Journal of Gravity
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© 2015 , Hindawi Publishing Corporation . All rights reserved.

Field Equations and Lagrangian for the Kaluza Metric Evaluated with Tensor Algebra Software
Tue, 06 Jan 2015 09:24:25 +0000
http://www.hindawi.com/journals/jgrav/2015/901870/
This paper calculates the Kaluza field equations with the aid of a computer package for tensor algebra, xAct. The xAct file is provided with this paper. We find that Thiry’s field equations are correct, but only under limited circumstances. The full fivedimensional field equations under the cylinder condition are provided here, and we see that most of the other references miss at least some terms from them. We go on to establish the remarkable Kaluza Lagrangian, and verify that the field equations calculated from it match those calculated with xAct, thereby demonstrating selfconsistency of these results. Many of these results can be found scattered throughout the literature, and we provide some pointers for historical purposes. But our intent is to provide a definitive exposition of the field equations of the classical, fivedimensional metric ansatz of Kaluza, along with the computer algebra data file to verify them, and then to recover the unique Lagrangian for the theory. In common terms, the Kaluza theory is an “” scalar field theory, but with unique electrodynamic couplings.
L. L. Williams
Copyright © 2015 L. L. Williams. All rights reserved.

Derivation of Field Equations in Space with the Geometric Structure Generated by Metric and Torsion
Thu, 11 Dec 2014 00:10:11 +0000
http://www.hindawi.com/journals/jgrav/2014/420123/
This paper is devoted to the derivation of field equations in space with the geometric structure generated by metric and torsion tensors. We also study the geometry of the space generated jointly and agreed on by the metric tensor and the torsion tensor. We showed that in such space the structure of the curvature tensor has special features and for this tensor we obtained analog RicciJacobi identity and evaluated the gap that occurs at the transition from the original to the image and vice versa, in the case of infinitely small contours. We have researched the geodesic lines equation. We introduce the tensor which is similar to the second fundamental tensor of hypersurfaces , but the structure of this tensor is substantially different from the case of Riemannian spaces with zero torsion. Then we obtained formulas which characterize the change of vectors in accompanying basis relative to this basis itself. Taking into considerations our results about the structure of such space we derived from the variation principle the general field equations (electromagnetic and gravitational).
Nikolay Yaremenko
Copyright © 2014 Nikolay Yaremenko. All rights reserved.

Macroscopic Theory of Dark Sector
Wed, 01 Oct 2014 12:22:14 +0000
http://www.hindawi.com/journals/jgrav/2014/586958/
A simple Lagrangian with squared covariant divergence of a vector field as a kinetic term turned out to be an adequate tool for macroscopic description of the dark sector. The zeromass field acts as the dark energy. Its energymomentum tensor is a simple additive to the cosmological constant. Massive fields describe two different forms of dark matter. The spacelike massive vector field is attractive. It is responsible for the observed plateau in galaxy rotation curves. The timelike massive field displays repulsive elasticity. In balance with dark energy and ordinary matter it provides a fourparametric diversity of regular solutions of the Einstein equations describing different possible cosmological and oscillating nonsingular scenarios of evolution of the Universe. In particular, the singular big bang turns into a regular inflationlike transition from contraction to expansion with the accelerated expansion at late times. The finetuned FriedmanRobertsonWalker singular solution is a particular limiting case at the lower boundary of existence of regular oscillating solutions in the absence of vector fields. The simplicity of the general covariant expression for the energymomentum tensor allows displaying the main properties of the dark sector analytically. Although the physical nature of dark sector is still unknown, the macroscopic theory can help analyze the role of dark matter in astrophysical phenomena without resorting to artificial model assumptions.
Boris E. Meierovich
Copyright © 2014 Boris E. Meierovich. All rights reserved.

