General Relativity and Quantum Cosmology

curated by isomorphisms

[gr-qc]

Authors: Fabrizio Canfora, Francisco Correa, Alex Giacomini, Julio Oliva

In this paper an intrinsically non-Abelian black hole solution for the SU(2) Einstein-Yang-Mills theory in four dimensions is constructed. The gauge field of this solution has the form of a meron whereas the metric is the one of a Reissner-Nordström black hole in which, however, the coefficient of the term is not an integration constant. Even if the stress-energy tensor of the Yang-Mills field is spherically symmetric, the field strength of the Yang-Mills field itself is not. A remarkable consequence of this fact, which allows to distinguish the present solution from essentially Abelian configurations, is the Jackiw, Rebbi, Hasenfratz, 't Hooft mechanism according to which excitations of bosonic fields moving in the background of a gauge field with this characteristic behave as Fermionic degrees of freedom.

[gr-qc]

Authors: Liu Zhao, Wei Xu, Pengfei Yu

Every classical Newtonian mechanical system can be equipped with a nonstandard Hamiltonian structure, in which the Hamiltonian is the square of the canonical Hamiltonian up to a constant shift, and the Poisson bracket is nonlinear. In such a formalism, time translation symmetry can be spontaneously broken, provided the potential function becomes negative. A nice analogy between time translation symmetry breaking and the Landau theory of second order phase transitions is established, together with several example cases illustrating time translation breaking ground states. In particular, the CDM model of FRW cosmology is reformulated as the time translation symmetry breaking ground states.

[gr-qc]

Authors: Biju Patla

An approximate analytical formula for the capacitance of a non-parallel plate capacitor with small values of inclination angles and distance separations of the plates is presented. Most applications involving position sensing that are employed in precision experiments and micromechanical devices often use a parallel plate approximation for modeling the capacitance. The analytical approximation presented here is based on the more general, but hard to implement formalism for small angles, and that may be used directly to compute the forces acting on the proof masses by taking the derivative of the capacitance.

Effects of varying the inclination angle, plate dimension and separation on the value of the capacitance per unit length are analyzed in detail. We use the formula derived in this paper to compute the acceleration of the proof mass due to the presence of sensing electrodes (used for positioning the proof masses) with an assumed tilt of rad as applicable to SR-POEM: an experiment aiming to test the weak equivalence principle -- a fundamental postulate of general relativity.

[gr-qc]

Authors: Saskia Grunau, Valeria Kagramanova, Jutta Kunz, Claus Lämmerzahl

We present analytical solutions of the geodesic equations of test particles and light in the five dimensional singly spinning black ring spacetime for special cases, since it does not appear possible to separate the Hamilton-Jacobi-equation for singly spinning black rings in general. Based on the study of the polynomials in the equations of motion we characterize the motion of test particles and light and discuss the associated orbits.

[gr-qc]

Authors: Christopher J. Fewster, Rainer Verch

Afshordi, Aslanbeigi and Sorkin have recently proposed a construction of a distinguished "S-J state" for scalar field theory in (bounded regions of) general curved spacetimes. We establish rigorously that the proposal is well-defined on globally hyperbolic spacetimes or spacetime regions that can be embedded as relatively compact subsets of other globally hyperbolic spacetimes, and also show that, whenever the proposal is well-defined, it yields a pure quasifree state. However, by explicitly considering portions of ultrastatic spacetimes, we show that the S-J state is not in general a Hadamard state. In the specific case where the Cauchy surface is a round 3-sphere, we prove that the representation induced by the S-J state is generally not unitarily equivalent to that of a Hadamard state, and indeed that the representations induced by S-J states on nested regions of the ultrastatic spacetime also fail to be unitarily equivalent in general. The implications of these results are discussed.

[gr-qc]

Authors: Xiao-Qing Shen, Shao-Feng Wu, Guo-Hong Yang

We study the spontaneously induced general relativity (GR) from the scalar-tensor gravity. We demonstrate by numerical methods that a novel inner core can be connected to the Schwarzschild exterior with cosmological constants and any sectional curvature. Deriving an analytic core metric for a general exterior, we show that all the nontrivial features of the core, including the locally holographic entropy packing, are universal for the general exterior in static spacetimes. We also investigate whether the f(R) gravity can accommodate the nontrivial core.

