International Journal of Modern Physics: Conference Series

I review the definition and types of (closed) trapped surfaces. Surprising global properties are shown, such as their "clairvoyance" and the possibility that they enter into flat portions of the spacetime. Several results on the interplay of trapped surfaces with vector fields and with spatial hypersurfaces are presented. Applications to the quasi-local definition of Black Holes are discussed, with particular emphasis set onto marginally trapped tubes, trapping horizons and the boundary of the region with closed trapped surfaces. Finally, the core of a trapped region is introduced, and its importance discussed.

We present an introduction to dynamical trapping horizons as quasi-local models for black hole horizons, from the perspective of an Initial Value Problem approach to the construction of generic black hole spacetimes. We focus on the geometric and structural properties of these horizons aiming, as a main application, at the numerical evolution and analysis of black hole spacetimes in astrophysical scenarios. In this setting, we discuss their dual role as an a priori ingredient in certain formulations of Einstein equations and as an a posteriori tool for the diagnosis of dynamical black hole spacetimes. Complementary to the first-principles discussion of quasi-local horizon physics, we place an emphasis on the rigidity properties of these hypersurfaces and their role as privileged geometric probes into near-horizon strong-field spacetime dynamics.

We discuss some of the physical aspects expected to be associated with black holes. These include Hawking radiation, horizon entropy and cosmic censorship. In particular we focus on whether these properties are more naturally associated to causally defined horizons or quasi-local horizons.

String theory/M-theory general predicts that axionic fields with a broad mass spectrum extending below 10^-10eV are produced after compactification to four dimensions. These axions/fields provoke a rich variety of cosmophysical phenomena on different scales depending on their masses and provide us new windows to probe the ultimate theory. In this article, after overviewing this axiverse idea¹, I take up the black hole instability as the most fascinating one among such axionic phenomena and explain its physical mechanism and astrophysical predictions.

Treating Einstein's theory as a gauge theory of Lorentz group, we decompose the gravitational connection (the gauge potential of Lorentz group) Γ_μ into the restricted connection of the maximal Abelian subgroup of Lorentz group and the valence connection which transforms covariantly under Lorentz gauge transformation. With this decomposition we show that the Einstein's theory can be decomposed into the restricted part made of the restricted connection which has the full Lorentz gauge invariance and the valence part made of the valence connection which plays the role of gravitational source of the restricted gravity. We show that there are two different Abelian decomposition of Einstein's theory, the light-like (or null) decomposition and the non light-like (or non-null) decomposition. In this decomposition the role of the metric g_μν is replaced by a four-index metric tensor g_μν which transforms covariantly under the Lorentz group, and the metric-compatibility condition ∇_αg_μν = 0 of the connection is replaced by the gauge and generally covariant condition . The decomposition shows the existence of a restricted theory of gravitation which has the full general invariance but is much simpler and has less physical degrees of freedom than Einstein's theory. Moreover, it tells that the restricted gravity can be written as an Abelian gauge theory, which implies that the graviton can be described by a massless spin-one field.

We introduce our numerical studies of gravitational collapses in five-dimensional (5D) space-time, with a purpose of studying the cosmic censorship hypothesis and the hoop conjecture. The first model is the collapse of spindle matter which was performed by Shapiro and Teukolsky (1991) who announced an appearance of a naked singularity in 4D. Comparing with 4D cases, we found that 5D collapses proceed more rapidly, the final configurations tend to be spherical, and apparent horizon (AH) forms in wider parameter ranges. We also observed positive evidence for formation of a naked singularity in highly spindle cases as well. The second model is the formation of black-ring in 5D. Our code does not include angular momentum, but the model would be helpful for basic understandings. We constructed an initial data sequence with ring-shaped matter, and observed the topology of AHs, if formed. We found a critical ring radius for ring-shaped AH, and it suggests a dynamical transition of AH topology from ring-shaped to spherical. We demonstrate such an example in time evolution.

Many alternative gravity theories use an independent connection which leads to torsion in addition to curvature. Some have argued that there is no physical need to use such connections, that one can always use the Levi-Civita connection and just treat torsion as another tensor field. We explore this issue here in the context of the Poincaré Gauge theory of gravity, which is usually formulated in terms of an affine connection for a Riemann-Cartan geometry (torsion and curvature). We compare the equations obtained by taking as the independent dynamical variables: (i) the orthonormal coframe and the connection and (ii) the orthonormal coframe and the torsion (contortion), and we also consider the coupling to a source. From this analysis we conclude that, at least for this class of theories, torsion should not be considered as just another tensor field.

