John Miritzis
It is argued that the solution space of the equation determining the class of $f(R)$ theories which admit an Einstein static universe should be broadened by including the algebraic roots.
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We reconsider the cosmic string perturbative solution to the classical fourth-order gravity field equations, obtained in Ref.\cite{CLA94}, and we obtain that static, cylindricaly symmetric gauge cosmic strings, with constant energy density, can contain only $β$-terms in the first order corrections to the interior gravitational field, while the exact exterior solution is a conical spacetime with deficit angle $D=8πμ$.
Some mathematical errors of the paper commented upon [W.-M. Suen, Phys. Rev. D 40, (1989) 315] are corrected.
We investigate whether or not an Einstein Static universe is a solution to the cosmological equations in $f(R)$ gravity. It is found that only one class of $f(R)$ theories admits an Einstein Static model, and that this class is neutrally stable with respect to vector and tensor perturbations for all equations of state on all scales. Scalar perturbations are only stable on all scales if the matter fluid equation of state satisfies $c_s^2>\frac{\sqrt{5}-1}{6}\approx 0.21$. This result is remarkably similar to the GR case, where it was found that the Einstein Static model is stable for $c_s^2>{1/…
We argue that several statements in Phys. Rev. Lett. 124, 081301 (2020) are not correct.
We critically examine the Roberts homothetic solution for the spherically symmetric Einstein-scalar field equations in double null coordinates, and show that the Roberts solution indeed solves the field equations only for one non-trivial case. We generalize this solution and discuss its relations with other known exact solutions.
We generalize for the case of arbitrary hydrodynamical matter the quasi-isotropic solution of Einstein equations near cosmological singularity, found by Lifshitz and Khalatnikov in 1960 for the case of radiation-dominated universe. It is shown that this solution always exists, but dependence of terms in the quasi-isotropic expansion acquires a more complicated form.
Purely time dependent solutions in four-dimensional Einstein-Cartan-Kalb-Ramond (ECKR) theory of gravity are shown not to be possible leading to a trivial vanishing of all Kalb-Ramond fields. This result seems to contradict previously results obtained by SenGupta et al. (Class. and Quantum Gravity 19(2002)677) where de Sitter spacetime solution is found as an example of opticaly active spacetime. It seems that only inhomogeneous KR fields are possible in four-dimensional torsioned spacetimes.
H. Akbar-Zadeh has recently proposed (J Geom Phys 17 (1995) 342) a new geometric formulation of Einstein-Maxwell system with source in terms of what are called "Generalized Einstein manifolds". We show that, contrary to the claim, Maxwell equations have not been derived in this formulation and that, the assumed equations can be identified only as source-free Maxwell equations in the proposed geometric set up. A genuine derivation of source-free Maxwell equations is presented within the same framework. We draw a conclusion that the proposed unification scheme can pertain only to source-free sit…
It is argued that in the paper by A.A. Garcia-Diaz and G. Gutierrez-Cano [Phys. Rev. D 100, 064068 (2019)] on nonlinear electrodynamics coupled to general relativity, along with some interesting results and useful observations, many statements are either inaccurate or incomplete. In particular, the authors only consider solutions with an electric charge, whereas their magnetic counterparts have features of equal interest, both similar to and different from those of electric ones. Moreover, it is not mentioned that in electric solutions with a regular center the Lagrangian function $L(f)$ ($f =…
The recent numerical results of Dubeibe et al. [arXiv:1812.08663] were interpreted as hinting at the existence of a fourth constant of motion (Carter's constant) for geodesics on Chazy-Curzon spacetimes. Here we show that, to the contrary, the geodesic dynamics of the single-particle Chazy-Curzon spacetime exhibit features of a non-integrable system: chaotic orbits in the meridian plane, and Birkhoff chains in the surface of section. Thus, one should not expect Liouville-integrability, nor a fourth constant, for this system.
A recent paper studies a modification of Einstein-aether theory in which the aether vector is restricted, at the level of the action, to be the gradient of a scalar. In this comment we note that this scalar version of Einstein-aether theory is equivalent to the projectable version of the IR limit of Hořava gravity when the potential for the scalar is constant. This provides a generally covariant formulation for projectable Hořava gravity.