Anisotropic Charged Fluid Sphere in Isotropic Coordinates
Tue, 02 Sep 2014 11:36:05 +0000
http://www.hindawi.com/journals/jgrav/2014/380320/
We have presented a class of charged superdense star models, starting with a static spherically symmetric metric in isotropic coordinates for anisotropic fluid by considering HajjBoutros(1986) type metric potential and a specific choice of electrical intensity E and anisotropy factor which involve charge parameter K and anisotropy parameter . The solution is well behaved for all the values of Schwarzschild compactness parameter u lying in the range , for all values of charge parameter K lying in the range , and for all values of anisotropy parameter lying in the range . With the increase in , the values of K and u decrease. Further, we have constructed a superdense star model with all degree of suitability. The solution so obtained is utilized to construct the models for superdense star like neutron stars and strange quark stars . For and , the maximum mass of neutron star is observed as and radius . Further for strange quark stars and are obtained.
Neeraj Pant, N. Pradhan, and Ksh. Newton Singh
Copyright © 2014 Neeraj Pant et al. All rights reserved.

LRS Bianchi TypeI Inflationary String Cosmological Model in BransDicke Theory of Gravitation
Thu, 21 Aug 2014 09:15:19 +0000
http://www.hindawi.com/journals/jgrav/2014/909374/
We investigate locally rotational symmetric (LRS) Bianchi type I space time coupled with scalar field. String cosmological models generated by a cloud of strings with particles attached to them are studied in the BransDicke theory. We assume that the expansion scalar is proportional to the shear scalar and also power law ansatz for scalar field. The physical behavior of the resulting model is discussed through different parameters.
R. Venkateswarlu and J. Satish
Copyright © 2014 R. Venkateswarlu and J. Satish. All rights reserved.

Gravitational Lagrangians, Mach’s Principle, and the Equivalence Principle in an Expanding Universe
Sun, 17 Aug 2014 08:23:00 +0000
http://www.hindawi.com/journals/jgrav/2014/415649/
Gravitational Lagrangians as derived by Fock for the EinsteinInfeldHoffmann approach, and by Kennedy assuming only a fourth rank tensor interaction, contain long range interactions. Here we investigate how these affect the local dynamics when integrated over an expanding universe out to the Hubble radius. Taking the cosmic expansion velocity into account in a heuristic manner it is found that these long range interactions imply Mach’s principle, provided the universe has the critical density, and that mass is renormalized. Suitable higher order additions to the Lagrangians make the formalism consistent with the equivalence principle.
Hanno Essén
Copyright © 2014 Hanno Essén. All rights reserved.

Study of Antigravity in an Model and in BransDicke Theory with Cosmological Constant
Sun, 17 Aug 2014 00:00:00 +0000
http://www.hindawi.com/journals/jgrav/2014/625836/
We study antigravity, that is, having an effective gravitational constant with a negative sign, in scalartensor theories originating from theory and in a BransDicke model with cosmological constant. For the theory case, we obtain the antigravity scalartensor theory in the Jordan frame by using a variant of the Lagrange multipliers method and we numerically study the time dependent effective gravitational constant. As we will demonstrate by using a specific model, although there is no antigravity in the initial model, it might occur or not in the scalartensor counterpart, mainly depending on the parameter that characterizes antigravity. Similar results hold true in the BransDicke model.
V. K. Oikonomou and N. Karagiannakis
Copyright © 2014 V. K. Oikonomou and N. Karagiannakis. All rights reserved.

Higgs Field in Universe: LongTerm Oscillation and Deceleration/Acceleration Phases
Sun, 20 Jul 2014 11:15:42 +0000
http://www.hindawi.com/journals/jgrav/2014/326749/
It is shown that the Einstein gravity and Higgs scalar field have (a) a longterm oscillation phase; (b) cosmological regular solutions with deceleration/acceleration phases. The first has a preceding contracting and subsequent expanding phases and between them there exists an oscillating phase with arbitrary time duration. The behavior of the second solution near to a flex point is in detail considered.
Vladimir Dzhunushaliev
Copyright © 2014 Vladimir Dzhunushaliev. All rights reserved.