In this paper, we will give a short review on quantum spring, which is a Casimir effect from the helix boundary condition that proposed in our earlier works. The Casimir force parallel to the axis of the helix behaves very much like the force on a spring that obeys the Hooke's law when the ratio r of the pitch to the circumference of the helix is small, but in this case, the force comes from a quantum effect, so we would like to call it quantum spring. On the other hand, the force perpendicular to the axis decreases monotonously with the increasing of the ratio r. Both forces are attractive and their behaviors are the same in two and three dimensions.

We study the cosmological dynamics of Brans-Dicke theory in which there are fermions with a coupling to BD scalar field as well as a self-interaction potential. The conditions that there exists a solution which is stable and represents a late-time accelerated expansion of the universe are found. It is shown that the late-time acceleration depends completely on the self-interaction of the fermion field if our investigation is restricted to the theory with positive BD parameter ω. Provided a negative ω is allowed, there will be another two class of stable solutions describing late-time accelerated expansion of the universe. Besides, we find that chameleon mechanism will be possessed in our theory when a suitable self-interaction of fermion field is considered.

In this paper, we study the late-time behavior of a torsion cosmology. We show that there is the late-time de Sitter attractor when the torsion parameter a₁ belongs to , which indicates the late-time behaviors of torsion cosmology insensitive to the initial condition and thus alleviates the fine-tuning problem. Furthermore, we discuss the evolution of statefinder parameters for torsion cosmology in the four different ranges of a₁, and find their typical characteristic different from the other cosmological models. Most of importance, we obtain three kinds of solutions with a constant affine scalar curvature and a kind of expression with the non-constant curvature. Using these expressions, we shall be able to predict the evolution over the late-time in torsion cosmology.

We argue that the dark energy that explains the observed accelerating expansion of the universe may arise due to the contribution to the vacuum energy of the QCD ghost in a time-dependent background. We show that the QCD ghost produces dark energy proportional to the Hubble parameter (Λ_QCD is the QCD mass scale) which has the right magnitude ~ (3 × 10^-3 eV)⁴.

We study the finite temperature Casimir effect between perfectly conducting parallel plates in (D + 1)-dimensional spacetime by using zeta-function regularization technique. We get the analytical results for Casimir energy, Casimir free energy, Casimir entropy and Casimir pressure expressed by Riemann zeta function and Bessel function and give the asymptotic expressions for low and high temperature limits. In the case of D = 3, through mathematic transformation, we reproduce the standard results in the literature which is in most times obtained by using Green's function regularization technique.

The influence of quantized electromagnetic fields on a nonrelativistic charged particle near a conducting plate is investigated by studying the the non-Markovian Langevin equation of the particle. This stochastic approach incorporates not only the stochastic noise manifested from electromagnetic vacuum fluctuations, but also dissipation backreaction on a charge in the form of the retarded Lorentz forces. Since the imposition of the boundary is expected to anisotropically modify the effects of the fields on the evolution of the particle, we consider the motion of a charge undergoing small-amplitude oscillations in the direction either parallel or normal to the plane boundary. Laplace transform technique is applied to find the solutions to these two configurations.

Gravity is specifically the attractive force between two masses separated at a distance. Is this force a derived or a fundamental interaction? We believe that all fundamental interactions are quantum in nature but a derived interaction may be classical. Severe challenges have appeared in many quantum theories of gravity. None of these theories has thus far attained its goal in quantizing gravity and some have met remarkable defeat. We are led to ponder whether gravitation is intrinsically classical and that there would exist a deeper and structurally different underlying theory which would give rise to classical gravitation, in the sense that statistical mechanics, quantum or classical, provides the underlying theory of classical thermodynamics.

In this article, we review recent studies on multiple dual 2D CFT descriptions of the Kerr-Newman black hole, in terms of the Kerr/CFT and Reissner-Nordström/CFT correspondences. A microscopic hair conjecture is suggested.

In this paper, following the work of Chen, Lü and Pope, we present the general metric for Kerr-(A)dS black holes with two rotations. The corresponding Klein-Gordon equation is separated explicitly, from which we develop perturbative expansions for the angular eigenvalues in powers of the rotation parameters with D ≥ 6.

We present a spectral multi-puncture initial data solver based on the LORENE library http://www.lorene.obspm.fr/. The solver generates multi black holes initial data with arbitrary linear momentum and spin within a moderate computational resource. The local convergence test shows that the solution rapidly converged to a high precision.

A brief report is given on hypercylindrical vacuum spacetime solutions and their geometrical properties. The five-dimensional Schwarzschild black string solution characterized by the mass density, which is known to reveal the so-called Gregory-Laflamme instability, turns out to be a special case of a wider class of hypercylindrical vacuum spacetime solutions characterized by two parameters, i.e., mass density and tension. Recent work on the solution space even including a momentum flow or a cosmological constant, higher dimensional extensions than five and some stability analysis under small perturbations are briefly summarized.