Einstein's Theory Of Gravitation Research Articles

Towards the theory of regular accelerating Universe in Riemann-Cartan space-time

The problems of modern cosmology and attempts of its solution are considered. The applying of gravitation theory in the Riemann-Cartan space-time as the most natural generalization of Einstein gravitation theory in order to solve the principal cosmological problems is discussed. The gravitation theory in the Riemann-Cartan space-time leading to the solution of the problem of cosmological singularity and dark energy problem is analyzed.

Entanglement with centers

Entanglement is a physical phenomenon that each state cannot be described individually. Entanglement entropy gives quantitative understanding to the entanglement. We use decomposition of the Hilbert space to discuss properties of the entanglement. Therefore, partial trace operator becomes important to define the reduced density matrix from different centers, which commutes with all elements in the Hilbert space, corresponding to different entanglement choices or different observations on entangling surface. Entanglement entropy is expected to satisfy the strong subadditivity. We discuss decomposition of the Hilbert space for the strong subadditivity and other related inequalities. The entanglement entropy with centers can be computed from the Hamitonian formulations systematically, provided that we know wavefunctional. In the Hamitonian formulation, it is easier to obtain symmetry structure. We consider massless $p$-form theory as an example. The massless $p$-form theory in ($2p+2)$-dimensions has global symmetry, similar to the electric-magnetic duality, connecting centers in ground state. This defines a duality structure in centers. Because it is hard to exactly compute the entanglement entropy from partial trace operator, we propose the Lagrangian formulation from the Hamitonian formulation to compute the entanglement entropy with centers. From the Lagrangian method and saddle point approximation, the codimension two surface term (leading order) in the Einstein gravity theory or holographic entanglement entropy should correspond to non-tensor product decomposition (center is not identity). Finally, we compute the entanglement entropy of the $SU(N)$ Yang-Mills lattice gauge theory in the fundamental representation using the strong coupling expansion in the extended lattice model to obtain spatial area term in total dimensions larger than two for $N>1$.

Lower-dimensional black hole chemistry

The connection between black hole thermodynamics and chemistry is extended to the lower-dimensional regime by considering the rotating and charged BTZ metric in the $(2+1)$-D and a $(1+1)$-D limits of Einstein gravity. The Smarr relation is naturally upheld in both BTZ cases, where those with $Q \ne 0$ violate the Reverse Isoperimetric Inequality and are thus superentropic. The inequality can be maintained, however, with the addition of a new thermodynamic work term associated with the mass renormalization scale. The $D\rightarrow 0$ limit of a generic $D+2$-dimensional Einstein gravity theory is also considered to derive the Smarr and Komar relations, although the opposite sign definitions of the cosmological constant and thermodynamic pressure from the $D>2$ cases must be adopted in order to satisfy the relation. The requirement of positive entropy implies a lower bound on the mass of a $(1+1)$-D black hole. Promoting an associated constant of integration to a thermodynamic variable allows one to define a "rotation" in one spatial dimension. Neither the $D=3$ nor the $D \rightarrow 2$ black holes exhibit any interesting phase behaviour.

Three theorems on near horizon extremal vanishing horizon geometries

EVH black holes are Extremal black holes with Vanishing Horizon area, where vanishing of horizon area is a result of having a vanishing one-cycle on the horizon. We prove three theorems regarding near horizon geometry of EVH black hole solutions to generic Einstein gravity theories in diverse dimensions. These generic gravity theories are Einstein–Maxwell-dilaton-Λ theories, and gauged or ungauged supergravity theories with U(1) Maxwell fields. Our three theorems are: (1) The near horizon geometry of any EVH black hole has a three dimensional maximally symmetric subspace. (2) If the energy momentum tensor of the theory satisfies strong energy condition either this 3d part is an AdS3, or the solution is a direct product of a locally 3d flat space and a d−3 dimensional part. (3) These results extend to the near horizon geometry of near-EVH black holes, for which the AdS3 part is replaced with BTZ geometry.

Gravitational crystal inside the black hole

Crystals, as quantum objects typically much larger than their lattice spacing, are counterexamples to a frequent prejudice that quantum effects should not be pronounced at macroscopic distances. We propose that the Einstein theory of gravity only describes a fluid phase and that a phase transition of crystallization can occur under extreme conditions such as those inside the black hole. Such a crystal phase with lattice spacing of the order of the Planck length offers a natural mechanism for pronounced quantum-gravity effects at distances much larger than the Planck length. A resolution of the black hole information paradox is proposed, according to which all information is stored in a crystal-phase remnant with size and mass much above the Planck scale.