We summarize our proof that the "Einstein-Gauss-Bonnet Gravity in Four-Dimensional Spacetime" introduced in Phys. Rev. Lett. 124, 081301 (2020) does not have consistent field equations, as such the theory does not exist. The proof is given in both the metric and the first order formalisms.
We show that in the exponential $f(T)$ model studied by E. Linder [arXiv:1005.3039, Phys.Rev.D 81, 127301 (2010)], it is impossible to have the crossing of the phantom divide line $w_{\mathrm{DE}}=-1$.
Recently, an approximated solution of the Einstein equations for a rotating body whose mass effects are negligible with respect to the rotational ones has been derived by Tartaglia. At first sight, it seems to be interesting because both external and internal metric tensors have been consistently found, together an appropriate source tensor; moreover, it may suggest possible experimental checks since the conditions of validity of the considered metric are well satisfied at Earth laboratory scales. However, it should be pointed out that reasonable doubts exist if it is physically meaningful bec…
We consider the Einstein equation with first order (semiclassical) quantum corrections. Although the quantum corrections contain up to fourth order derivatives of the metric, the solutions which are physically relevant satisfy a reduced equations which contain derivatives no higher than second order. We obtain the reduced equations for a range of stress-energy tensors. These reduced equations are suitable for numerical solution, are expected to contain fewer numerical instabilities than the original fourth order equations, and yield only physically relevant solutions. We give analytic and nume…
We study the stability of Schwarzschild-Tangherlini (ST) black holes in fourth-order gravity which provides a higher dimensional linearized massive equation. The linearized-Ricci tensor perturbation is employed to exhibit unstable modes featuring the Gregory-Laflamme (GL) instability of higher dimensional black strings, in comparison to the stable ST black holes in Einstein gravity. It turns out that the GL instability of the ST black holes in the fourth-order gravity originates from the massiveness, but not a nature of fourth-order derivative theories giving ghost states.
This is the second paper in a series describing a numerical implementation of the conformal Einstein equation. This paper deals with the technical details of the numerical code used to perform numerical time evolutions from a "minimal" set of data. We outline the numerical construction of a complete set of data for our equations from a minimal set of data. The second and the fourth order discretisations, which are used for the construction of the complete data set and for the numerical integration of the time evolution equations, are described and their efficiencies are compared. By using the …
We consider cosmological dynamics in fourth order gravity with both $f(R)$ and $Φ(\mathcal {G})$ correction to the Einstein gravity ($\mathcal{G}$ is the Gauss-Bonnet term). The particular case for which both terms are equally important on power-law solutions is described. These solutions and their stability are studied using the dynamical system approach. We also discuss condition of existence and stability of de Sitter solution in a more general situation of power-law $f$ and $Φ$.
For the non-tachyonic curvature squared action we show that the expanding Bianchi-type I models tend to the dust-filled Einstein-de Sitter model for t tending to infinity if the metric is averaged over the typical oscillation period. Applying a conformal equivalence between curvature squared action and a minimally coupled scalar field (which holds for all dimensions > 2) the problem is solved by discussing a massive scalar field in an anisotropic cosmological model.
Comment on ''The space-time line element for static ellipsoidal objects''
该文评论指出，所提出的椭球体度规不满足真空爱因斯坦方程，因其产生非零压力，而非真空解。
We show that the black hole perturbations of the Hayward static solution to the massless Einstein-Klein-Gordon equations are actually gauge artifacts resulting from the linearization of a coordinate transformation.