Consistent Extension of Quasidilaton Massive Gravity
Sun, 20 Jul 2014 07:18:48 +0000
http://www.hindawi.com/journals/jgrav/2014/413835/
This paper is devoted to the Hamiltonian analysis of extension of the quasidilaton massive gravity as was proposed recently in
[arXiv:1306.5502]. We show that, for given formulation of the theory, the additional primary constraint that is responsible for the elimination of the BoulwareDeser ghost is missing. We compare this situation with the quasidilaton massive gravity. Finally, we propose the ghostfree extension of quasidilaton massive gravity.
Josef Klusoň
Copyright © 2014 Josef Klusoň. All rights reserved.

Numerical Relativity as a Tool for Studying the Early Universe
Tue, 22 Apr 2014 12:11:13 +0000
http://www.hindawi.com/journals/jgrav/2014/407197/
Numerical simulations are becoming a more effective tool for conducting detailed investigations into the evolution of our universe. In this paper, we show how the framework of numerical relativity can be used for studying cosmological models. The author is working to develop a largescale simulation of the dynamical processes in the early universe. These take into account interactions of dark matter, scalar perturbations, gravitational waves, magnetic fields, and turbulent plasma. The code described in this report is a GRMHD code based on the Cactus framework and is structured to utilize one of several different differencing methods chosen at runtime. It is being developed and tested on the University of Houston’s Maxwell cluster.
David Garrison
Copyright © 2014 David Garrison. All rights reserved.

Absorption and Scattering Cross Section of Regular Black Holes
Wed, 26 Mar 2014 00:00:00 +0000
http://www.hindawi.com/journals/jgrav/2014/231727/
By using the partial wave method, we investigate the absorption of massless scalar wave from regular black hole. We numerically carry out the absorption cross section and find that the larger angular momentum quantum number is, the smaller the corresponding maximum value of partial absorption cross section is. Comparing with Schwarzschild case, the absorption cross section of regular black holes is strengthened in both low and high frequency regions, and the absorption cross section oscillates around the geometric optical value in the high frequency region. Generally speaking, the scattering flux is strengthened and its scattering width becomes narrower in the forward direction. There are obvious contrast of scattering properties of different type of regular black hole.
Hai Huang, Ping Liao, Juhua Chen, and Yongjiu Wang
Copyright © 2014 Hai Huang et al. All rights reserved.

Creation of Entangled Universes Avoids the Big Bang Singularity
Sun, 12 Jan 2014 00:00:00 +0000
http://www.hindawi.com/journals/jgrav/2014/382675/
The creation of universes in entangled pairs may avoid the initial singularity and it would have observable consequences in a large macroscopic universe like ours, at least in principle. In this paper we describe the creation of an entangled pair of universes from a double instanton, which avoids the initial singularity, in the case of a homogeneous and isotropic universe with a conformally coupled massless scalar field. The thermodynamical properties of interuniversal entanglement might have observable consequences on the properties of our single universe provided that the thermodynamics of entanglement is eventually related to the classical formulation of thermodynamics.
Salvador J. RoblesPérez
Copyright © 2014 Salvador J. RoblesPérez. All rights reserved.

FiveDimensional SpaceTimes with a Variable Gravitational and Cosmological Constant
Thu, 02 Jan 2014 13:13:28 +0000
http://www.hindawi.com/journals/jgrav/2014/874739/
We have presented cosmological models in fivedimensional KaluzaKlein spacetime with a variable gravitational constant () and cosmological constant (). We have investigated Einsteinâ€™s field equations for fivedimensional KaluzaKlein spacetime in the presence of perfect fluid with time dependent and . A variety of solutions have been found in which increases and decreases with time , which matches with current observation. The properties of fluid and kinematical parameters have been discussed in detail.
Sanjay Oli
Copyright © 2014 Sanjay Oli. All rights reserved.