Spinor and Twistor Geometry in Einstein Gravity and Finsler Modifications

We present a generalization of the spinor and twistor geometry for on (pseudo) Riemannian manifolds enabled with nonholonomic distributions or for Finsler-Cartan spaces modelled on tangent Lorentz bundles. Nonholonomic (Finsler) twistors are defined as solutions of generalized twistor equations determined by spin connections and frames adapted to nonlinear connection structures. We show that the constructions for local twistors can be globalized using nonholonomic deformations with "auxiliary" metric compatible connections completely determined by the metric structure and/or the Finsler fundamental function. We explain how to perform such an approach in the Einstein gravity theory formulated in Finsler like variables with conventional nonholonomic 2+2 splitting.

About Nonlinear Classic Field Theory of Connected Charges

On the basis of an exact solution for the field of a charge in a uniformly accelerated noninertial frame of reference (NFR) and formulated Equivalent Situation Postulate the nonlinear electrostatic theory of bound charges has been constructed. Proposed method is outside of the flat space-time, however the curvature is not directly connected with the Einstein gravitational theory. The method proposed eliminates divergence of the proper energy and makes classical electrodynamics consistent at any sufficiently small distances.

<i>f(R)</i> View of Lyttleton-Bondi Cosmological Model in Peres Spacetime

Over the last few years, among various alternatives to the Einstein theory of gravity, especially f(R) theories of gravity have received more importance due to number of interesting results in cosmology and astrophysics. Pandey [10] gave an f(R) theory of gravity to obtain conformally invariant gravitational waves in which field equations have the form given by (3). In this paper we have investigated Lyttleton Bondi Cosmological model in view of field equations of f(R) theory of gravity for Generalized Peres spacetime and finally a wave like solution is obtained.

Holography, entanglement entropy, and conformal field theories with boundaries or defects

We study entanglement entropy (EE) in conformal field theories (CFTs) in Minkowski space with a planar boundary or with a planar defect of any codimension. In any such boundary CFT (BCFT) or defect CFT (DCFT), we consider the reduced density matrix and associated EE obtained by tracing over the degrees of freedom outside of a (hemi-)sphere centered on the boundary or defect. Following Casini, Huerta, and Myers, we map the reduced density matrix to a thermal density matrix of the same theory on hyperbolic space. The EE maps to the thermal entropy of the theory on hyperbolic space. For BCFTs and DCFTs dual holographically to Einstein gravity theories, the thermal entropy is equivalent to the Bekenstein-Hawking entropy of a hyperbolic black brane. We show that the horizon of the hyperbolic black brane coincides with the minimal area surface used in Ryu and Takayanagi's conjecture for the holographic calculation of EE. We thus prove their conjecture in these cases. We use our results to compute the R\'enyi entropies and EE in DCFTs in which the defect corresponds to a probe brane in a holographic dual.

