of such spacetimes should be the sum of the two horizons' areas. In this work we apply the recently developed formalism using the Gibbons-Hawking-York boundary term and the near horizon symmetries to derive the total entropy of such two horizon spacetimes. We construct a suitable general geometric set up for general stationary axisymmetric spaceti…
We present a new ``universal property'' of entropy, that is the ``entropy sum'' relation of black holes in four dimensional (anti-)de-Sitter asymptotical background. They depend only on the cosmological constant with the necessary effect of the un-physical ``virtual'' horizon included in the spacetime where only the cosmological constant, mass of black hole, rotation parameter and Maxwell field exist. When there is more extra matter field in the spacetime, one will find the ``entropy sum'' is also dependent of the strength of these extra matter field. For both cases, we conclude that the ``ent…
Quantum gravity in 2+1 dimensions with a positive cosmological constant can be represented as an SL(2,C) Chern-Simons gauge theory. The symmetric vacuum of this theory is a degenerate configuration for which the gauge fields and spacetime metric vanish, while de Sitter space corresponds to a highly excited thermal state. Carlip's approach to black hole entropy can be adapted in this context to determine the statistical entropy of de Sitter space. We find that it equals one-quarter the area of the de Sitter horizon, in agreement with the semiclassical formula.
Unlike the extremal Reissner - Nordström black hole in ordinary spacetime, the one in anti-de Sitter spacetime is a minimum of action and has zero entropy if quantization is carried out after extremalization. However, if extremalization is carried out after quantization, then the entropy is a quarter of the area as in the usual case.
The entropy for a black hole in a de Sitter space is approached within the framework of spacetime foam. A simple model, made by $N$ wormholes in a semiclassical approximation, is taken under examination to compute the entropy for such a case. An extension to the extreme case when the black hole and cosmological horizons are equal is discussed.
We investigate the Schwarzschild-Anti-deSitter (SAdS) and SdS BH thermodynamics in 5d higher derivative gravity. The interesting feature of higher derivative gravity is the possibility for negative (or zero) SdS (or SAdS) BH entropy which depends on the parameters of higher derivative terms. The appearence of negative entropy may indicate a new type instability where a transition between SdS (SAdS) BH with negative entropy to SAdS (SdS) BH with positive entropy would occur or where definition of entropy should be modified.
We consider the entropy of a quantum scalar field on a background black hole geometry in asymptotically anti-de Sitter space-time, using the ``brick wall'' approach. In anti-de Sitter space, the theory has no infra-red divergences, and all ultra-violet divergences can be absorbed into a renormalization of the coupling constants in the one-loop effective gravitational Lagrangian. We then calculate the finite renormalized entropy for the Schwarzschild-anti-de Sitter and extremal Reissner-Nordstrom-anti-de Sitter black holes, and show that, at least for large black holes, the entropy is entirely …
The thermodynamic properties of the de Rham-Gabadadze-Tolley (dRGT) black hole in the asymptotically de Sitter (dS) spacetime are investigated by using Rényi entropy. It has been found that the black hole with asymptotically dS spacetime described by the standard Gibbs-Boltzmann statistics cannot be thermodynamically stable. Moreover, there generically exist two horizons corresponding to two thermodynamic systems with different temperatures, leading to a nonequilibrium state. Therefore, in order to obtain the stable dRGT black hole, we use the alternative Rényi statistics to analyze the thermo…
We investigate a recent proposal for defining a conserved mass in asymptotically de Sitter spacetimes that is based on a conjectured holographic duality between such spacetimes and Euclidean conformal field theory. We show that an algorithm for deriving such terms in asymptotically anti de Sitter spacetimes has an asymptotically de Sitter counterpart, and derive the explicit form for such terms up to 9 dimensions. We show that divergences of the on-shell action for de Sitter spacetime are removed in any dimension in inflationary coordinates, but in covering coordinates a linear divergence rema…
In this paper, we discuss the tunneling of scalar particles near the event horizon of stationary and nonstationary Kerr-de Sitter black hole using Lorentz violation theory in curved space time. The modified form of Hamilton-Jacobi equation is derived from the Klein-Gordon equation by applying Lorentz violation theory. The Hawking temperatures derived from stationary and nonstationary Kerr-de Sitter black holes are modified due to Lorentz violation theory. It is noted that the change in Bekenstein-Hawking entropy and modified Hawking temperatures of stationary and nonstationary Kerr-de Sitter b…
We consider Kerr-de Sitter spacetimes and evaluate their mass, angular momentum and entropy according to the boundary counterterm prescription. We provide a physicall interpretation for angular velocity and angular momentum at future/past infinity. We show that the entropy of the four-dimensional Kerr-de Sitter spacetimes is less than of pure de Sitter spacetime in agreement to the entropic N-bound. Moreover, we show that maximal mass conjecture which states any asymptotically de Sitter spacetime with mass greater than de Sitter has a cosmological singularity is respected by asymptotically de …
It has been argued recently that the entropy of black holes might be associated with soft scalar, graviton and photon states at the event horizon, as number of such possible soft states is proportional to the horizon area. However, the coefficient of proportionality between the number of soft states and the horizon area of a black hole has not been established. Here, similar arguments are applied to de Sitter spacetime and it is shown that soft scalar gravitational modes account for the full de Sitter entropy $S=\frac{1}{4}M_{P}^{2}A$ with the correct numerical prefactor in front of the horizo…
We argue that de Sitter universes with a small cosmological constant are entropically favored to have three spatial dimensions. The conclusion relies on the causal-patch description of de Sitter space, where fiducial observers experience local thermal equilibrium up to a stretched horizon, on the holographic principle, and on some assumptions about the nature of gravity and the constituents of Hawking/Unruh radiation.
