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From the viewpoint of holography, the phase structure of a 5-dimensional Reissner-Nordström-AdS black hole is probed by the two-point correlation function, Wilson loop, and entanglement entropy. As the case of thermal entropy, we find for all the probes that the black hole undergoes a Hawking-Page phase transition, a first-order phase transition, and a second-order phase transition successively before it reaches a stable phase. In addition, for these probes, we find that the equal area law for the first-order phase transition is valid always and the critical exponent of the heat capacity for the second-order phase transition coincides with that of the mean field theory regardless of the size of the boundary region.

Phase structure of the quintessence Reissner-Nordstr\"{o}m-AdS black hole is probed with the nonlocal observables such as holographic entanglement entropy and two point correlation function. Our result shows that, as the case of the thermal entropy, both the observables exhibit the similar Van der Waals-like phase transition. To reinforce the conclusion, we further check the equal area law for the first order phase transition and critical exponent of the heat capacity for the second order phase transition. We also discuss the effect of the state parameter on the phase structure of the nonlocal observables., Comment: 16 pages, 6 figures. arXiv admin note: text overlap with arXiv:1511.00383

With the non-local observables such as two point correlation function and holographic entanglement entropy, we probe the phase structure of the Born-Infeld-anti-de Sitter black holes. We find for the case $bQ>0.5$, the phase structure is similar to that of the Reissner-Nordstr��m-AdS black hole, namely the black hole undergoes a Hawking-Page phase transition, a first order phase transition, and a second order phase transition. While for the case $bQ, 20 pages, many figures. arXiv admin note: text overlap with arXiv:1512.08855

The Van der Waals-like phase transition is observed in temperature-thermal entropy plane in spherically symmetric charged Gauss-Bonnet-AdS black hole background. In terms of AdS/CFT, the non-local observables such as holographic entanglement entropy, Wilson loop, and two point correlation function of very heavy operators in the field theory dual to spherically symmetric charged Gauss-Bonnet-AdS black hole have been investigated. All of them exhibit the Van der Waals-like phase transition for a fixed charge parameter or Gauss-Bonnet parameter in such gravity background. Further, with choosing various values of charge or Gauss-Bonnet parameter, the equal area law and the critical exponent of the heat capacity are found to be consistent with phase structures in temperature-thermal entropy plane., Some statements about the analogy between the black hole phase transition in $T-S$ plane and Van der Waals-like phase transition in $P-V$ plane are added. This is the published version

In the near future, gravitational wave detection is set to become an important observational tool for astrophysics. It will provide us with an excellent means to distinguish different gravitational theories. In effective form, many gravitational theories can be cast into an f(R) theory. In this article, we study the dynamics and gravitational waveform of an equal-mass binary black hole system in f(R) theory. We reduce the equations of motion in f(R) theory to the Einstein-Klein-Gordon coupled equations. In this form, it is straightforward to modify our existing numerical relativistic codes to simulate binary black hole mergers in f(R) theory. We considered binary black holes surrounded by a shell of scalar field. We solve the initial data numerically using the Olliptic code. The evolution part is calculated using the extended AMSSNCKU code. Both codes were updated and tested to solve the problem of binary black holes in f(R) theory. Our results show that the binary black hole dynamics in f(R) theory is more complex than in general relativity. In particular, the trajectory and merger time are strongly affected. Via the gravitational wave, it is possible to constrain the quadratic part parameter of f(R) theory in the range |a_2, 14 pages, 16 figures

The gravitational lensing effect is important to the detection of electromagnetic signals in astrophysics. The gravitational wave lensing effect has also been found significant to gravitational wave detection in the past decade. Recent analysis shows that the lensing events for advanced detectors could be quite plausible. The black holes in our Milky Way Galaxy may play the role of lens objects. These facts motivate us to study the lensing effects on gravitational wave signals for advanced detectors. Taking advanced LIGO and Einstein Telescope for examples, we investigate the lensing effects on the parameter extraction of gravitational wave signals. Using the Markov chain Monte Carlo simulation together with matched filtering methods, we find that the lensing effect for a lens object with small mass is negligible. But when the mass of the lens object increases to larger than 1000M(circle dot) the lensing effect becomes important. Using the template without lensing corrections would result in loss of signal detections. In contrast if we consider templates with lensing effects, the lensed signal may provide much information about the lens black hole. These facts may give us a new way to determine the parameters of the lensing object. For example, this kind of signal may also help us estimate the mass and the distance of the supermassive black hole hosted at the center of our Galaxy.

We study in detail the phase structure of a holographic p-wave superconductor model in a five dimensional Einstein-Maxwell-complex vector field theory with a negative cosmological constant. To construct complete phase diagrams of the model, we consider both the soliton and black hole backgrounds. In both two cases, there exist second order, first order and zeroth order phase transitions, and the so-called "retrograde condensation" also happens. In particular, in the soliton case with the mass of the vector field being beyond a certain critical value, we find a series of phase transitions happen such as "insulator/superconductor/insulator/superconductor", as the chemical potential continuously increases. We construct complete phase diagrams in terms of temperature and chemical potential and find some new phase boundaries., 47 pages, 25 figures, added references, modified some figures