Maxwell’s Equal Area Law and the HawkingPage Phase Transition
Wed, 27 Nov 2013 13:40:00 +0000
http://www.hindawi.com/journals/jgrav/2013/525696/
We study the phases of a Schwarzschild black hole in the AntideSitter background geometry. Exploiting fluid/gravity duality, we construct the Maxwell equal area isotherm in the temperatureentropy plane, in order to eliminate negative heat capacity BHs. The construction we present here is reminiscent of the isobar cut in the pressurevolume plane which eliminates unphysical part of the Van der Walls curves below the critical temperature. Our construction also modifies the HawkingPage phase transition. Stable BHs are formed at the temperature , while pure radiation persists for . turns out to be below the standard HawkingPage temperature and there are no unstable BHs as in the usual scenario. Also, we show that, in order to reproduce the correct BH entropy , one has to write a black hole equation of state, that is, , in terms of the geometrical volume .
Euro Spallucci and Anais Smailagic
Copyright © 2013 Euro Spallucci and Anais Smailagic. All rights reserved.

Is EinsteinCartan Theory Coupled to Light Fermions Asymptotically Safe?
Thu, 12 Sep 2013 11:03:01 +0000
http://www.hindawi.com/journals/jgrav/2013/812962/
The difference between Einstein's general relativity and its Cartan extension is analyzed within
the scenario of asymptotic safety of quantum gravity. In particular, we focus on the fourfermion
interaction which distinguishes the EinsteinCartan theory from its Riemannian limit.
Eckehard W. Mielke
Copyright © 2013 Eckehard W. Mielke. All rights reserved.

FirstOrder Light Deflection by EinsteinStrauss Vacuole Method
Thu, 01 Aug 2013 08:43:48 +0000
http://www.hindawi.com/journals/jgrav/2013/686950/
We resolve here an outstanding problem plaguing conformal gravity in its
role in making consistent astrophysical predictions. Though its static
spherically symmetric solution incorporates all the successes of
Schwarzschild gravity, the fit to observed galactic rotation curves requires
, while the observed increase in the Schwarzschild light
deflection by galaxies appears to demand . Here we show that,
contrary to common knowledge, there is an increase in the
Schwarzschild deflection angle in the vicinity of galaxies due purely to the
effect of , when the idea of the EinsteinStrauss vacuole model
is employed. With the inconsistency now out of the way, conformal gravity should be
regarded as a good theory explaining light deflection by galaxies.
Debasish Saha, Amarjit Tamang, Ramil Izmailov, Carlo Cattani, and Kamal K. Nandi
Copyright © 2013 Debasish Saha et al. All rights reserved.

Spin Foam Models with Finite Groups
Wed, 24 Jul 2013 08:47:47 +0000
http://www.hindawi.com/journals/jgrav/2013/549824/
Spin foam models, loop quantum gravity, and group field theory are discussed as quantum gravity candidate theories and usually involve a continuous Lie group. We advocate here to consider quantum gravityinspired models with finite groups, firstly as a test bed for the full theory and secondly as a class of new lattice theories possibly featuring an analogue diffeomorphism symmetry. To make these notes accessible to readers outside the quantum gravity community, we provide an introduction to some essential concepts in the loop quantum gravity, spin foam, and group field theory approach and point out the many connections to the lattice field theory and the condensedmatter systems.
Benjamin Bahr, Bianca Dittrich, and James P. Ryan
Copyright © 2013 Benjamin Bahr et al. All rights reserved.

Nonsingular Einsteinian Cosmology: How Galactic Momentum Prevents Cosmic Singularities
Mon, 22 Jul 2013 12:56:08 +0000
http://www.hindawi.com/journals/jgrav/2013/617142/
It is shown how Einstein's equation can account for the evolution of the universe without an initial singularity and can explain the inflation epoch as a momentum dominated era in which energy from matter and radiation drove extremely accelerated expansion of space. It is shown how an object with momentum loses energy to the expanding universe and how this energy can contribute to accelerated spatial expansion more effectively than vacuum energy, because virtual particles, the source of vacuum energy, can have negative energy, which can cancel any positive energy from the vacuum. Radiation and matter with momentum have positive but decreasing energy in the expanding universe, and the energy lost by them can contribute to accelerated spatial expansion between galactic clusters, making dark energy a classical effect that can be explained by general relativity without quantum mechanics, and, as (13) and (15) show, without an initial singularity or a big bang. This role of momentum, which was overlooked in the Standard Cosmological Model, is the basis of a simpler model which agrees with what is correct in the old model and corrects what is wrong with it.
Kenneth J. Epstein
Copyright © 2013 Kenneth J. Epstein. All rights reserved.

