Black Holes in Gravity with Conformal Anomaly and Logarithmic Term in Black Hole Entropy

We present a class of exact analytic and static, spherically symmetric black hole solutions in the semi-classical Einstein equations with Weyl anomaly. The solutions have two branches, one is asymptotically flat and the other asymptotically de Sitter. We study thermodynamic properties of the black hole solutions and find that there exists a logarithmic correction to the well-known Bekenstein-Hawking area entropy. The logarithmic term might come from non-local terms in the effective action of gravity theories. The appearance of the logarithmic term in the gravity side is quite important in the sense that with this term one is able to compare black hole entropy up to the subleading order, in the gravity side and in the microscopic statistical interpretation side.Comment: Revtex, 10 pages. v2: minor changes and to appear in JHE

Cosmology with minimal length uncertainty relations

We study the effects of the existence of a minimal observable length in the phase space of classical and quantum de Sitter (dS) and Anti de Sitter (AdS) cosmology. Since this length has been suggested in quantum gravity and string theory, its effects in the early universe might be expected. Adopting the existence of such a minimum length results in the Generalized Uncertainty Principle (GUP), which is a deformed Heisenberg algebra between minisuperspace variables and their momenta operators. We extend these deformed commutating relations to the corresponding deformed Poisson algebra in the classical limit. Using the resulting Poisson and Heisenberg relations, we then construct the classical and quantum cosmology of dS and Ads models in a canonical framework. We show that in classical dS cosmology this effect yields an inflationary universe in which the rate of expansion is larger than the usual dS universe. Also, for the AdS model it is shown that GUP might change the oscillatory nature of the corresponding cosmology. We also study the effects of GUP in quantized models through approximate analytical solutions of the Wheeler-DeWitt (WD) equation, in the limit of small scale factor for the universe, and compare the results with the ordinary quantum cosmology in each case.Comment: 11 pages, 4 figures, to appear in IJMP

An Interacting Dark Energy Model for the Expansion History of the Universe

We explore a model of interacting dark energy where the dark energy density is related by the holographic principle to the Hubble parameter, and the decay of the dark energy into matter occurs at a rate comparable to the current value of the Hubble parameter. We find this gives a good fit to the observational data supporting an accelerating Universe, and the model represents a possible alternative interpretation of the expansion history of the Universe.Comment: 6 pages, 2 figures, Phys. Rev. D versio

Relationship between five-dimensional black holes and de Sitter spaces

We study a close relationship between the topological anti-de Sitter (TAdS)-black holes and topological de Sitter (TdS) spaces including the Schwarzschild-de Sitter (SdS) black hole in five-dimensions. We show that all thermal properties of the TdS spaces can be found from those of the TAdS black holes by replacing $k$ by $-k$. Also we find that all thermal information for the cosmological horizon of the SdS black hole is obtained from either the hyperbolic-AdS black hole or the Schwarzschild-TdS space by substituting $m$ with $-m$. For this purpose we calculate thermal quantities of bulk, (Euclidean) conformal field theory (ECFT) and moving domain wall by using the A(dS)/(E)CFT correspondences. Further we compute logarithmic corrections to the Bekenstein-Hawking entropy, Cardy-Verlinde formula and Friedmann equation due to thermal fluctuations. It implies that the cosmological horizon of the TdS spaces is nothing but the event horizon of the TAdS black holes and the dS/ECFT correspondence is valid for the TdS spaces in conjunction with the AdS/CFT correspondence for the TAdS black holes.Comment: 17 page

Thermodynamic Curvature of the BTZ Black Hole

Some thermodynamic properties of the Ba\~nados-Teitelboim-Zanelli (BTZ) black hole are studied to get the effective dimension of its corresponding statistical model. For this purpose, we make use of the geometrical approach to the thermodynamics: Considering the black hole as a thermodynamic system with two thermodynamic variables (the mass $M$ and the angular momemtum $J$), we obtain two-dimensional Riemannian thermodynamic geometry described by positive definite Ruppeiner metric. From the thermodynamic curvature we find that the extremal limit is the critical point. The effective spatial dimension of the statistical system corresponding to the near-extremal BTZ black holes is one. Far from the extremal point, the effective dimension becomes less than one, which leads to one possible speculation on the underlying structure for the corresponding statistical model.Comment: 19 pages, LaTeX with revtex macro, 4 figures in eps file