[gr-qc]

Authors: Yen Chin Ong, Pisin Chen

Electrically charged black holes with flat event horizon in anti-de Sitter space have received much attention due to various applications in Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence, from modeling the behavior of quark-gluon plasma to superconductor. Crucial to the physics on the dual field theory is the fact that when embedded in string theory, black holes in the bulk may become vulnerable to instability caused by brane pair-production. Since dilaton arises naturally in the context of string theory, we study the effect of coupling dilaton to Maxwell field on the stability of flat charged AdS black holes. In particular, we study the stability of Gao-Zhang black holes, which are locally asymptotically anti-de Sitter. We find that for dilaton coupling parameter \alpha > 1, flat black holes are stable against brane pair production, however for 0 < \alpha < 1, the black holes eventually become unstable as the amount of electrical charges is increased. Such instability however, behaves somewhat differently from that of flat Reissner-Nordström black holes. In addition, we prove that the Seiberg-Witten action of charged dilaton AdS black hole of Gao-Zhang type with flat event horizon (at least in 5-dimension) is always logarithmically divergent at infinity for finite values of \alpha, and is finite and positive in the case \alpha tends to infinity . We also comment on the robustness of our result for other charged dilaton black holes that are not of Gao-Zhang type.

[gr-qc]

Authors: Edward Anderson

I approach the Problem of Time and other foundations of Quantum Cosmology using a combined histories, timeless and semiclassical approach. This approach is along the lines pursued by Halliwell. It involves the timeless probabilities for dynamical trajectories entering regions of configuration space, which are computed within the semiclassical regime. Moreover, the objects that Halliwell uses in this approach commute with the Hamiltonian constraint, H. This approach has not hitherto been considered for models that also possess nontrivial linear constraints, Lin. This paper carries this out for some concrete relational particle models (RPM's). If there is also commutation with Lin - the Kuchar observables condition - the constructed objects are Dirac observables. Moreover, this paper shows that the problem of Kuchar observables is explicitly resolved for 1- and 2-d RPM's. Then as a first route to Halliwell's approach for nontrivial linear constraints that is also a construction of Dirac observables, I consider theories for which Kuchar observables are formally known, giving the relational triangle as an example. As a second route, I apply an indirect method that generalizes both group-averaging and Barbour's best matching. For conceptual clarity, my study involves the simpler case of Halliwell 2003 sharp-edged window function. I leave the elsewise-improved softened case of Halliwell 2009 for a subsequent Paper II. Finally, I provide comments on Halliwell's approach and how well it fares as regards the various facets of the Problem of Time and as an implementation of QM propositions.

[gr-qc]

Authors: Maxim Eingorn, Alexander Zhuk

In this letter, we consider the six-dimensional Kaluza-Klein models with spherical compactification of the internal space. Here, we investigate the case of bare gravitating compact objects with the dustlike equation of state in the external (our) space and an arbitrary equation of state in the internal space, where is the energy density of the source. This gravitating mass is spherically symmetric in the external space and uniformly smeared over the internal space. In the weak field approximation, the conformal variations of the internal space volume generate the admixture of the Yukawa potential to the usual Newton's gravitational potential. For sufficiently large Yukawa masses, such admixture is negligible and the metric coefficients of the external spacetime coincide with the corresponding expressions of General Relativity. Then, these models satisfy the classical gravitational tests. However, we show that gravitating masses acquire effective relativistic pressure in the external space. Such pressure contradicts the observations of compact astrophysical objects (e.g., the Sun). The equality (i.e. tension) is the only possibility to preserve the dustlike equation of state in the external space. Therefore, in spite of agreement with the gravitational experiments for an arbitrary value of , tension () plays a crucial role for the considered models.

[gr-qc]

Authors: Samuel Lepe, Francisco Peña

We study a cosmology by considering entropic issues. We make a bare/effective description of the equation of state of the cosmic fluid through a bare (\omega)/effective (\omega_eff) conservation equation. In the bare case, where we have a non conserved equation of state for the cosmic fluid, we describe the change in the sign of the inhomogeneus term at different times of the cosmic evolution. We show that by a redefinition of the adiabatic \omega -parameter we can recover the usual scheme for the cosmic evolution. In the effective case we show also that if the evolution is driven by dust or cosmological constant, the universe evolves on the thermal equilibrium. Additionally, by incorporating a quantum correction only cosmological constant can drive an evolution on thermal equilibrium.

[gr-qc]

Authors: Nikodem J. Poplawski

The Einstein-Cartan-Sciama-Kibble theory of gravity naturally extends general relativity to account for the intrinsic spin of matter. Spacetime torsion, generated by spin of Dirac fields, induces gravitational repulsion in fermionic matter at extremely high densities and prevents the formation of singularities. Accordingly, the big bang is replaced by a bounce that occurred when the energy density was on the order of (in natural units), where is the fermion number density and is the number of thermal degrees of freedom. If the early Universe contained only the known standard-model particles (), then the energy density at the big bounce was about 15 times larger than the Planck energy. The minimum scale factor of the Universe (at the bounce) was about times smaller than its present value, giving . If more fermions existed in the early Universe, then the spin-torsion coupling causes a bounce at a lower energy and larger scale factor. Recent observations of high-energy photons from gamma-ray bursts indicate that spacetime may behave classically even at scales below the Planck length, supporting the classical spin-torsion mechanism of the big bounce. Such a classical bounce prevents the matter in the contracting Universe from reaching the conditions at which a quantum bounce could possibly occur.

