Journal of Gravity The latest articles from Hindawi © 2017 , Hindawi Limited . All rights reserved. Non-Perfect-Fluid Space-Times in Thermodynamic Equilibrium and Generalized Friedmann Equations Thu, 17 Nov 2016 05:46:59 +0000 We determine the energy-momentum tensor of nonperfect fluids in thermodynamic equilibrium and, respectively, near to it. To this end, we derive the constitutive equations for energy density and isotropic and anisotropic pressure as well as for heat-flux from the corresponding propagation equations and by drawing on Einstein’s equations. Following Obukhov on this, we assume the corresponding space-times to be conform-stationary and homogeneous. This procedure provides these quantities in closed form, that is, in terms of the structure constants of the three-dimensional isometry group of homogeneity and, respectively, in terms of the kinematical quantities expansion, rotation, and acceleration. In particular, we find a generalized form of the Friedmann equations. As special cases we recover Friedmann and Gödel models as well as nontilted Bianchi solutions with anisotropic pressure. All of our results are derived without assuming any equations of state or other specific thermodynamic conditions a priori. For the considered models, results in literature are generalized to rotating fluids with dissipative fluxes. Konrad Schatz, Horst-Heino von Borzeszkowski, and Thoralf Chrobok Copyright © 2016 Konrad Schatz et al. All rights reserved. Transformation Groups for a Schwarzschild-Type Geometry in Gravity Wed, 02 Nov 2016 06:43:28 +0000 We know that the Lorentz transformations are special relativistic coordinate transformations between inertial frames. What happens if we would like to find the coordinate transformations between noninertial reference frames? Noninertial frames are known to be accelerated frames with respect to an inertial frame. Therefore these should be considered in the framework of general relativity or its modified versions. We assume that the inertial frames are flat space-times and noninertial frames are curved space-times; then we investigate the deformation and coordinate transformation groups between a flat space-time and a curved space-time which is curved by a Schwarzschild-type black hole, in the framework of gravity. We firstly study the deformation transformation groups by relating the metrics of the flat and curved space-times in spherical coordinates; after the deformation transformations we concentrate on the coordinate transformations. Later on, we investigate the same deformation and coordinate transformations in Cartesian coordinates. Finally we obtain two different sets of transformation groups for the spherical and Cartesian coordinates. Emre Dil and Talha Zafer Copyright © 2016 Emre Dil and Talha Zafer. All rights reserved. Clusters of Galaxies in a Weyl Geometric Approach to Gravity Sun, 16 Oct 2016 09:44:49 +0000 A model for the dark halos of galaxy clusters, based on the Weyl geometric scalar tensor theory of gravity (WST) with a MOND-like approximation, is proposed. It is uniquely determined by the baryonic mass distribution of hot gas and stars. A first heuristic check against empirical data for 19 clusters (2 of which are outliers), taken from the literature, shows encouraging results. Modulo a caveat resulting from different background theories (Einstein gravity plus versus WST), the total mass for 15 of the outlier reduced ensemble of 17 clusters seems to be predicted correctly (in the sense of overlapping error intervals). Erhard Scholz Copyright © 2016 Erhard Scholz. All rights reserved. On Gravitational Entropy of de Sitter Universe Mon, 18 Jul 2016 16:32:55 +0000 The paper deals with the calculation of the gravitational entropy in the context of teleparallel gravity for de Sitter space-time. In such a theory it is possible to define gravitational energy and pressure; thus we use those expressions to construct the gravitational entropy. We use the temperature as a function of the cosmological constant and write the first law of thermodynamics from which we obtain the entropy. In the limit we find that the entropy is proportional to volume, for a specific temperature’s choice; we find that as well. We also identify a phase transition in de Sitter space-time by analyzing the specific heat. S. C. Ulhoa and E. P. Spaniol Copyright © 2016 S. C. Ulhoa and E. P. Spaniol. All rights reserved. Noether Gauge Symmetries for Petrov Type D-Levi-Civita Space-Time in Spherical and Cylindrical Coordinates Tue, 07 Jun 2016 08:03:58 +0000 Petrov Type D-Levi-Civita (DLC) space-time is considered in two different coordinates, that is, spherical and cylindrical. Noether gauge symmetries and their corresponding conserved quantities for respective metric with the restricted range of parameters and coordinates are discussed. Adil Jhangeer and Tayyaba Naz Copyright © 2016 Adil Jhangeer and Tayyaba Naz. All rights reserved. Spacetime Causal Structure and Dimension from Horismotic Relation Wed, 25 May 2016 14:04:36 +0000 A reflexive relation on a set can be a starting point in defining the causal structure of a spacetime in General Relativity and other relativistic theories of gravity. If we identify this relation as the relation between lightlike separated events (the horismos relation), we can construct in