Caustic Singularity in Ho?ava-Lifshitz Gravity

In this note we search for a family of solutions with Caustic singularity in non relativistic-renormalizable Hořava-Lifshitz (HL) theory without the general covariant. We show that in infrared (IR) limit and with a deviation from λ=1 we have no caustic singularity. Also in ultraviolet (UV) regime and for Ricci flat 3-dimensional (3d) spaces and codimension 1 and for λ≠1 the non linear terms should help bouncing this kind of most dangerous would be caustics. But if 3d curvature does not vanish, higher curvature terms do help caustics even in codimension one. Thus the arguments in (J. Cosmol. Astropart. Phys. 0909:005, 2009) are satisfied correctly.     

Black Hole Entropy of IR Modified Ho?ava-Lifshitz Gravity in Quantum Statistics Perspective

In this paper we investigate quantum statistical entropy for the Kehagias-Sfetsos black hole in IR modified Hořava-Lifshitz gravity by using t’ Hooft’s brick-wall method and generalized uncertainty principle method. By carefully calculating, we obtain the brick-wall entropy S _BWM =A/4 and the generalized uncertainty principle entropy S _GUP =A/96πγ. It is found if we view from quantum statistics, the brick-wall entropy and generalized uncertainty principle entropy may possibly is proportional to the event horizon area. This type area entropy is also justified by Wang et al. (Phys. Rev. D 81:083006, 2010). The study of the quantum statistical entropy may shed light on the understand of Hořava-Lifshitz gravity.     

U(1) Invariant $F(\tilde{R})$ Hořava–Lifshitz gravity

This paper is devoted to the study of various aspects of projectable F(R) Hořava–Lifshitz (HL) gravity. We show that some versions of F(R) HL gravity may have stable de Sitter solution and unstable flat-space solution. In this case, the problem of scalar graviton does not appear because flat space is not vacuum state. Generalizing the U(1) HL theory proposed in , we formulate U(1) extension of scalar theory and of F(R) Hořava–Lifshitz gravity. The Hamiltonian approach for such the theory is developed in full detail. It is demonstrated that its Hamiltonian structure is the same as for the non-relativistic covariant HL gravity. The spectrum analysis performed around the flat background indicates the consistency of the theory because it contains a graviton with only transverse polarization. Finally, we analyze the spatially flat FRW equations for U(1) invariant F(R) Hořava–Lifshitz gravity.     

Study of Thermodynamic Quantities in Generalized Gravity Theories

In this work, we have studied the thermodynamic quantities like temperature of the universe, heat capacity and squared speed of sound in generalized gravity theories like Brans-Dicke, Hořava-Lifshitz and f(R) gravities. We have considered the universe filled with dark matter and dark energy. Also we have considered the equation of state parameters for open, closed and flat models. We have observed that in all cases the equation of state behaves like quintessence. The temperature and heat capacity of the universe are found to decrease with the expansion of the universe in all cases. In Brans-Dicke and f(R) gravity theories the squared speed of sound is found to exhibit increasing behavior for open, closed and flat models and in Hořava-Lifshitz gravity theory it is found to exhibit decreasing behavior for open and closed models with the evolution of the universe. However, for flat universe, the squared speed of sound remains constant in Hořava-Lifshitz gravity.     

Stability of the Einstein static universe in IR modified Hořava gravity

Recently, Hořava proposed a power counting renormalizable theory for (3+1)-dimensional quantum gravity, which reduces to Einstein gravity with a non-vanishing cosmological constant in IR, but possesses improved UV behaviors. In this work, we analyze the stability of the Einstein static universe by considering linear homogeneous perturbations in the context of an IR modification of Hořava gravity, which implies a ‘soft’ breaking of the ‘detailed balance’ condition. The stability regions of the Einstein static universe is parameterized by the linear equation of state parameter w=p/ρ and the parameters appearing in the Hořava theory, and it is shown that a large class of stable solutions exists in the respective parameter space.     

String Cosmological Solutions in Self-Creation Theory of Gravitation

We have studied the problem of cosmic strings for Bianchi-I, II, VIII and IX string cosmological models in Barber’s (Gen. Relativ. Gravit. 14:117, 1982) second self—creation theory of gravitation. We have obtained some classes of solutions by considering different functional form for metric potentials. It is also observed that due to the presence of scalar field, the power index ‘m’ of the metric coefficients has a range of values.     