Growth index after the Planck results

The growth index ${\ensuremath{\gamma}}_{L}$ was proposed to investigate the possible deviation from the standard $\ensuremath{\Lambda}\mathrm{CDM}$ model and Einstein's gravity theory in a dynamical perspective. Recently, thanks to the measurement of the cosmic growth rate via the redshift-space distortion, one can understand the evolution of the density contrast through $f{\ensuremath{\sigma}}_{8}(z)$, where $f(z)=d\mathrm{ln}\ensuremath{\delta}/d\mathrm{ln}a$ is the growth rate of matter and ${\ensuremath{\sigma}}_{8}(z)$ is the rms amplitude of the density contrast $\ensuremath{\delta}$ at the comoving $8{h}^{\ensuremath{-}1}\text{ }\text{ }\mathrm{Mpc}$ scale. In this paper, we use the redshift-space distortion data points to study the growth index on the bases of Einstein's gravity theory and a modified gravity theory under the assumption of $f={\ensuremath{\Omega}}_{m}(a{)}^{{\ensuremath{\gamma}}_{L}}$. The cosmic background evolution is fixed by the cosmic observations from the type Ia supernovae SNLS3 data, cosmic microwave background radiation data from Planck, and baryon acoustic oscillations. Via the Markov Chain Monte Carlo method, we find the following ${\ensuremath{\gamma}}_{L}$ values for Einstein's gravity with a cosmological constant ($w=\mathrm{const}$) dark energy and a modified gravity theory in the 1, 2, and $3\ensuremath{\sigma}$ regions, respectively: ${0.675}_{\ensuremath{-}0.0662\ensuremath{-}0.120\ensuremath{-}0.155}^{+0.0611+0.129+0.178}$, ${0.745}_{\ensuremath{-}0.0819\ensuremath{-}0.146\ensuremath{-}0.190}^{+0.0755+0.157+0.205}$, and ${0.555}_{\ensuremath{-}0.0167\ensuremath{-}0.0373\ensuremath{-}0.0516}^{+0.0193+0.0335+0.0436}$. In Einstein's gravity theory, the values of the growth index ${\ensuremath{\gamma}}_{L}$ show an almost $2\ensuremath{\sigma}$ deviation from the theoretical prediction of $6/11$ for the $\ensuremath{\Lambda}\mathrm{CDM}$ model. However, in the modified gravity framework, a deviation from Einstein's relativity is not detected in the $1\ensuremath{\sigma}$ region. This implies that the currently available cosmic observations do not predict an alternative modified gravity theory beyond the $\ensuremath{\Lambda}\mathrm{CDM}$ model under Einstein's gravity, but that the simple assumption of $f={\ensuremath{\Omega}}_{m}^{{\ensuremath{\gamma}}_{L}}$ should be improved.

Geometrodynamics of Lovelock black holes

Lovelock gravity is arguably the most natural higher curvature, higher dimensional generalization of Einstein's theory of gravity. As shown in a previous paper (Kunstatter et al. arXiv:1210.1566; Kunstatter et al. Classical Quantum Gravity, 29, 092001 (2012) (Fast Track); arXiv:1201.4904.), the Hamiltonian for spherically symmetric Lovelock gravity is as simple as that of general relativity when written in terms of geometrodynamical variables (i.e., the areal radius and mass function). This result paves the way to the study of critical phenomena in black hole formation and the quantum mechanics of Lovelock black holes.

Maximum entropy principle for self-gravitating perfect fluid in Lovelock gravity

We consider a static self-gravitating system consisting of perfect fluid with isometries of an $(n-2)$-dimensional maximally symmetric space in Lovelock gravity theory. A straightforward analysis of the time-time component of the equations of motion suggests a generalized mass function. Tolman-Oppenheimer-Volkoff like equation is obtained by using this mass function and gravitational equations. We investigate the maximum entropy principle in Lovelock gravity, and find that this Tolman-Oppenheimer-Volkoff equation can also be deduced from the so called "maximum entropy principle" which is originally customized for Einstein gravity theory. This investigation manifests a deep connection between gravity and thermodynamics in this generalized gravity theory.

Charge expulsion from black brane horizons, and holographic quantum criticality in the plane

Quantum critical behavior in 2+1 dimensions is established via holographic methods in a 5+1-dimensional Einstein gravity theory with gauge potential form fields of rank 1 and 2. These fields are coupled to one another via a tri-linear Chern-Simons term with strength k. The quantum phase transition is physically driven by the expulsion of the electric charge from inside the black brane horizon to the outside, where it gets carried by the gauge fields which acquire charge thanks to the Chern-Simons interaction. At a critical value k=k_c, zero temperature, and any finite value of the magnetic field, the IR behavior is governed by a near-horizon Lifshitz geometry. The associated dynamical scaling exponent depends on the magnetic field. For k<k_c, the flow towards low temperature is governed by a Reissner-Nordstrom-like black brane whose charge and entropy density are non-vanishing at zero temperature. For k > k_c, the IR flow is towards the purely magnetic brane in AdS_6. Its near-horizon geometry is AdS_4 \times R^2, so that the entropy density vanishes quadratically with temperature, and all charge is carried by the gauge fields outside of the horizon.