This is a comment on a reply (gr-qc/9601040) to a comment (gr-qc/9606045) on a paper of Hellaby & Dray (gr-qc/9404001), repeating the identification of an important mistake which is still being denied by the authors: their proposed solutions do not satisfy the Einstein- Klein-Gordon equations at a change of signature. Substitution of the proposed solutions into the Einstein-Klein-Gordon equations in unit normal coordinates yields Dirac delta terms describing source layers at the junction. Hellaby & Dray's criticisms of this straightforward calculation are absurd: it does not involve "imaginary…
We present techniques for successfully performing numerical relativity simulations of binary black holes with fourth-order accuracy. Our simulations are based on a new coding framework which currently supports higher order finite differencing for the BSSN formulation of Einstein's equations, but which is designed to be readily applicable to a broad class of formulations. We apply our techniques to a standard set of numerical relativity test problems, demonstrating the fourth-order accuracy of the solutions. Finally we apply our approach to binary black hole head-on collisions, calculating the …
The necessity of this Comment was invoked by numerous mistakes, erroneous discussions and misleading citations curiously collected in the paper of F.J.Ernst, V.S.Manko and E.Ruiz and concerning the interrelations between two integral equation methods developed for solution of Einstein - Maxwell equations more than twenty five years ago. At first, we clarify the origin of the errors in the paper of F.J.Ernst, V.S.Manko and E.Ruiz which gave rise to so curious authors "conclusions" as that the monodromy transform integral equations "...are simple combinations of Sibgatullin's integral equations …
Comments on the paper 'Static solutions of the Vlasov-Einstein system' by G. Wolansky
本文指出了Wolansky关于Einstein-Vlasov系统静态解存在性证明中的错误，并探讨了带障碍变分问题及能量-Casimir泛函局部极小值的求解困难。
We investigate the classical stability of Schwarzschild-AdS black hole in a massive theory of the Einstein-Weyl gravity. It turns out that the linearized Einstein tensor perturbations exhibit unstable modes featuring the Gregory-Laflamme instability of five-dimensional AdS black string, in contrast to the stable Schwarzschild-AdS black hole in the Einstein-Weyl gravity. We confirm that the instability of the black hole in the Einstein-Weyl gravity arises from the massiveness but not a feature of fourth-order derivative theory giving ghost states.
An analytic understanding of the geodesic structure around non-Kerr spacetimes will result in a powerful tool that could make the mapping of spacetime around massive quiescent compact objects possible. To this end, I present an analytic closed form expression for the components of a the fourth order Killing tensor for Stationary Axisymmetric Vacuum (SAV) Spacetimes. It is as yet unclear what subset of SAV spacetimes admit this solution. The solution is written in terms of an integral expression involving the metric functions and two specific Greens functions. A second integral expression has t…
We study the Einstein-singleton theory during de Sitter inflation since it provides a way of degenerate fourth-order scalar theory. We obtain an exact solution expressed in terms of the exponential-integral function by solving the degenerate fourth-order scalar equation in de Sitter spacetime. Furthermore, we find that its power spectrum blows negatively up in the superhorizon limit, while it is negatively scale-invariant in the subhorizon limit. This suggests that the Einstein-singleton theory contains the ghost-instability and thus, it is not suitable for developing a slow-roll inflation mod…
The Wilson approximate dynamics and the Einstein dynamics are compared for binary systems. At the second post-Newtonian approximation, genuine two-body aspects are found to differ by up to 114\%. In the regime of a formal innermost stable circular orbit (ISCO) the both dynamics differ by up to 7\%.
The field equations following from a Lagrangian L(R) will be deduced and solved for special cases. If L is a non-linear function of the curvature scalar, then these equations are of fourth order in the metric. In the introduction we present the history of these equations beginning with the paper of H. Weyl from 1918, who first discussed them as alternative to Einstein's theory. In the third part, we give details about the cosmic no hair theorem, i.e., the details how within fourth order gravity with L= R + R^2 the inflationary phase of cosmic evolution turns out to be a transient attractor. Fi…
Comment: Exact vacuum solution with Hopf structure in general relativity
指出Harada最近宣称的Kerr-Schild解与已知NUT解之一等距。
The convergence properties of numerical Regge calculus as an approximation to continuum vacuum General Relativity is studied, both analytically and numerically. The Regge equations are evaluated on continuum spacetimes by assigning squared geodesic distances in the continuum manifold to the squared edge lengths in the simplicial manifold. It is found analytically that, individually, the Regge equations converge to zero as the second power of the lattice spacing, but that an average over local Regge equations converges to zero as (at the very least) the third power of the lattice spacing. Numer…
Kossowski and Kriele derived boundary conditions on the metric at a surface of signature change. We point out that their derivation is based not only on certain smoothness assumptions but also on a postulated form of the Einstein field equations. Since there is no canonical form of the field equations at a change of signature, their conclusions are not inescapable. We show here that a weaker formulation is possible, in which less restrictive smoothness assumptions are made, and (a slightly different form of) the Einstein field equations are satisfied. In particular, in this formulation it is p…
We comment on the paper [1] by Albert Einstein from 1918 to Willem De Sitter's solution [2] of the Einstein field equation from today's point of view. To this end, we start by describing the geometry of the De Sitter space-time and present its importance for the inflationary cosmological model.
