Bekenstein Entropy Research Articles

The plasma puddle as a perturbative black hole

We argue that the weak coupling regime of a large N gauge theory in the Higgs phase contains black hole-like objects. These so-called ``plasma puddles'' are meta-stable lumps of hot plasma lying in locally un-Higgsed regions of space. They decay via O(1/N) thermal radiation and, perhaps surprisingly, absorb all incident matter. We show that an incident particle of energy E striking the plasma puddle will shower into an enormous number of decay products whose multiplicity grows linearly with E, and whose average energy is independent of E. Once these ultra-soft particles reach the interior they are thermalized by the plasma within, and so the object appears ``black.'' We determine some gross properties like the size and temperature of the the plasma puddle in terms of fundamental parameters in the gauge theory. Interestingly, demanding that the plasma puddle emit thermal Hawking radiation implies that the object is black (i.e. absorbs all incident particles), which implies classical stability, which implies satisfaction of the Bekenstein entropy bound. Because of the AdS/CFT duality and the many similarities between plasma puddles and black holes, we conjecture that black objects are a robust feature of quantum gravity.

Stability and Thermodynamics of Brane Black Holes

We consider scalar and axial gravitational perturbations of black hole solutions in brane world scenarios. We show that perturbation dynamics is surprisingly similar to the Schwarzschild case with strong indications that the models are stable. Quasinormal modes and late-time tails are discussed. We also study the thermodynamics of these scenarios verifying the universality of Bekenstein's entropy bound as well as the applicability of 't Hooft's brickwall method.

Stability and thermodynamics of brane black holes

We consider scalar and axial gravitational perturbations of black hole solutions in brane world scenarios. We show that perturbation dynamics is surprisingly similar to the Schwarzschild case with strong indications that the models are stable. Quasinormal modes and late-time tails are discussed. We also study the thermodynamics of these scenarios verifying the universality of Bekenstein's entropy bound as well as the applicability of 't Hooft's brickwall method.

Holography and entropy bounds in the plane wave matrix model

As a quantum theory of gravity, matrix theory should provide a realization of the holographic principle, in the sense that a holographic theory should contain one binary degree of freedom per Planck area. We present evidence that Bekenstein's entropy bound, which is related to area differences, is manifest in the plane wave matrix model. If holography is implemented in this way, we predict crossover behavior at strong coupling when the energy exceeds ${N}^{2}$ in units of the mass scale.

Entanglement system, Casimir energy and black hole

We investigate the connection between the entanglement system in Minkowski spacetime and the black hole using the scaling analysis. Here we show that the entanglement system satisfies the Bekenstein entropy bound. Even though the entropies of two systems are the same form, the entanglement energy is different from the black hole energy. Introducing the Casimir energy of the vacuum energy fluctuations rather than the entanglement energy, it shows a feature of the black hole energy. Hence the Casimir energy is more close to the black hole than the entanglement energy. Finally, we find that the entanglement system behaves like the black hole if the gravitational effects are included properly.

Electrostatic self-energy and Bekenstein entropy bound in the massive Schwinger model

We obtain the electrostatic energy of two opposite charges near the horizon of stationary black-holes in the massive Schwinger model. Besides the confining aspects of the model, we discuss the Bekenstein entropy upper bound of a charged object using the generalized second law. We show that despite the massless case, in the massive Schwinger model the entropy of the black hole and consequently the Bekenstein bound are altered by the vacuum polarization.

Holographic Weyl entropy bounds

We consider the entropy bounds recently conjectured by Fischler, Susskind, and Bousso, and proven in certain cases by Flanagan, Marolf, and Wald (FMW). One of the FMW derivations supposes a covariant form of the Bekenstein entropy bound, the consequences of which we explore. The derivation also suggests that the entropy contained in a vacuum spacetime, e.g., Schwarzschild spacetime, may be related to the shear on congruences of null rays. We find evidence for this intuition, but in a surprising way. We compare the covariant entropy bound to certain earlier discussions of black hole entropy, and comment on the separate roles of quantum mechanics and gravity in the entropy bound.