"Microscopic" approach to the Ricci dark energy

A derivation of the Ricci dark energy from quantum field theory of fluctuating "matter" fields in a classical gravitational background is presented. The coupling to the dark energy, the parameter 'a', is estimated in the framework of our formalism, and qualitatively it appears to be within observational expectations.Comment: 7 page

A shortcut to (sun)flowers: Kernels in logarithmic space or linear time

We investigate whether kernelization results can be obtained if we restrict kernelization algorithms to run in logarithmic space. This restriction for kernelization is motivated by the question of what results are attainable for preprocessing via simple and/or local reduction rules. We find kernelizations for d-Hitting Set(k), d-Set Packing(k), Edge Dominating Set(k) and a number of hitting and packing problems in graphs, each running in logspace. Additionally, we return to the question of linear-time kernelization. For d-Hitting Set(k) a linear-time kernelization was given by van Bevern [Algorithmica (2014)]. We give a simpler procedure and save a large constant factor in the size bound. Furthermore, we show that we can obtain a linear-time kernel for d-Set Packing(k) as well.Comment: 18 page

OM Theory and V-duality

We show that the (M5, M2, M2$'$, MW) bound state solution of eleven dimensional supergravity recently constructed in hep-th/0009147 is related to the (M5, M2) bound state one by a finite Lorentz boost along a M5-brane direction perpendicular to the M2-brane. Given the (M5, M2) bound state as a defining system for OM theory and the above relation between this system and the (M5, M2, M2', MW) bound state, we test the recently proposed V-duality conjecture in OM theory. Insisting to have a decoupled OM theory, we find that the allowed Lorentz boost has to be infinitesimally small, therefore resulting in a family of OM theories related by Galilean boosts. We argue that such related OM theories are equivalent to each other. In other words, V-duality holds for OM theory as well. Upon compactification on either an electric or a `magnetic' circle (plus T-dualities as well), the V-duality for OM theory gives the known one for either noncommutative open string theories or noncommutative Yang-Mills theories. This further implies that V-duality holds in general for the little m-theory without gravity.Comment: 17 pages, typos corrected and references adde

Entanglement Entropy and Wilson Loop in St\"{u}ckelberg Holographic Insulator/Superconductor Model

We study the behaviors of entanglement entropy and vacuum expectation value of Wilson loop in the St\"{u}ckelberg holographic insulator/superconductor model. This model has rich phase structures depending on model parameters. Both the entanglement entropy for a strip geometry and the heavy quark potential from the Wilson loop show that there exists a "confinement/deconfinement" phase transition. In addition, we find that the non-monotonic behavior of the entanglement entropy with respect to chemical potential is universal in this model. The pseudo potential from the spatial Wilson loop also has a similar non-monotonic behavior. It turns out that the entanglement entropy and Wilson loop are good probes to study the properties of the holographic superconductor phase transition.Comment: 23 pages,12 figures. v2: typos corrected, accepted in JHE

Cyclic cosmology from Lagrange-multiplier modified gravity

We investigate cyclic and singularity-free evolutions in a universe governed by Lagrange-multiplier modified gravity, either in scalar-field cosmology, as well as in $f(R)$ one. In the scalar case, cyclicity can be induced by a suitably reconstructed simple potential, and the matter content of the universe can be successfully incorporated. In the case of $f(R)$-gravity, cyclicity can be induced by a suitable reconstructed second function $f_2(R)$ of a very simple form, however the matter evolution cannot be analytically handled. Furthermore, we study the evolution of cosmological perturbations for the two scenarios. For the scalar case the system possesses no wavelike modes due to a dust-like sound speed, while for the $f(R)$ case there exist an oscillation mode of perturbations which indicates a dynamical degree of freedom. Both scenarios allow for stable parameter spaces of cosmological perturbations through the bouncing point.Comment: 8 pages, 3 figures, references added, accepted for publicatio