The entropy spectrum of a spherically symmetric black hole was derived without the quasinormal modes in the work of Majhi and Vagenas. Extending this work to rotating black holes, we quantize the entropy and the horizon area of a Kerr anti-de Sitter black hole by two methods. The spectra of entropy and area are obtained via the Bohr-Sommerfeld quantization rule and the adiabatic invariance in the first way. By addressing the wave function of emitted (absorbed) particles, the entropy and the area are quantized in the second one. Both results show that the entropy and the area spectra are equall…
We study the holographic representation of the entanglement entropy, recently proposed by Ryu and Takayanagi, in a braneworld context. The holographic entanglement entropy of a de Sitter brane embedded in an anti-de Sitter (AdS) spacetime is evaluated using geometric quantities, and it is compared with two kinds of de Sitter entropy: a quarter of the area of the cosmological horizon on the brane and entropy calculated from the Euclidean path integral. We show that the three entropies coincide with each other in a certain limit. Remarkably, the entropy obtained from the Euclidean path integral …
We investigate thermodynamic and dynamical stability of a family of six-dimensional braneworld solutions with de Sitter branes. First, we investigate thermodynamic stability in terms of de Sitter entropy. We see that the family of solutions is divided into two distinct branches: the high-entropy branch and the low-entropy branch. By analogy with ordinary thermodynamics, the high-entropy branch is expected to be stable and the low-entropy branch to be unstable. Next, we investigate dynamical stability by analyzing linear perturbations around the solutions. Perturbations are decomposed into scal…
As quotient spaces, Minkowski and de Sitter are fundamental spacetimes in the sense that they are known "a priori", independently of Einstein equation. They represent different non-gravitational backgrounds for the construction of physical theories. If general relativity is constructed on a de Sitter spacetime, the underlying kinematics will no longer be ruled by Poincaré, but by the de Sitter group. In this case the definition of diffeomorphism changes, producing concomitant changes in the notions of energy and entropy. These changes are explicitly discussed for the case of the Schwarzschild …
In this paper, the effect of the space-time dimension on effective thermodynamic quantities in (n+2)-dimensional Reissoner-Nordstrom-de Sitter space has been stud ied. Based on derived effective thermodynamic quantities, conditions for the phase transition are obtained. The result shows that the accelerating cosmic expansion can be attained by the entropy force arisen from the interaction between horizons of black holes and our universe, which provides a possible way to explain the physical mechanism for the accelerating cosmic expansion.