Black holes in de Sitter space: Masses, energies, and entropy bounds

In this paper we consider spacetimes in vacuum general relativity---possibly coupled to a scalar field---with a positive cosmological constant $\ensuremath{\Lambda}.$ We employ the isolated horizons (IH) formalism where the boundary conditions imposed are that of two horizons, one of black hole type and the other, serving as outer boundary, a cosmological horizon. As particular cases, we consider the Schwarzschild--de Sitter spacetime, in both $2+1$ and $3+1$ dimensions. Within the IH formalism, it is useful to define two different notions of energy for the cosmological horizon, namely, the ``mass'' and the ``energy.'' Empty de Sitter space provides a striking example of such a distinction: its horizon energy is zero but the horizon mass takes a finite value given by $\ensuremath{\pi}/(2\sqrt{\ensuremath{\Lambda}}).$ For both horizons we study their thermodynamic properties, compare our results with those of Euclidean Hamiltonian methods and construct some generalized Bekenstein entropy bounds. We discuss these new entropy bounds and compare them with some recently proposed entropy bounds in the cosmological setting.

Entropy bounds for charged and rotating systems

It was shown in a previous work that, for systems in which the entropy is an extensive function of the energy and volume, the Bekenstein and the holographic entropy bounds predict new results. In this paper, we go further and derive improved upper bounds to the entropy of extensive charged and rotating systems. Furthermore, it is shown that for charged and rotating systems (including non-extensive ones), the total energy that appears in both the Bekenstein entropy bound (BEB) and the causal entropy bound (CEB) can be replaced by the internal energy of the system. In addition, we propose possible corrections to the BEB and the CEB.

Extensive entropy bounds

It is shown that, for systems in which the entropy is an extensive function of the energy and volume, the Bekenstein and the holographic entropy bounds predict new results. More explicitly, the Bekenstein entropy bound leads to the entropy of thermal radiation (the Unruh-Wald bound) and the spherical entropy bound implies the ``causal entropy bound.'' Surprisingly, the first bound shows a close relationship between black hole physics and the Stephan-Boltzmann law (for the energy and entropy flux densities of the radiation emitted by a hot blackbody). Furthermore, we find that the number of different species of massless fields is bounded by $\ensuremath{\sim}{10}^{4}.$

ESSENTIAL AND INESSENTIAL FEATURES OF HAWKING RADIATION

There are numerous derivations of the Hawking effect available in the literature. They emphasise different features of the process, and sometimes make markedly different physical assumptions. This article presents a "minimalist" argument, and strips the derivation of as much excess baggage as possible. All that is really necessary is quantum physics plus a slowly evolving future apparent horizon (not an event horizon). In particular, neither the Einstein equations nor Bekenstein entropy are necessary (nor even useful) in deriving Hawking radiation.

Holography and entropy bounds in Gauss–Bonnet gravity

We discuss the holography and entropy bounds in Gauss–Bonnet gravity theory. By applying a Geroch process to an arbitrary spherically symmetric black hole, we show that the Bekenstein entropy bound always keeps its form as SB=2πER, independent of gravity theories. As a result, the Bekenstein–Verlinde bound also remains unchanged. Along the Verlinde's approach, we obtain the Bekenstein–Hawking bound and Hubble bound, which are different from those in Einstein gravity. Furthermore, we note that when HR=1, the three cosmological entropy bounds become identical as in the case of Einstein gravity. But the corresponding Friedmann equation in Gauss–Bonnet gravity can no longer be cast to the form of cosmological Cardy formula.

What can the quantum liquid say on the brane black hole, the entropy of extremal black hole and the vacuum energy?

Using quantum liquids one can simulate the behavior of the quantum vacuum in the presence of the event horizon. The condensed matter analogs demonstrate that in most cases the quantum vacuum resists to formation of the horizon, and even if the horizon is formed different types of the vacuum instability develop, which are faster than the process of Hawking radiation. Nevertheless, it is possible to create the horizon on the quantum-liquid analog of the brane, where the vacuum life-time is long enough to consider the horizon as the quasistationary object. Using this analogy we calculate the Bekenstein entropy of the nearly extremal and extremal black holes, which comes from the fermionic microstates in the region of the horizon -- the fermion zero modes. We also discuss how the cancellation of the large cosmological constant follows from the thermodynamics of the vacuum.

