Ratbay Myrzakulov, Lorenzo Sebastiani
In this paper we analyze spherically symmetric static vacuum solutions with various topologies in mimetic gravity. When the Einstein's tensor is different from zero, a new class of solutions different from the Schwarzschild one emerges from the theory. We analyze the feature of the new solutions and we study the planar motion for the spherical case.
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In this work, we analyse static spherically symmetric solutions in the framework of mimetic gravity, an extension of general relativity where the conformal degree of freedom of gravity is isolated in a covariant fashion. Here we extend previous works by considering in addition a potential for the mimetic field. An appropriate choice of such potential allows for the reconstruction of a number of interesting cosmological and astrophysical scenarios. We explicitly show how to reconstruct such a potential for a general static spherically symmetric space-time. A number of applications and scenarios…
Newtonian and Post-Newtonian Aspects of Mimetic Gravity
本文对模拟引力开展最低阶后牛顿展开，分析太阳系尺度含义，证明非平凡模拟贡献的静态球对称时空不渐近平坦，并以准对数势项解释星系旋转曲线。
In this paper, we look for the vacuum static spherically symmetric solution in the mimetic gravity scenario based on the conformal invariance principle. The trivial solution is a stealth Schwarzschild black hole with scalar hair where the mimetic field does not contribute to the background. However, a solution with two naked singularities shows up when the mimetic scalar field contributes to the background. We show that one of these singularities is the same as the singularity at the center of standard Schwarzschild black hole while the other appears due to caustics formation. However, we cons…
Mimetic gravity is a Weyl-symmetric extension of General Relativity, related to the latter by a singular disformal transformation, wherein the appearance of a dust-like perfect fluid can mimic cold dark matter at a cosmological level. Within this framework, it is possible to provide an unified geometrical explanation for dark matter, the late-time acceleration, and inflation, making it a very attractive theory. In this review, we summarize the main aspects of mimetic gravity, as well as extensions of the minimal formulation of the model. We devote particular focus to the reconstruction techniq…
Inequivalence of mimetic gravity with models of loop quantum gravity
本文通过多个独立论证证明模拟引力与圈量子引力模型不等价，并指出涌现修正引力框架可高效分析此类问题，揭示了圈量子引力内不同实现方法的共存性。
We revisit the non-singular black hole solution in (extended) mimetic gravity with a limiting curvature from a Hamiltonian point of view. We introduce a parameterization of the phase space which allows us to describe fully the Hamiltonian structure of the theory. We write down the equations of motion that we solve in the regime deep inside the black hole, and we recover that the black hole has no singularity, due to the limiting curvature mechanism. Then, we study the relation between such black holes and effective polymer black holes which have been introduced in the context of loop quantum g…
We combine the unimodular gravity and mimetic gravity theories into a unified theoretical framework, which is proposed to provide a suggestive proposal for a framework that may assist in the discussion and solution search of the cosmological constant problem and of the dark matter issue. After providing the formulation of the unimodular mimetic gravity and investigating all the new features that the vacuum unimodular gravity implies, by using the underlying reconstruction method, we realize some well known cosmological evolutions, with some of these being exotic for the ordinary Einstein-Hilbe…
In this paper we study under which conditions the Reissner-Nordström-anti de Sitter black hole can be a solution of the vacuum mimetic $F(R)$ gravity with Lagrange multiplier and mimetic scalar potential. As we demonstrate, the resulting picture in the mimetic $F(R)$ gravity case, is different in comparison to the ordinary $F(R)$ gravity case, with the two descriptions resulting to a different set of constraints that need to hold true. We also investigate the metric perturbations in the mimetic $F(R)$ gravity case, for the Reissner-Nordström-anti de Sitter black hole metric, at first order of …
The vacuum, static, and spherically symmetric solutions in the mimetic Born-Infeld gravity are studied. The mimetic Born-Infeld gravity is a reformulation of the Eddington-inspired-Born-Infeld (EiBI) model under the mimetic approach. Due to the mimetic field, the theory contains non-trivial vacuum solutions different from those in Einstein gravity. We find that with the existence of the mimetic field, the spacelike singularity inside a Schwarzschild black hole could be altered to a lightlike singularity, even though the curvature invariants still diverge at the singularity. Furthermore, in thi…
We disclose the effects of an extra longitudinal degree of freedom on the evolution of perturbations in the framework of mimetic gravity. We consider a flat Friedmann-Robertson-Walker (FRW) background and explore the linear perturbations by adopting the spherically symmetric collapse formalism. By suitably choosing the potential of the mimetic field, we are able to solve the perturbed field equations in the linear regime and derive the matter density contrast δm in terms of the redshift parameter z. We observe that δm starts growing at the early stages and as the universe expands, it grows fas…