a natural way the entire causal structure: causal and chronological relations, causal curves, and a topology. By imposing a simple additional condition, the structure gains a definite number of dimensions. This construction works with both continuous and discrete spacetimes. The dimensionality is obtained also in the discrete case, so this approach can be suited to prove the fundamental conjecture of causal sets. Other simple conditions lead to a differentiable manifold with a conformal structure (the metric up to a scaling factor) as in Lorentzian manifolds. This structure provides a simple and general reconstruction of the spacetime in relativistic theories of gravity, which normally requires topological structure, differential structure, and geometric structure (which decomposes in the conformal structure, giving the causal relations and the volume element). Motivations for such a reconstruction come from relativistic theories of gravity, where the conformal structure is important, from the problem of singularities, and from Quantum Gravity, where various discretization methods are pursued, particularly in the causal sets approach. O. C. Stoica Copyright © 2016 O. C. Stoica. All rights reserved. The Energy Conservation in Our Universe and the Pressureless Dark Energy Wed, 15 Jul 2015 07:16:12 +0000 Recent observations confirm that a certain amount of unknown dark energy exists in our universe so that the current expansion of our universe is accelerating. It is commonly believed that the pressure of the dark energy is negative and the density of the dark energy is almost a constant throughout the universe expansion. In this paper, we show that the law of energy conservation in our universe has to be modified because more vacuum energy is gained due to the universe expansion. As a result, the pressure of dark energy would be zero if the total energy of our universe is increasing. This pressureless dark energy model basically agrees with the current observational results. Man Ho Chan Copyright © 2015 Man Ho Chan. All rights reserved. Symmetry and the Arrow of Time in Theoretical Black Hole Astrophysics Tue, 14 Jul 2015 11:28:39 +0000 While the basic laws of physics seem time-reversal invariant, our understanding of the apparent irreversibility of the macroscopic world is well grounded in the notion of entropy. Because astrophysics deals with the largest structures in the Universe, one expects evidence there for the most pronounced entropic arrow of time. However, in recent theoretical astrophysics work it appears possible to identify constructs with time-reversal symmetry, which is puzzling in the large-scale realm especially because it involves the engines of powerful outflows in active galactic nuclei which deal with macroscopic constituents such as accretion disks, magnetic fields, and black holes. Nonetheless, the underlying theoretical structure from which this accreting black hole framework emerges displays a time-symmetric harmonic behavior, a feature reminiscent of basic and simple laws of physics. While we may expect such behavior for classical black holes due to their simplicity, manifestations of such symmetry on the scale of galaxies, instead, surprise. In fact, we identify a parallel between the astrophysical tug-of-war between accretion disks and jets in this model and the time symmetry-breaking of a simple overdamped harmonic oscillator. The validity of these theoretical ideas in combination with this unexpected parallel suggests that black holes are more influential in astrophysics than currently recognized and that black hole astrophysics is a more fundamental discipline. David Garofalo Copyright © 2015 David Garofalo. All rights reserved. Elementary Superconductivity in Nonlinear Electrodynamics Coupled to Gravity Sun, 05 Jul 2015 13:56:06 +0000 Source-free equations of nonlinear electrodynamics minimally coupled to gravity admit regular axially symmetric asymptotically Kerr-Newman solutions which describe charged rotating black holes and electromagnetic spinning solitons (lumps). Asymptotic analysis of solutions shows, for both black holes and solitons, the existence of de Sitter vacuum interior which has the properties of a perfect conductor and ideal diamagnetic and displays superconducting behaviour which can be responsible for practically unlimited lifetime of the electron. Superconducting current flows on the equatorial ring replacing the Kerr ring singularity of the Kerr-Newman geometry. Interior de Sitter vacuum supplies the electron with the finite positive electromagnetic mass related to the interior de Sitter vacuum of the electroweak scale and to breaking of space-time symmetry, which allows explaining the mass-square differences for neutrino and the appearance of the minimal length scale in the annihilation reaction . Irina Dymnikova Copyright © 2015 Irina Dymnikova. All rights reserved. Field Equations and Lagrangian for the Kaluza Metric Evaluated with Tensor Algebra Software Tue, 06 Jan 2015 09:24:25 +0000 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 five-dimensional 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 self-consistency 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, five-dimensional 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 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 