[gr-qc]

Authors: Ahmed Farag Ali (Benha U.)

We investigate the impact of the Generalized Uncertainty Principle (GUP), proposed by some approaches to quantum gravity such as String Theory and Doubly Special Relativity Theories (DSR) on the production of mini black holes, and show that the minimum black hole mass is formed at energies higher than the energy scales of LHC which possibly agrees with the recent experimental results of LHC [arXiv:1012.3375, arXiv:1206.5663] .

[gr-qc]

Authors: Pao-Yu Wang, Chien-Wen Chen, Pisin Chen

We confront two types of phantom dark energy potential with observational data. The models we consider are the power-law potential, , and the exponential potential, . We fit the models to the latest observations from SN-Ia, CMB and BAO, and obtain tight constraints on parameter spaces. Furthermore, we apply the goodness-of-fit and the information criteria to compare the fitting results from phantom models with that from the cosmological constant and the quintessence models presented in our previous work. The results show that the cosmological constant is statistically most preferred, while the phantom dark energy fits slightly better than the quintessence does.

[gr-qc]

Authors: Dong-il Hwang, Bum-Hoon Lee, Ewan D. Stewart, Dong-han Yeom, Heeseung Zoe

In this paper, we compare dispersions of a scalar field in Euclidean quantum gravity and stochastic inflation. We use Einstein gravity with a minimally coupled scalar field and a quadratic potential. We restrict our attention to small mass and small field cases. In Euclidean approach, we introduce the ground state wave function which is approximated by instantons. In stochastic approach, we introduce probability distribution of Hubble patches that can be approximated by a locally homogeneous universes up to a smoothing scale. We are assuming that the ground state wave function should correspond the stationary state of the probability distribution of the stochastic universe. By comparing the dispersion of both approaches, we conclude mainly three results. (1) For a statistical distribution with a certain value, we can find a corresponding instanton in the Euclidean side and it should be a complex-valued instanton. (2) The finite scale factor of the Euclidean approach corresponds the smoothing scale of the stochastic side; the universe is homogeneous up to the scale factor. (3) In addition, as the mass increases a critical value, both approaches break at the same time. Hence, generation of inhomogeneity in stochastic approach and the instability of classicality in Euclidean approach are related.

[gr-qc]

Authors: Lukas Hollenstein, Rajeev Kumar Jain, Federico R. Urban

The origin of large-scale magnetic fields in cosmic structures and the intergalactic medium is still poorly understood. We explore the effects of non-minimal couplings of electromagnetism on the cosmological evolution of currents and magnetic fields. In this context, we revisit the mildly non-linear plasma dynamics around recombination that are known to generate weak magnetic fields. We use the covariant approach to obtain a fully general and non-linear evolution equation for the plasma currents and derive a generalised Ohm's law valid on large scales as well as in the presence of non-minimal couplings to cosmological (pseudo-)scalar fields. Due to the sizable conductivity of the plasma and the stringent observational bounds on such couplings, we conclude that modifications of the standard (adiabatic) evolution of magnetic fields are severely limited in these scenarios.

[gr-qc]

Authors: Alexandre M. Baranov

An approach to construction of static models is demonstrated for a fluid ball. Five examples are considered. Two of them are exact solutions of the Einstein equations; the other three are connected with the Airy special functions, the hypergeometric functions and the Heun functions.

[gr-qc]

Authors: Victor H. Cardenas

The most studied way to explain the current accelerated expansion of the universe is to assume the existence of dark energy; a new component that fill the universe, does not clumps, currently dominates the evolution, and has a negative pressure. In this work I study an alternative model proposed by Lima et al. \cite{lima96}, which does not need an exotic equation of state, but assumes instead the existence of gravitational particle creation. Because this model fits the supernova observations as well as the CDM model, I perform in this work a thorough study of this model considering an explicit spatial curvature. I found that in this scenario we can alleviate the cosmic coincidence problem, basically showing that these two components, dark matter and dark energy, are of the same nature, but they act at different scales. I also shown the inadequacy of some particle creation models, and also I study a previously propose new model that overcome these difficulties.