Starting from a local action for mimetic gravity that includes higher derivatives of a scalar field $ϕ$, we derive a gauge-fixed canonical action of the theory in the ADM canonical formalism in the time gauge $ϕ=t$. This reduced action reveals (i) a non-vanishing conserved physical Hamiltonian that is a sum of two terms, the expression for the Hamiltonian constraint of general relativity and a function of the expansion scalar, and (ii) a reduced symplectic structure that geometrically provides the Dirac brackets. As applications of our general analysis, we compute the physical Hamiltonians and…
The dynamics of the vacuum Kantowski-Sachs space-time are studied in the so-called limiting curvature mimetic gravity theory. It is shown that in this theory the vacuum Kantowski-Sachs space-time is always singular. While the departures from general relativity due to the limiting curvature mimetic theory do provide an upper bound on the magnitude of the expansion scalar, both its rate of oscillations and the magnitude of the directional Hubble rates increase without bound and cause curvature invariants to diverge. Also, since the radial scale factor does not vanish in finite (past) time, in th…
The Eddington-inspired-Born-Infeld (EiBI) model is reformulated within the mimetic approach. In the presence of a mimetic field, the model contains non-trivial vacuum solutions which could be free of spacetime singularity because of the Born-Infeld nature of the theory. We study a realistic primordial vacuum universe and prove the existence of regular solutions, such as primordial inflationary solutions of de Sitter type or bouncing solutions. Besides, the linear instabilities present in the EiBI model are found to be avoidable for some interesting bouncing solutions in which the physical metr…
Regular black holes and their relationship to polymerized models and mimetic gravity
本文利用广义 LTB 嵌入形式体系研究规则黑洞，提出重构算法从给定度规构造有效球对称模型及扩展 mimetic 引力拉格朗日量，并将其推广到非均匀尘埃坍缩模型。
Vacuum 5-D Einstein equations with spherical symmetry and t-dependence are considered. For the case of separating variables several classes of exact solutions are obtained. Effective matter, induced by geometrical scalar field is analyzed.
There is undetermined potential function $V(ϕ)$ in the action of mimetic gravity which should be resolved through physical means. In general relativity(GR), the static spherically symmetric(SSS) solution to the Einstein equation is a benchmark and its deformation also plays a crucial role in mimetic gravity. The equation of motion is provided with high nonlinearity, but we can reduce primal nonlinearity to a frequent Riccati form in the SSS case of mimetic gravity. In other words, we obtain an expression of solution to the functional differential equation of motion with any potential function.…
According to Birkhoff's theorem the only spherically symmetric solution of the vacuum Einstein field equations is the Schwarzschild solution. Inspite of imposing asymptotically flatness and staticness as initial conditions we obtain that these equations have general solutions with the Schwarzschild metric as merely a special and simplest form of them. It is possible to have perfect and smooth metrics with the same Newtonian and post-Newtonian limits of Schwarzschild by a convenient and correct selection.
It is shown that among the four classes of the static spherically symmetric solution of the vacuum Brans-Dicke theory of gravity only two are really independent. Further by matching exterior and interior (due to physically reasonable spherically symmetric matter source) scalar fields it is found that only Brans class I solution with certain restriction on solution parameters may represent exterior metric for a nonsingular massive object. The physical viability of the black hole nature of the solution is investigated. It is concluded that no physical black hole solution different from the Schwa…
The Lagrangian derivation of the Equations of Motion for topological static spherically symmetric metrics in $\mathcal F (R,G)$-modified gravity is presented and the related solutions are discussed. In particular, a new topological solution for the model $\mathcal F (R,G)=R+\sqrt{G}$ is found. The black hole solutions and the First Law of thermodynamic are analyzed. Furthermore, the coupling with electromagnetic field is also considered and a Maxwell solution is derived.
Different versions of consistent canonical realizations of hypersurface deformations of spherically symmetric space-times have been derived in models of loop quantum gravity, modifying the classical dynamics and sometimes also the structure of space-time. Based on a canonical version of effective field theory, this paper provides a unified treatment, showing that modified space-time structures are generic in this setting. The special case of Euclidean gravity demonstrates agreement also with existing operator calculations.
The exact static and spherically symmetric solutions of the vacuum field equations for a Higgs Scalar-Tensor theory (HSTT) are derived in Schwarzschild coordinates. It is shown that in general there exists no Schwarzschild horizon and that the fields are only singular (as naked singularity) at the center (i.e. for the case of a pont-particle). However, the Schwarzschild solution as in usual general relativity (GR) is obtained for the vanishing limit of Higgs field excitations.