Runaway solutions can be avoided in fourth order gravity by a doubling of the matter operator algebra with a symmetry constraint with respect to the exchange of observable and hidden degrees of freedom together with the change in sign of the ghost and the dilaton fields. The theory is classically equivalent to Einstein gravity, while its non-unitary Newtonian limit is compatible with the wavelike properties of microscopic particles and the classical behavior of macroscopic bodies, as well as with a trans-Planckian regularization of collapse singularities. A unified reading of ordinary and blac…
A fourth order generalized f(R) gravity theory (FOG) is considered with the Einstein-Hilbert action $R+aR^{2}+bR_{μν}R^{μν},$ $R_{μν}$ being Ricci\'{}s tensor and R the curvature scalar. The field equations are applied to spherical bodies where Newtonian gravity is a good approximation. The result is that for $0\leq a\sim -b<<R^{2}$, $R$ being the body radius, the gravitational field outside the body contains two Yukawas, one attractive and the other one repulsive, in addition to the Newtonian term. For $a\sim -b>>R^{2}$ the gravitational field near the body is zero but at distances greater th…
We reveal an underlying flaw in Reginald T. Cahill's recently promoted quantum foam inflow theory of gravity. It appears to arise from a confusion of the idea of the Galilean invariance of the acceleration of an individual flow with what is obtained as an acceleration when a homogeneous flow is superposed with an inhomogeneous flow. We also point out that the General Relativistic covering theory he creates by substituting a generalized Painleve-Gullstrand metric into Einstein's field equations leads to absurd results.
We revisit some properties of AdS$_2$ Einstein-Maxwell gravity with the aim of reconciling apparently conflicting results in prior literature. We show that the two dimensional theory can be obtained as a dimensional reduction of the three dimensional Einstein gravity with the CSS boundary condition. In general, this theory on AdS$_2$ can be viewed as an effective theory of the near horizon geometry of a (near-)extremal black hole. We provide an interpretation of our results in terms of the microscopic description of an extremal black hole.
An approximation to General Relativity is presented that agrees with the Einstein field equations up to and including the fourth post-Newtonian (PN) order. This approximation is formulated in a fully constrained scheme: all involved equations are explicitly elliptic except the wave equation that describes the two independent degrees of freedom of the gravitational field. The formalism covers naturally the conformal-flat-condition (CFC) approach by Isenberg, Wilson, and Mathews and the improved second PN-order exact approach CFC+. For stationary configurations, like Kerr black holes, agreement …
Starting with the MacDowell-Mansouri formulation of gravity with a $SO(4,1)$ gauge group, we introduce new parameters into the action to include the non-dynamical Holst term, and the topological Nieh-Yan and Pontryagin classes. Then, we consider the new parameters as fields and analyze the solutions coming from their equations of motion. The new fields introduce torsional contributions to the theory that modify Einstein's equations.