Ricci-Jacobi 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 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 zero-mass field acts as the dark energy. Its energy-momentum tensor is a simple additive to the cosmological constant. Massive fields describe two different forms of dark matter. The space-like massive vector field is attractive. It is responsible for the observed plateau in galaxy rotation curves. The time-like massive field displays repulsive elasticity. In balance with dark energy and ordinary matter it provides a four-parametric 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 inflation-like transition from contraction to expansion with the accelerated expansion at late times. The fine-tuned Friedman-Robertson-Walker 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 energy-momentum 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 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 Hajj-Boutros-(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 Type-I Inflationary String Cosmological Model in Brans-Dicke Theory of Gravitation Thu, 21 Aug 2014 09:15:19 +0000 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 Brans-Dicke 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 Gravitational Lagrangians as derived by Fock for the Einstein-Infeld-Hoffmann 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 Brans-Dicke Theory with Cosmological Constant Sun, 17 Aug 2014 00:00:00 +0000 We study antigravity, that is, having an effective gravitational constant with a negative sign, in scalar-tensor theories originating from theory and in a Brans-Dicke model with cosmological constant. For the theory case, we obtain the antigravity scalar-tensor 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 scalar-tensor counterpart, mainly depending on the parameter that characterizes antigravity. Similar results hold true in the Brans-Dicke model. V. K. Oikonomou and N. Karagiannakis Copyright © 2014 V. K. Oikonomou and N. Karagiannakis. All rights reserved. Higgs Field in Universe: Long-Term Oscillation and Deceleration/Acceleration Phases Sun, 20 Jul 2014 11:15:42 +0000 It is shown that the Einstein gravity and Higgs scalar field have (a) a long-term 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 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 Boulware-Deser ghost is missing. We compare this situation with the quasidilaton massive gravity. Finally, we propose the ghost-free 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 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 large-scale 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 run-time. 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 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 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. Robles-Pérez Copyright © 2014 Salvador J. Robles-Pérez. All rights reserved. Five-Dimensional Space-Times with a Variable Gravitational and Cosmological Constant Thu, 02 Jan 2014 13:13:28 +0000 We have presented cosmological models in five-dimensional Kaluza-Klein space-time with a variable gravitational constant () and cosmological constant (). We have investigated Einstein’s field equations for five-dimensional Kaluza-Klein space-time 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 Hawking-Page Phase Transition Wed, 27 Nov 2013 13:40:00 +0000 We study the phases of a Schwarzschild black hole in the Anti-deSitter background geometry. Exploiting fluid/gravity duality, we construct the Maxwell equal area isotherm   in the temperature-entropy plane, in order to eliminate negative heat capacity BHs. The construction we present here is reminiscent of the isobar cut in the pressure-volume plane which eliminates unphysical part of the Van der Walls curves below the critical temperature. Our construction also modifies the Hawking-Page phase transition. Stable BHs are formed at the temperature , while pure radiation persists for . turns out to be below the standard Hawking-Page 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 Einstein-Cartan Theory Coupled to Light Fermions Asymptotically Safe? Thu, 12 Sep 2013 11:03:01 +0000 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 four-fermion interaction which distinguishes the Einstein-Cartan theory from its Riemannian limit. Eckehard W. Mielke Copyright © 2013 Eckehard W. Mielke. All rights reserved. First-Order Light Deflection by Einstein-Strauss Vacuole Method Thu, 01 Aug 2013 08:43:48 +0000 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 Einstein-Strauss 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 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 gravity-inspired 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 condensed-matter 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 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 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 Stefan-Boltzmann 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. Pierre-Henri Chavanis Copyright © 2013 Pierre-Henri Chavanis. All rights reserved. Gravitational Force between the Black Hole and Light Particle in XRBs Tue, 09 Jul 2013 14:15:36 +0000 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 X-ray 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 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.