If one tries to view de Sitter as a true (as opposed to a meta-stable) vacuum, there is a tension between the finiteness of its entropy and the infinite-dimensionality of its Hilbert space. We invetsigate the viability of one proposal to reconcile this tension using $q$-deformation. After defining a differential geometry on the quantum de Sitter space, we try to constrain the value of the deformation parameter by imposing the condition that in the undeformed limit, we want the real form of the (inherently complex) quantum group to reduce to the usual SO(4,1) of de Sitter. We find that this for…
For an ordinary thermodynamical system the Poincaré recurrence time is exponentially large in the Boltzmann entropy of the system. It turns out, that for a system with dynamical chaos it is determined by the Kolmogorov-Sinai entropy and can be considerably shorter. It is shown in this note that for the de Sitter space with strong mixing properties the mean recurrence time is equal to the inverse Hubble constant. This means that our universe can have a finite lifetime bounded by the current age of the universe. After this time, the universe should recycle itself and this process has neither a b…
We consider the entanglement entropy of a free massive scalar field in the one parameter family of $α$-vacua in de Sitter space by using a method developed by Maldacena and Pimentel. An $α$-vacuum can be thought of as a state filled with particles from the point of view of the Bunch-Davies vacuum. Of all the $α$-vacua we find that the entanglement entropy takes the minimal value in the Bunch-Davies solution. We also calculate the asymptotic value of the Rényi entropy and find that it increases as $α$ increases. We argue these feature stem from pair condensation within the non-trivial $α$-vacua…
We investigate a solution of the exactly renormalized Liouville action to foresee the fate of the two-dimensional de Sitter space. We work in the semiclassical region with a large matter central charge $c$. Instead of de Sitter expansion, it performs a slow-roll inflation with the parameters $ε=(1/2)η=6/c$. An inflaton field is induced in the effective theory to describe quantum effects of the Liouville theory. The geometric entropy increases logarithmically with the Hubble radius. We propose that de Sitter entropy is carried by superhorizon modes of the metric. It can be directly estimated fr…
De Sitter spacetime is known to have a cosmological horizon that enjoys thermodynamic-like properties similar to those of a black hole horizon. In this note we show that a universal argument can be given for the entropy of de Sitter spacetime in arbitrary dimensions, by generalizing a recent near horizon symmetry plus conformal field theory argument of Carlip for black hole entropy. The implications of this argument are also discussed.
We study some kinematical aspects of quantum fields on causal sets. In particular, we are interested in free scalar fields on a fixed background causal set. We present various results building up to the study of the entanglement entropy of de Sitter horizons using causal sets. We begin by obtaining causal set analogs of Green functions for this field. First we construct the retarded Green function in a Riemann normal neighborhood (RNN) of an arbitrary curved spacetime. Then, we show that in de Sitter and patches of anti-de Sitter spacetimes the construction can be done beyond the RNN. This all…
It has been proposed that spacetimes with a U(1) isometry group have contributions to the entropy from Misner strings as well as from the area of $d-2$ dimensional fixed point sets. In this paper we test this proposal by constructing Taub-Nut-AdS and Taub-Bolt-AdS solutions which are examples of a new class of asymptotically locally anti-de Sitter spaces. We find that with the additional contribution from the Misner strings, we exactly reproduce the entropy calculated from the action by the usual thermodynamic relations. This entropy has the right parameter dependence to agree with the entropy…
Using entanglement in dS/CFT correspondence, we show that a 4-dimensional de Sitter spacetime in the bulk fluctuates. We calculated the fluctuations of the entanglement entropy, which backreacts with the geometry of the bulk spacetime indicated by the fluctuations of the horizon radius. The variance of the fluctuations is suppressed by $G_N$ and multiplied by $H_{dS}^2$. Therefore, it will be more significant during the primordial era where it is also well described by de Sitter geometry. We also show that the distribution of the fluctuations is also skewed with the local non-linearity paramet…
A metric is proposed to explore the noncommutative form of the Anti-de Sitter space due to quantum effects. It has been proved that the non commutativity in AdS space induces a single component gravitoelectric field. The holographic Ryu-Takayanagi (RT) algorithm is then applied to compute the entanglement entropy in dual $CFT_2$. This calculation can be exploited to compute UV-IR cutoff dependent central charge of the certain noncommutative $CFT_2$. This non commutative computation of the entanglement entropy can be interpreted in the form of the surface/state correspondence. We have shown tha…
We present a proposal to relate the de Sitter Conjecture (dSC) to the Covariant Entropy Bound (CEB). By assuming an early phase of accelerated expansion where the CEB is satisfied, we take into account a contribution from extra-dimensions to the four-dimensional entropy which restricts the values of the usual slow-roll parameters. We show in this context that the dSC inequalities follow from the CEB -- including their mutual exclusion -- in both single and multi-field inflationary scenarios. We also observe that the order one constants, c and c' in the conjecture are given in terms of physical…
The basic equations of the thermodynamic system give the relationship between the internal energy, entropy and volume of two neighboring equilibrium states. By using the functional relationship between the state parameters in the basic equation, we give the differential equation satisfied by the entropy of spacetime. We can obtain the expression of the entropy by solving the differential equationy. This expression is the sum of entropy corresponding to the two event horizons and the interaction term. The interaction term is a function of the ratio of the locations of the black hole horizon and…