We discuss the instabilities appearing in the cosmological model with a quasi de Sitter phase following from a fourth-order gravity theory. Both the classical equation as well as the quantization in form of a Wheeler - De Witt equation are conformally related to the analogous model with Einstein's theory of gravity with a minimally coupled scalar field. Results are: 1. In the non-tachyonic case, classical fourth-order gravity is not more unstable than Einstein's theory itself. 2. The well-known classically valid conformal relation is also (at least for some typical cases) valid on the level of…
The Fokker action of point-particle binaries at the fourth post-Newtonian (4PN) approximation of general relativity has been determined previously. However two ambiguity parameters associated with infra-red (IR) divergencies of spatial integrals had to be introduced. These two parameters were fixed by comparison with gravitational self-force (GSF) calculations of the conserved energy and periastron advance for circular orbits in the test-mass limit. In the present paper together with a companion paper, we determine both these ambiguities from first principle, by means of dimensional regulariza…
We give a definition and derive the equations of motion for the center of mass and angular momentum of an axially symmetric, isolated system that emits gravitational and electromagnetic radiation. A central feature of this formulation is the use of Newman-Unti cuts at null infinity that are generated by worldlines of the spacetime. We analyze some consequences of the results and comment on the generalization of this work to general asymptotically flat spacetimes.
We study a class of almost scale-invariant modified gravity theories, using a particular form of $f(R, G) = αR^2 + βG \log G$ where $R$ and $G$ are the Ricci and Gauss-Bonnet scalars, respectively and $α$, $β$ are arbitrary constants. We derive the Einstein-like field equations to first order in cosmological perturbation theory in longitudinal gauge.
The cosmology of general fourth order corrections to Einstein gravity is considered, both for a homogeneous and isotropic background and for general tensor perturbations. It is explicitly shown how the standard cosmological history can be (approximately) reproduced and under what condition the evolution of the tensor modes remain (approximately) unchanged. Requiring that the deviations from General Relativity are small during inflation sharpens the current constraints on such corrections terms by some thirty orders of magnitude. Taking a more conservative approach and requiring only that cosmo…
Pauli-Villars and the ultraviolet completion of Einstein gravity
本文通过Pauli-Villars正规化程序构造了一个无鬼、幺正且功率计数可重整的二阶加四阶导数引力理论，作为标准量子Einstein引力的紫外完备。
Einstein field equations are second-order differential equations. In this paper, we propose a new gravity theory with pure fourth-order field equations, which we call 4G for brevity. We discuss the applications of 4G in cosmology, gravitational waves, and local gravitational systems. 4G predicts the scale factor $a\propto t^{4/3}$ for the matter-dominated universe, and $a\propto t$ for the radiation-dominated universe. The former can explain the late-time acceleration without suffering from the coincidence and fine-tuning problems, while the latter can solve the horizon problem. 4G is a massle…
We review and strengthen the arguments given by Einstein to derive his first gravitational field equation for static fields and show that, although it was ultimately rejected, it follows from General Relativity (GR) for negligible pressure. Using this equation and considerations folowing directly from the equivalence principle (EP), we show how Schwarzschild metric and other vacum metrics can be obtained immediately. With this results and some basic principles, we obtain the metric in the general spherically symmetric case and the corresponding hydrostatic equilibrium equation. For this metric…
The fourth order Weyl gravity theory of Mannheim and Kazanas is based on replacing the Einstein-Hilbert action with the square of the Weyl tensor, and on modifying the matter action of the standard model of particle physics to make it conformally invariant. This theory has been suggested as a model of both dark matter and dark energy. We argue that the conformal invariance is not a fundamental property of the theory, and instead is an artifact of the choice of variables used in its description. We deduce that in the limit of weak fields and slow motions the theory does not agree with the predi…
In 1989, Burnett conjectured that, under appropriate assumptions, the limit of highly oscillatory solutions to the Einstein vacuum equations is a solution of the Einstein--massless Vlasov system. In a recent breakthrough, Huneau--Luk (arXiv:1907.10743) gave a proof of the conjecture in U(1)-symmetry and elliptic gauge. They also require control on up to fourth order derivatives of the metric components. In this paper, we give a streamlined proof of a stronger result and, in the spirit of Burnett's original conjecture, we remove the need for control on higher derivatives. Our methods also apply…
The interface between a big bubble of true AdS$_D$ vacuum expanding inside a false AdS$_D$ vacuum is a model of an inflating $D-1$ dimensional universe. It looks like an interesting setup to study fundamentals of inflation. A recent computation shows that the prediction of this model for the wavefunction of the universe disagrees with that of Hartle and Hawking. We show that this discrepancy is because the effective $D-1$ dimensional description of the model is spin-$0$ (Nordström) gravity rather than spin-2 (Einstein) gravity.