A Cosmological Model Based on a Quadratic Equation of State Unifying Vacuum Energy, Radiation, and Dark Energy
Thu, 18 Jul 2013 11:22:17 +0000
http://www.hindawi.com/journals/jgrav/2013/682451/
We consider a cosmological model based on a quadratic equation of state (where is the Planck density and is the cosmological density) “unifying” vacuum energy, radiation, and dark energy. For , it reduces to leading to a phase of early accelerated expansion (early inflation) with a constant density equal to the Planck density g/m3 (vacuum energy). For , we recover the equation of state of radiation . For , we get leading to a phase of late accelerated expansion (late inflation) with a constant density equal to the cosmological density g/m3 (dark energy). The temperature is determined by a generalized StefanBoltzmann law. We show a nice “symmetry” between the early universe (vacuum energy + radiation) and the late universe (radiation + dark energy). In our model, they are described by two polytropic equations of state with index and respectively. Furthermore, the Planck density in the early universe plays a role similar to that of the cosmological density in the late universe. They represent fundamental upper and lower density bounds differing by 122 orders of magnitude. We add the contribution of baryonic matter and dark matter considered as independent species and obtain a simple cosmological model describing the whole evolution of the universe. We study the evolution of the scale factor, density, and temperature. This model gives the same results as the standard CDM model for , where is the Planck time and completes it by incorporating the phase of early inflation in a natural manner. Furthermore, this model does not present any singularity at and exists eternally in the past (although it may be incorrect to extrapolate the solution to the infinite past). Our study suggests that vacuum energy, radiation, and dark energy may be the manifestation of a unique form of “generalized radiation.” By contrast, the baryonic and dark matter components of the universe are treated as different species. This is at variance with usual models (quintessence, Chaplygin gas, ...) trying to unify dark matter and dark energy.
PierreHenri Chavanis
Copyright © 2013 PierreHenri Chavanis. All rights reserved.

Gravitational Force between the Black Hole and Light Particle in XRBs
Tue, 09 Jul 2013 14:15:36 +0000
http://www.hindawi.com/journals/jgrav/2013/232676/
The present research paper derives a formula for gravitational force acting between the black hole and light particle passing near the radius of event horizon of black holes and calculates also their values of different test black holes existing in only Xray binaries (XRBs).
Dipo Mahto, Md Shams Nadeem, Mahendra Ram, and Kumari Vineeta
Copyright © 2013 Dipo Mahto et al. All rights reserved.

On Noncommutative Corrections of Gravitational Energy in Teleparallel Gravity
Thu, 13 Jun 2013 08:18:08 +0000
http://www.hindawi.com/journals/jgrav/2013/217813/
We use the theory of teleparallelism equivalent to general relativity based on noncommutative spacetime coordinates. In this context, we write the corrections of the Schwarzschild solution. We propose the existence of a Weitzenböck spacetime that matches the corrected metric tensor. As an important result, we find the corrections of the gravitational energy in the realm of teleparallel gravity due to the noncommutativity of spacetime. Then we interpret such corrections as a manifestation of quantum theory in gravitational field.
S. C. Ulhoa and R. G. G. Amorim
Copyright © 2013 S. C. Ulhoa and R. G. G. Amorim. All rights reserved.