European satellite to test Einstein's gravitational theory

European satellite to test Einstein's gravitational theory

Fractional Dynamics from Einstein Gravity, General Solutions, and Black Holes

We study the fractional gravity for spacetimes with non-integer dimensions. Our constructions are based on a geometric formalism with the fractional Caputo derivative and integral calculus adapted to nonolonomic distributions. This allows us to define a fractional spacetime geometry with fundamental geometric/physical objects and a generalized tensor calculus all being similar to respective integer dimension constructions. Such models of fractional gravity mimic the Einstein gravity theory and various Lagrange-Finsler and Hamilton-Cartan generalizations in nonholonomic variables. The approach suggests a number of new implications for gravity and matter field theories with singular, stochastic, kinetic, fractal, memory etc processes. We prove that the fractional gravitational field equations can be integrated in very general forms following the anholonomic deformation method for constructing exact solutions. Finally, we study some examples of fractional black hole solutions, fractional ellipsoid gravitational configurations and imbedding of such objects in fractional solitonic backgrounds.

THERMODYNAMICAL LAWS IN HOŘAVA–LIFSHITZ GRAVITY

In this work, we investigate the validity of the GSL of thermodynamics in the universe (open, closed and flat) governed by Hořava–Lifshitz (HL) gravity. If the universe contains barotropic fluid, we obtain the corresponding solutions. The validity of the GSL is examined by two approaches: (i) the robust approach and (ii) the effective approach. In the robust approach, we consider that the universe contains only matter fluid. Also, the effect of the gravitational sector of HL gravity is incorporated through the modified black hole entropy on the horizon. The effective approach is that all extra information of HL gravity is cast into an effective dark energy fluid, and so we consider that the universe contains matter fluid plus this effective fluid. This approach is essentially the same as Einstein's gravity theory. The general prescription for the validity of the GSL is discussed. Graphically, we show that the GSL may be satisfied for the open, closed and flat universes on the different horizons with different conditions.

A de Sitter Farey tail

We consider quantum Einstein gravity in three dimensional de Sitter space. The Euclidean path integral is formulated as a sum over geometries, including both perturbative loop corrections and nonperturbative instanton corrections coming from geometries with nontrivial topology. These nontrivial geometries have a natural physical interpretation. Conventional wisdom states that the sphere is the unique Euclidean continuation of de Sitter space. However, when considering physics only in the causal patch of a single observer other Euclidean geometries, in this case lens spaces, contribute to physical observables. This induces quantum gravitational effects which lead to deviations from the standard thermal behavior obtained by analytic continuation from the three sphere. The sum over these geometries can be formulated as a sum over cosets of the modular group; this is the de Sitter analog of the celebrated ``black hole Farey Tail.'' We compute the vacuum partition function including the sum over these geometries. Perturbative quantum corrections are computed to all orders in perturbation theory using the relationship between Einstein gravity and Chern-Simons theory, which is checked explicitly at tree and one-loop level using heat kernel techniques. The vacuum partition function, including all instanton and perturbative corrections, is shown to diverge in a way which cannot be regulated using standard field theory techniques.

STATIC SPHERICALLY SYMMETRIC SCALAR FIELD SPACETIMES WITH C0 MATCHING

All the classes of static massless scalar field models currently available in the Einstein theory of gravity necessarily contain a strong curvature naked singularity. We obtain here a family of solutions for static massless scalar fields coupled to gravity, which does not have any strong curvature singularity. This class of models contain a thin shell of singular matter, which has a physical interpretation. The central curvature singularity is, however, avoided which is common to all static massless scalar field spacetime models known so far. Our result thus points out that the full class of solutions in this case may contain non-singular models, which is an intriguing possibility.

The deformable universe

The concept of smooth deformations of a Riemannian manifolds, recently evidenced by the solution of the Poincar\'e conjecture, is applied to Einstein's gravitational theory and in particular to the standard FLRW cosmology. We present a brief review of the deformation of Riemannian geometry, showing how such deformations can be derived from the Einstein-Hilbert dynamical principle. We show that such deformations of space-times of general relativity produce observable effects that can be measured by four-dimensional observers. In the case of the FLRW cosmology, one such observable effect is shown to be consistent with the accelerated expansion of the universe.

Cosmological Classicalization: Maintaining Unitarity under Relevant Deformations of the Einstein-Hilbert Action

Generic relevant deformations of Einstein's gravity theory contain additional degrees of freedom that have a multifaceted stabilization dynamics on curved spacetimes. We show that these relevant degrees of freedom are self-protected against unitarity violations by the formation of classical field lumps that eventually merge to a new background geometry. The transition is heralded by the massive decay of the original vacuum and evolves through a strong coupling regime. This process fits in the recently proposed classicalization mechanism and extends it further to free field dynamics on curved backgrounds.