There has been considerable interest in the possible cosmic string configurations and Y. Yang has recently derived intriguing obstructions to the existence of cylindrically symmetric solutions in the Bogomol'nyi critical phase of the Einstein-Maxwell-Higgs system. In this comment, we would like to mention some earlier results and recent progress which were not reflected there but are important in connection with the obstructions he claimed. Some of his obstructions are not consistent with the ealier results. Also, we give a new condition stronger than those found before.
Recently in Phys. Rev. D 88, 027504 (2013) Yoon has suggested that there may be problems for the non-relativistic limit of the conformal gravity theory. Here we show that Yoon's results only hold because of the assumption that gravitational sources can be treated the same way that they are treated in standard Newton-Einstein gravity. Since such an assumption violates the theory's underlying conformal invariance,Yoon's conclusions are invalidated.
The linear- and quadratic-in-spin contributions to the binding potential and gravitational-wave flux from binary systems are derived to next-to-next-to-leading order in the Post-Newtonian (PN) expansion of general relativity, including finite-size and tail effects. The calculation is carried out through the worldline effective field theory framework. We find agreement in the overlap with the available PN literature and test-body limit. As a direct application, we complete the knowledge of spin effects in the evolution of the orbital phase for aligned-spin circular orbits to fourth PN order. We…
Ibohal, Ishwarchandra and Singh proposed a class of exact, non-vacuum and conformally flat solutions of Einstein's equations whose stress tensor $T_{ab}$ has negative pressure. We show that $T_{ab}$ corresponds to an anisotropic fluid and the equation of state parameter seems not to be $ω= -1/2$. We consider the authors' constant cannot be the mass of a test particle but is related to a Rindler acceleration of a spherical distribution of uniformly accelerating observers.
It has been recently claimed in [arXiv:2211.12327] that an action of the Einstein-Palatini form plus a torsionless Pontryagin term (multiplied by a constant) represents a counterexample to the conclusions of [arXiv:0705.1879], namely, that Lovelock gravity is the only case in which the metric and metric-affine formulations of gravity are equivalent. However, given that the Pontryagin term (multiplied by a constant) can be written as a total D-divergence, it is a textbook matter to realise that the addition of such (or any other) D-divergence only affects at the boundary, leaving invariant the …
Einstein gravity with extra dimensions or alternative gravity theories might suggest that the gravity propagation speed can be different from the light speed. Such a difference may play a vital role in the primordial universe. In recent, Kopeikin and Fomalont claimed the first measurement of the gravity speed by VLBI. However, the measurement has no relevance with the speed of gravity as I had shown before the observation was done. It seems that our conclusion has been established well by re-examining recent papers with great care.
Recently a family of solutions of Einstein equations in backgrounds with broken Lorentz invariance was found ArXiv:0712.1136. We show that the gravitational solution recently obtained by Kachru, Liu and Mulligan in ArXiv:0808.1725 is a part of the former solution which was derived earlier in the framework of extra dimensional theories. We show how the energy-momentum and Einstein tensors are related and establish a correspondence between parameters which govern Lorentz invariance violation. Then we demonstrate that scaling behavior of two point correlation functions of local operators in scala…
Several time dependent backgrounds, with perfect fluid matter, can be used to construct solutions of Einstein equations in the presence of a negative cosmological constant along with some matter sources. In this work we focus on the non-vacuum Kasner-AdS geometry and its solitonic generalization. To characterize these space-times, we provide ways to embed them in higher dimensional flat space-times. General space-like geodesics are then studied and used to compute the two point boundary correlators within the geodesic approximation.
We construct a classical solution of an Einstein-Yang-Mills system with a fourth order term with respect to the field strength of the Yang-Mills field. The solution provides a spontaneous compactification proposed by Cremmer and Scherk; ten-dimensional space-time with a cosmological constant is compactified to the four-dimensional Minkowski space with a six-dimensional sphere S^6 on which an instanton solution exists. The radius of the sphere is not a modulus but is determined by the gauge coupling and the four-derivative coupling constants and the Newton's constant. We also construct a soluti…
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