ScalarTensor Bianchi VI Models
Wed, 05 Jun 2013 16:31:56 +0000
http://www.hindawi.com/journals/jgrav/2013/491905/
We study how may vary the gravitational and the cosmological “constants,” ( and ) in several scalartensor theories with Bianchi III, , and symmetries. By working under the hypothesis of selfsimilarity we find exact solutions for two different theoretical models, which are the JordanBransDicke (JBD) with and the usual JBD model with potential (that mimics the behaviour of . We compare both theoretical models, and some physical and geometrical properties of the solutions are also discussed putting special emphasis on the study of the isotropization of the solutions.
J. A. Belinchón
Copyright © 2013 J. A. Belinchón. All rights reserved.

Collapse of a Relativistic SelfGravitating Star with Radial Heat Flux: Impact of Anisotropic Stresses
Wed, 22 May 2013 16:38:46 +0000
http://www.hindawi.com/journals/jgrav/2013/659605/
We develop a simple model for a selfgravitating spherically symmetric relativistic star which begins to collapse from an initially static configuration by dissipating energy in the form of radial heat flow. We utilize the model to show how local anisotropy affects the collapse rate and thermal behavior of gravitationally evolving systems.
Ranjan Sharma and Shyam Das
Copyright © 2013 Ranjan Sharma and Shyam Das. All rights reserved.

More on Superconductors via Gauge/Gravity Duality with Nonlinear Maxwell Field
Sun, 12 May 2013 13:37:41 +0000
http://www.hindawi.com/journals/jgrav/2013/782512/
We have developed the recent investigations on the secondorder phase transition in the holographic superconductor using the probe limit for a nonlinear Maxwell field strength coupled to a massless scalar field. By analytical methods, based on the variational SturmLiouville minimization technique, we study the effects of the spacetime dimension and the nonlinearity parameter on the critical temperature and the scalar condensation of the dual operators on the boundary. Further, as a motivated result, we analytically deduce the DC conductivity in the low and zero temperatures regime. Especially in the zero temperature limit and in two dimensional toy model, we thoroughly compute the conductivity analytically. Our work clarifies more features of the holographic superconductors both in different space dimensions and on the effect of the nonlinearity in Maxwell's strength field.
Davood Momeni, Muhammad Raza, and Ratbay Myrzakulov
Copyright © 2013 Davood Momeni et al. All rights reserved.

Gravitational Fields of Conical Mass Distributions
Thu, 04 Apr 2013 12:50:08 +0000
http://www.hindawi.com/journals/jgrav/2013/546913/
The gravitational field of conical mass distributions is formulated using the general theory of relativity. The gravitational metric tensor is constructed and applied to the motion of test particles and photons in this gravitational field. The expression for gravitational time dilation is found to have the same form as that in spherical, oblate spheroidal, and prolate spheroidal gravitational fields and hence confirms an earlier assertion that this gravitational phenomena is invariant in form with various mass distributions. It is shown using the pure radial equation of motion that as a test particle moves closer to the conical mass distribution along the radial direction, its radial speed decreases.
Chifu Ebenezer Ndikilar
Copyright © 2013 Chifu Ebenezer Ndikilar. All rights reserved.

Stiff Fluid in Accelerated Universes with Torsion
Sun, 31 Mar 2013 15:49:23 +0000
http://www.hindawi.com/journals/jgrav/2013/306417/
The flat Friedmann universes filled by stiff fluid and a nonminimally
coupled material scalar field with polynomial potentials of the
fourth degree are considered in the framework of the
EinsteinCartan theory. Exact general solution is obtained for arbitrary positive values of the coupling constant . A comparative analysis of the cosmological models with and without stiff fluid is carried out. Some effects of stiff fluid are
elucidated. It is shown that singular models with a de Sitter asymptotic and with the powerlaw asymptotic at late times are possible. It is found that is a specific value of the coupling constant. It is demonstrated that the bouncing models without the particle horizon and with an accelerated expansion by a de Sitter law of an evolution at late times are admissible.
Almaz Galiakhmetov
Copyright © 2013 Almaz Galiakhmetov. All rights reserved.