Statistical interpretation of the Bekenstein entropy for systems with a stretched horizon.

For the two-charge extremal holes in string theory we show that the Bekenstein entropy obtained from the area of the stretched horizon has a statistical interpretation as a "coarse graining entropy": different microstates give geometries that differ near r = 0, and the stretched horizon cuts off the metric at r = b where these geometries start to differ.

A note on the Cardy–Verlinde formula

We generalize the results of hep-th/0008140 to the case of the (n+1)-dimensional closed FRW universe satisfying a general equation of state of the form p=w\rho. We find that the entropy of the universe can no longer be expressed in a form similar to the Cardy formula, when w\neq 1/n. As a result, in general the entropy formula does not coincide with the Friedmann equation when the conjectured bound on the Casimir energy is saturated. Furthermore, the conjectured bound on the Casimir energy generally does not lead to the Hubble and the Bekenstein entropy bounds.

BLACK HOLE ENTROPY BY THE BRICK-WALL METHOD IN FOUR AND FIVE DIMENSIONS WITH U(1) CHARGES

Using the brick-wall method we compute the statistical entropy of a scalar field in a nontrivial background, in two different cases. These backgrounds are generated by four- and five-dimensional black holes with four and three U(1) charges respectively. The Bekenstein entropy formula is generally obeyed, but corrections are discussed in the latter case.

Bekenstein bound, holography and brane cosmology in charged black hole backgrounds

We obtain a Bekenstein entropy bound for charged objects in arbitrary dimensions (D ≥ 4) using the D-bound recently proposed by Bousso. With the help of thermodynamics of conformal field theories corresponding to anti-de sitter (AdS) Reissner–Norström (RN) black holes, we discuss the relation between the Bekenstein and Bekenstein–Verlinde bounds. In particular, we propose a Bekenstein–Verlinde-like bound for the charged systems. In the Einstein–Maxwell theory with a negative cosmological constant, we discuss the brane cosmology with positive tension using the Binetruy–Deffayet–Langlois approach. The resulting Friedman–Robertson–Walker equation can be identified with the one obtained by the moving domain wall approach in the AdS RN black hole background. Finally we also address the holographic property of the brane universe.

SUPERSTRINGS, GAUGE FIELDS AND BLACK HOLES

There has been spectacular progress in the development of string and superstring theories since its inception thirty years ago. Development in this area has never been impeded by the lack of experimental confirmation. Indeed, numerous bold and imaginative strides have been taken and the sheer elegance and logical consistency of the arguments have served as a primary motivation for string theorists to push their formulations ahead. In fact the development in this area has been so rapid that new ideas quickly become obsolete. On the other hand, this rapid development has proved to be the greatest hindrance for novices interested in this area. These notes serve as a gentle introduction to this topic. In these elementary notes, we briefly review the RNS formulation of superstring theory, GSO projection, D-branes, bosonic strings, dualities, dynamics of D-branes and the microscopic description of Bekenstein entropy of a black hole.

Monopoles and the Emergence of Black Hole Entropy

One of the remarkable features of black holes is that they possess a thermodynamic description, even though they do not appear to be statistical systems. We use self-gravitating magnetic monopole solutions as tools for understanding the emergence of this description as one goes from an ordinary spacetime to one containing a black hole. We describe how causally distinct regions emerge as a monopole solution develops a horizon. We define an entropy that is naturally associated with these regions and that has a clear connection with the Hawking–Bekenstein entropy in the critical black hole limit.

GRAVITY, PARTICLE PHYSICS AND THEIR UNIFICATION

We explain the need for a theory of quantum gravity and some general ideas about string theory, including the idea of the derivation of the Hawking Bekenstein entropy formula for extremal black holes. We then give a general description of the correspondence between the large N limit of certain gauge theories and string theory on spacetimes with boundaries.