We study a holographic p-wave superconductor model in a four dimensional Einstein-Maxwell-complex vector field theory with a negative cosmological constant. The complex vector field is charged under the Maxwell field. We solve the full coupled equations of motion of the system and find black hole solutions with the vector hair. The vector hairy black hole solutions are dual to a thermal state with the U(1) symmetry as well as the spatial rotational symmetry breaking spontaneously. Depending on two parameters, the mass and charge of the vector field, we find a rich phase structure: zeroth order, first order and second order phase transitions can happen in this model. We also find "retrograde condensation" in which the hairy black hole solution exists only for the temperatures above a critical value with the free energy much larger than the black hole without hair. We construct the phase diagram for this system in terms of the temperature and charge of the vector field., v3: 26 pages, 15 figures, references added, extra arguments added, to appear in JHEP

We study the Wilson line response in the holographic superconducting phase transitions in Gauss-Bonnet gravity. In the black brane background case, the Little-Parks periodicity is independent of the Gauss-Bonnet parameter, while in the AdS soliton case, there is no evidence for the Little-Parks periodicity. We further study the impact of the Gauss-Bonnet term on the holographic phase transitions quantitatively. The results show that such quantum corrections can effectively affect the occurrence of the phase transitions and the response to the Wilson line., 19 pages, 6 figures, 2 tables, references added

In this paper we study the non-Gaussian features of the primordial fluctuations in loop quantum cosmology with the inverse volume corrections. The detailed analysis is performed in the single field slow-roll inflationary models. However, our results reflect the universal characteristics of bispectrum in loop quantum cosmology. The main corrections to the scalar bispectrum come from two aspects: one is the modifications to the standard Bunch-Davies vacuum, the other is the corrections to the background dependent variables, such as slow-roll parameters. Our calculations show that the loop quantum corrections make $f_{{\rm NL}}$ of the inflationary models increase 0.1%. Moreover, we find that two new shapes arise, namely $\mathcal F_{1}$ and $\mathcal F_{2}$. The former gives a unique loop quantum feature which is less correlated with the local, equilateral and single types, while the latter is highly correlated with the local one., Comment: matched to the published version. 30 pages, 4 figures

The covariant entropy bound conjecture is an important hint for the quantum gravity, with several versions available in the literature. For cosmology, Ashtekar and Wilson-Ewing ever show the consistence between the loop gravity theory and one version of this conjecture. Recently, S. He and H. Zhang proposed a version for the dynamical horizon of the universe, which validates the entropy bound conjecture for the cosmology filled with perfect fluid in the classical scenario when the universe is far away from the big bang singularity. However, their conjecture breaks down near big bang region. We examine this conjecture in the context of the loop quantum cosmology. With the example of photon gas, this conjecture is protected by the quantum geometry effects as expected., Comment: 4 pages, 2 figures, revised version

A well-motivated extension of higher order holonomy corrections in loop quantum cosmology (LQC) for the k=0 Friedmann-Robertson-Walker model is investigated at the level of heuristic effective dynamics. It reveals that the quantum bounce is generic, regardless of the order of corrections, and the matter density remains finite, bounded from above by an upper bound in the regime of the Planckian density, even if all orders of corrections are included. This observation provides further evidence that the quantum bounce is essentially a consequence of the loopy nature (i.e. intrinsic discreteness) of LQC and LQC is fundamentally different from the Wheeler-DeWitt theory; it also encourages one to construct the quantum theory of LQC with the higher order holonomy corrections, which might be understood as related to the higher j representations in the Hamiltonian operator of loop quantum gravity.

Wormhole and time machine are very interesting objects in general relativity. However, they need exotic matters which are impossible in classical level to support them. But if we introduce the quantum effects of gravity into the stress-energy tensor, these peculiar objects can be constructed self-consistently. Fortunately, loop quantum cosmology (LQC) has the potential to serve as a bridge connecting the classical theory and quantum gravity. Therefore it provides a simple way for the study of quantum effect in the semiclassical case. As is well known, loop quantum cosmology is very successful to deal with the behavior of early universe. In the early stage, if taken the quantum effect into consideration, inflation is natural because of the violation of every kind of local energy conditions. Similar to the inflationary universe, the violation of the averaged null energy condition is the necessary condition for the traversable wormholes. In this paper, we investigate the averaged null energy condition in LQC in the framework of effective Hamiltonian, and find out that LQC do violate the averaged null energy condition in the massless scalar field coupled model., 5 pages

Loop quantum cosmology (LQC) is very powerful to deal with the behavior of early universe. And the effective loop quantum cosmology gives a successful description of the universe in the semiclassical region. We consider the apparent horizon of the Friedmann-Robertson-Walker universe as a thermodynamical system and investigate the thermodynamics of LQC in the semiclassical region. The effective density and effective pressure in the modified Friedmann equation from LQC not only determine the evolution of the universe in LQC scenario but are actually also found to be the thermodynamic quantities. This result comes from the energy definition in cosmology (the Misner-Sharp gravitational energy) and is consistent with thermodynamic laws. We prove that within the framework of loop quantum cosmology, the elementary equation of equilibrium thermodynamics is still valid., Comment: 4 pages

Loop quantum cosmology (LQC) predicts a nonsingular evolution of the universe through a bounce in the high energy region. But LQC has an ambiguity about the quantization scheme. Recently, the authors in [Phys. Rev. D 77, 124008 (2008)] proposed a new quantization scheme. Similar to others, this new quantization scheme also replaces the big bang singularity with the quantum bounce. More interestingly, it introduces a quantum singularity, which is traversable. We investigate this novel dynamics quantitatively with a tachyon scalar field, which gives us a concrete example. Our result shows that our universe can evolve through the quantum singularity regularly, which is different from the classical big bang singularity. So this singularity is only a week singularity., 7 pages, 3 figures. Accepted for publication in Physical Review D