Microscopic Black Hole Pairs in Highly-Excited States

We consider the quantum mechanics of a system consisting of two identical, Planck-size Schwarzschild black holes revolving around their common center of mass. We find that even in a very highly-excited state such a system has very sharp, discrete energy eigenstates, and the system performs very rapid transitions from a one stationary state to another. For instance, when the system is in the 100th excited state, the life times of the energy eigenstates are of the order of $10^{-30}$ s, and the energies of gravitons released in transitions between nearby states are of the order of $10^{22}$ eV.Comment: 22 pages, 3 figures, uses RevTe

Higher order dilaton gravity: brane equations of motion in the covariant formulation

Dilaton gravity with general brane localized interactions is investigated. Models with corrections up to arbitrary order in field derivatives are considered. Effective gravitational equations of motion at the brane are derived in the covariant approach. Dependence of such brane equations on the bulk quantities is discussed. It is shown that the number of the bulk independent brane equations of motion depends strongly on the symmetries assumed for the model and for the background. Examples with two and four derivatives of the fields are presented in more detail.Comment: 32 pages, references added, discussion extended, typos corrected, version to be publishe

Ten Proofs of the Generalized Second Law

Ten attempts to prove the Generalized Second Law of Thermodyanmics (GSL) are described and critiqued. Each proof provides valuable insights which should be useful for constructing future, more complete proofs. Rather than merely summarizing previous research, this review offers new perspectives, and strategies for overcoming limitations of the existing proofs. A long introductory section addresses some choices that must be made in any formulation the GSL: Should one use the Gibbs or the Boltzmann entropy? Should one use the global or the apparent horizon? Is it necessary to assume any entropy bounds? If the area has quantum fluctuations, should the GSL apply to the average area? The definition and implications of the classical, hydrodynamic, semiclassical and full quantum gravity regimes are also discussed. A lack of agreement regarding how to define the "quasi-stationary" regime is addressed by distinguishing it from the "quasi-steady" regime.Comment: 60 pages, 2 figures, 1 table. v2: corrected typos and added a footnote to match the published versio

A Bisognano-Wichmann-like Theorem in a Certain Case of a Non Bifurcate Event Horizon related to an Extreme Reissner-Nordstr\"om Black Hole

Thermal Wightman functions of a massless scalar field are studied within the framework of a ``near horizon'' static background model of an extremal R-N black hole. This model is built up by using global Carter-like coordinates over an infinite set of Bertotti-Robinson submanifolds glued together. The analytical extendibility beyond the horizon is imposed as constraints on (thermal) Wightman's functions defined on a Bertotti-Robinson sub manifold. It turns out that only the Bertotti-Robinson vacuum state, i.e. $T=0$, satisfies the above requirement. Furthermore the extension of this state onto the whole manifold is proved to coincide exactly with the vacuum state in the global Carter-like coordinates. Hence a theorem similar to Bisognano-Wichmann theorem for the Minkowski space-time in terms of Wightman functions holds with vanishing ``Unruh-Rindler temperature''. Furtermore, the Carter-like vacuum restricted to a Bertotti-Robinson region, resulting a pure state there, has vanishing entropy despite of the presence of event horizons. Some comments on the real extreme R-N black hole are given

Conformal Tightness of Holographic Scaling in Black Hole Thermodynamics

The near-horizon conformal symmetry of nonextremal black holes is shown to be a mandatory ingredient for the holographic scaling of the scalar-field contribution to the black hole entropy. This conformal tightness is revealed by semiclassical first-principle scaling arguments through an analysis of the multiplicative factors in the entropy due to the radial and angular degrees of freedom associated with a scalar field. Specifically, the conformal SO(2,1) invariance of the radial degree of freedom conspires with the area proportionality of the angular momentum sums to yield a robust holographic outcome.Comment: 23 pages, 1 figure. v2 & v3: expanded explanations and proofs, references added, typos corrected; v3: published versio

Nonsingular and accelerated expanding universe from effective Yang-Mills theory

The energy-momentum tensor coming from one-parameter effective Yang- Mills theory is here used to describe the matter-energy content of the homogeneous and isotropic Friedmann cosmology in its early stages. The behavior of all solutions is examined. Particularly, it is shown that only solutions corresponding to an open model allow the universe to evolve into an accelerated expansion. This result appears as a possible mechanism for an inflationary phase produced by a vector field. Further, depending on the value of some parameters characterizing the system, the resulting models are classified as singular or nonsingular.Comment: 15 pages, 7 figures, some discussions were simplified and new remarks were introduce

A geometrical origin for the covariant entropy bound

Causal diamond-shaped subsets of space-time are naturally associated with operator algebras in quantum field theory, and they are also related to the Bousso covariant entropy bound. In this work we argue that the net of these causal sets to which are assigned the local operator algebras of quantum theories should be taken to be non orthomodular if there is some lowest scale for the description of space-time as a manifold. This geometry can be related to a reduction in the degrees of freedom of the holographic type under certain natural conditions for the local algebras. A non orthomodular net of causal sets that implements the cutoff in a covariant manner is constructed. It gives an explanation, in a simple example, of the non positive expansion condition for light-sheet selection in the covariant entropy bound. It also suggests a different covariant formulation of entropy bound.Comment: 20 pages, 8 figures, final versio

Geometric entropy, area, and strong subadditivity

The trace over the degrees of freedom located in a subset of the space transforms the vacuum state into a density matrix with non zero entropy. This geometric entropy is believed to be deeply related to the entropy of black holes. Indeed, previous calculations in the context of quantum field theory, where the result is actually ultraviolet divergent, have shown that the geometric entropy is proportional to the area for a very special type of subsets. In this work we show that the area law follows in general from simple considerations based on quantum mechanics and relativity. An essential ingredient of our approach is the strong subadditive property of the quantum mechanical entropy.Comment: Published versio