Hořava gravity and gravitons at a conformal point

Recently Hořava proposed a renormalizable gravity theory with higher derivatives by abandoning the Lorentz invariance in UV. Here, I construct the Hořava model at λ = 1/3, where a local anisotropic Weyl symmetry exists in the UV limit, in addition to the foliation-preserving diffeomorphism. By considering linear perturbations around Minkowski vacuum for the non-projectable version of the Hořava model, I show that the scalar graviton mode is completely disappeared and only the usual tensor graviton modes remain in the physical spectrum. The existence of the UV conformal symmetry is unique to the theory with the detailed balance and this may explain the importance of the detailed balance condition in quantum gravity.     

On Axially Symmetric Domain Walls and Cosmic Strings in Bimetric Theory

It is shown that the axially symmetric thick domain walls and cosmic strings do not survive in the frame work of bimetric theory of gravitation proposed by Rosen (Gen. Relativ. Gravit. 4:435, 1973). Hence vacuum models are presented and studied.     

Inhomogeneous Plane Symmetric String Cosmological Models in Bimetric Theory

It is shown that the inhomogeneous plane symmetric perfect fluid distribution and cosmic strings do not survive in frame work of bimetric theory of gravitation proposed by Rosen (Gen. Relativ. Gravit. 4:435, 1973). Hence vacuum models are presented and studied.     

<Emphasis Type="Italic">z</Emphasis> = 3 Lifshitz-Hořava model and fermi-point scenario of emergent gravity

Recently Hořava proposed a model for gravity which is described by the Einstein action in the infrared, but lacks the Lorentz invariance in the high-energy region where it experiences the anisotropic scaling. We test this proposal using two condensed matter examples of emergent gravity: acoustic gravity and gravity emerging in the fermionic systems with Fermi points. We suggest that quantum hydrodynamics, which together with the quantum gravity is the non-renormalizable theory, may exhibit the anisotropic scaling in agreement with the proposal. The Fermi point scenario of emergent general relativity demonstrates that under general conditions, the infrared Einstein action may be distorted, i.e., the Hořava parameter λ is not necessarily equal 1 even in the low energy limit. The consistent theory requires special hierarchy of the ultra-violet energy scales and the fine-tuning mechanism for the Newton constant. The article is published in the original.     

Spherically Symmetric Cosmic Strings in Bimetric Theory

Spherically symmetric space-time is considered in bimetric theory of gravitation formulated by Rosen (Gen. Relativ. Gravit. 4:435, [1973]) in the presence of perfect fluid, massive scalar field and cosmic string. It is shown that either macro cosmological model represented by perfect fluid or cosmic string do not exist and only a vacuum model can be constructed whereas in case of a micro cosmological model represented by a scalar field exists and the model is obtained.     

Dilaton Dark Energy Model in f(R), f(T) and Ho?ava-Lifshitz Gravities

In this work, we have considered dilaton dark energy model in Weyl-scaled induced gravitational theory in presence of barotropic fluid. It is to be noted that the dilaton field behaves as a quintessence. Here we have discussed the role of dilaton dark energy in modified gravity theories, namely f(R),f(T) and Hořava-Lifshitz gravities and analyzed the behavior of the dilaton field and the corresponding potential in respect to these modified gravity theories instead of Einstein’s gravity. In f(R) and f(T) gravities, we have considered some particular forms of f(R) and f(T) and we have shown that the potentials always increase with the dilaton fields. But in Hořava-Lifshitz gravity, it has been seen that the potential always decreases as dilation field increases.     

Magnetized cosmological models in bimetric theory of gravitation

Bianchi type-III magnetized cosmological model when the field of gravitation is governed by either a perfect fluid or cosmic string is investigated in Rosen’s [1] bimetric theory of gravitation. To complete determinate solution, the condition, viz., A=(BC) ⁿ , where n is a constant, between the metric potentials is used. We have assumed different equations of state for cosmic string [2] for the complete solution of the model. Some physical and geometrical properties of the exhibited model are discussed and studied.     

Modified dispersion relations in Hořava–Lifshitz gravity and Finsler brane models

We study possible links between quantum gravity phenomenology encoding Lorentz violations as nonlinear dispersions, the Einstein–Finsler gravity models, EFG, and nonholonomic (non-integrable) deformations to Hořava–Lifshitz, HL, and/or Einstein’s general relativity, GR, theories. EFG and its scaling anisotropic versions formulated as Hořava–Finsler models, HF, are constructed as covariant metric compatible theories on (co) tangent bundle to Lorentz manifolds and respective anisotropic deformations. Such theories are integrable in general form and can be quantized following standard methods of deformation quantization, A-brane formalism and/or (perturbatively) as a nonholonomic gauge like model with bi-connection structure. There are natural warping/trapping mechanisms, defined by the maximal velocity of light and locally anisotropic gravitational interactions in a (pseudo) Finsler bulk spacetime, to four dimensional (pseudo) Riemannian spacetimes. In this approach, the HL theory and scenarios of recovering GR at large distances are generated by imposing nonholonomic constraints on the dynamics of HF, or EFG, fields.     

Black Hole Thermodynamics of Hořava-Lifshitz and IR Modified Ho řava-Lifshitz Gravity Theory

Recently, a renormalizable model of gravity has been proposed by Hoř ava, which might be an ultraviolet completion of general relativity and it reduces to Einstein gravity with a non-vanishing cosmological constant in infrared approximation. Kehagias and Sfetsos have added a relevant operator proportional to the 3D geometry Ricci scalar to the original Hoř ava-Lifshitz theory action, which “softly” deviated from detailed-balance. This does not modify the ultraviolet properties of the theory. However, it modifies the infrared approximation and the Minkowski vacuum can be allowed in the infrared Hořava-Lifshitz gravity theory. The static spherical symmetric black hole solutions have been obtained in the Hořava-Lifshitz and infrared Hořava-Lifshitz gravity theory. Based on the metric of the black holes, Hawking radiation of massless scalar particles is investigated using Damour-Ruffini method. Then the black hole thermodynamics property will also be discussed.     

The absence of the Kerr black hole in the Hořava–Lifshitz gravity

We show that the Kerr metric does not exist as a fully rotating black hole solution to modified Hořava–Lifshitz (HL) gravity with Λ _W =0 and λ=1. We do this by showing that the Kerr metric does not satisfy the full equations derived from modified HL gravity.     

Spin and torsion in general relativity II: Geometry and field equations

From physical arguments space-time is assumed to possess a connection is Christoffel's symbol built up from the metric g _ij and already appearing in General Relativity (GR). Cartan's torsion tensor and the contortion tensor K _ij ^k , in contrast to the theory presented here, both vanish identically in conventional GR. Using the connection introduced above, in this series of articles we will discuss the consequences for GR in the framework of a consistent formalism. There emerges a theory describing in a unified way gravitation and a very weakspin-spin contact interaction. In Part I of this work† we discussed the foundations of the theory. In this Part II we present in section 3 the geometrical apparatus necessary for the formulation of the theory. In section 4 we take the curvature scalar (or rather its density) as Lagrangian density of the field. In this way we obtain in subsection 4.1 the field equations in their explicit form. In particular it turns out that torsion is essentially proportional to spin. We then derive the angular momentum and the energy-momentum theorems (subsections 4.2-4); the latter yields a force proportional to curvature, acting on any matter with spin. In subsection 4.5 we compare the theory so far developed with GR. Torsion leads to a universal spin-spin contact     

Nucleon Properties Below the Critical Point Temperature

In this paper, we extended our work (Abu-Shady, Int. J. Theory Phys. 49:2425, 2010) to include nucleon properties. The field equations have been solved in the mean-field approximation using the effective mesonic potential at finite temperature. We found that the nucleon first mass increases up to \frac45 T_c\frac{4}{5} T_{c} MeV (where T _c is the critical point temperature) then decreases at higher values of temperature which approach the critical temperature (T _c ). In addition, we found that the magnetic moments of the proton and neutron can be increased by increasing the temperature up to the critical temperature. Moreover, we examined the axial coupling constant g _A (0), and the pion-nucleon coupling constant g _πNN (0) as functions of temperature. The obtained results are compared with previous works. From the results, we conclude that finite temperature plays a significant role in the change of behavior of nucleon properties.     

Early and late-time cosmic acceleration in non-minimal Yang–Mills-<Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">G</Emphasis>) gravity

In this paper we show that power-law inflation can be realized in non-minimal gravitational coupling of Yang–Mills field with a general function of the Gauss–Bonnet invariant in the framework of Einstein gravity. Such a non-minimal coupling may appear due to quantum corrections. We also discuss the non-minimal Yang–Mills-f(G) gravity in the framework of modified Gauss–Bonnet action which is widely studied recently. It is shown that both inflation and late-time cosmic acceleration are possible in such a theory.     

String Cloud with Quark Matter in Self-creation Cosmology

We have constructed Bianchi type-III cosmological model with strange quark matter attached to the string cloud in Barber’s (Gen. Relativ. Gravit. 14:117, 1982) second self-creation theory of gravitation which is inflationary. Further it is obtained that the theory leads to Einstein theory at initial epoch and at infinite future.