Event Horizon Telescope observations exclude compact objects in baseline mimetic gravity
本研究通过事件视界望远镜对M87*和Sgr A*的观测，排除了基线模拟引力中的裸奇点和黑洞候选体，因其阴影性质异常，从而否定了该理论在宇宙学尺度上解释暗区的能力。
The Schwarzschild-deSitter metric is the known solution of Einstein field equations with cosmological constant term for vacuum spherically symmetric space around a point mass M. Recently it has been reported that in a $Lamda$-dominant world the Schwarzschild type coordinate systems are disqualified by redshift-magnitude test as a proper frame of reference(gr-qc/9812092). We derive the solution in a FRW type coordinate system which is qualified according to the mentioned test. Asymptotically it approachs to the non-static form of deSitter metric. The obtained metric is transformable to Schwarzs…
Spherically symmetric static vacuum solutions have been built in $f(T)$ models of gravity theory. We apply some conditions on the metric components; then the new vacuum spherically symmetric solutions are obtained. Also, by extracting metric coefficients we determine the analytical form of $f(T)$.
An analitical approximation of $<ϕ^2>$ for a massive scalar field in a zero temperature vacuum state in static spherically symmetric spacetimes is obtained. The calculations are based on the method for computing vacuum expectations values for scalar fields in general static spherically symmetric spacetimes derived by Anderson, Hiscock and Samuel [Phys. Rev. D {\bf 51}, 4337 (1995)]. The analitical approximation is used to compute $<ϕ^2>$ in Schwarzschild and wormhole spacetimes.
We study the foliation of a $D$-dimensional spherically symmetric black-hole spacetime with $D\ge 5$ by two kinds of one-parameter family of maximal hypersurfaces: a reflection-symmetric foliation with respect to the wormhole slot and a stationary foliation that has an infinitely long trumpet-like shape. As in the four-dimensional case, the foliations by the maximal hypersurfaces have the singularity avoidance nature irrespective of dimensionality. This indicates that the maximal slicing condition will be useful for simulating higher-dimensional black-hole spacetimes in numerical relativity. F…
We investigate the vacuum and charged spherically symmetric static solutions of the Einstein equations on cosmological background. The background metric is not flat, but curved, with constant - curvature spatial sections. Both vacuum and charged cases contain two branches. The first branches transform into the Schwarzschild and Reissner-Nordström solutions if the background metric goes to the Minkovski one. The second branches describe wormholes and have no Einstein limit.
We study the first cosmological implications of the mimetic theory of massive gravity recently proposed by Chamseddine and Mukhanov. This is a novel theory of ghost-free massive gravity which additionally contains a mimetic dark matter component. In an echo of other modified gravity theories, there are self-accelerating solutions which contain a ghost instability. In the ghost-free region of parameter space, the effect of the graviton mass on the cosmic expansion history amounts to an effective negative cosmological constant, a radiation component, and a negative curvature term. This allows us…
Static and spherically symmetric vacuum spacetimes with non-expanding principal null directions in $f(R)$ gravity
本文刻画了 f(R) 引力中主零方向非膨胀的静态球对称真空解，发现除 Nariai 时空外，在特定理论下存在四个非常数 Ricci 标量的新解，并简述其几何性质。
An analysis of conformal geodesics in the Schwarzschild-de Sitter and Schwarzschild-anti de Sitter families of spacetimes is given. For both families of spacetimes we show that initial data on a spacelike hypersurface can be given such that the congruence of conformal geodesics arising from this data cover the whole maximal extension of canonical conformal representations of the spacetimes without forming caustic points. For the Schwarzschild-de Sitter family, the resulting congruence can be used to obtain global conformal Gaussian systems of coordinates of the conformal representation. In the…
We consider the problem of picking a physically motivated vacuum state on a spherically symmetric spacetime with an extra conformal Killing vector, as opposed to an extra Killing vector as in the Schwarzschild case. Considering a conformal symmetry instead of a symmetry allows us to consider spacetimes that are dynamical and not static (like Schwarzschild). The extra conformal symmetry allows us to calculate the response of particle detectors however. We look at the specific example of a self-similar LTB spacetime that represents a spherically symmetric but inhomogeneous cosmology. We remark t…
Static spherically symmetric Kundt vacuum solutions of higher-derivative gravities
本文研究了具有宇宙学常数的二次引力理论及六阶引力中的特定模型的静态球对称Kundt解，分析了曲率奇点及引力波解的构造。
Gravitational wave constraints on the Paneitz operator
本文研究 Paneitz 运算符在扩展仿射引力理论中的行为，探讨其通过引力波传播速度修正对真空能量的可能影响。
Spherically symmetric static topological black hole solutions associated with some extended higher order gravitational models in the presence of a Maxwell-field are derived by means of simple Lagrangian method, based on spherically symmetric reduction. Some new topological black hole solutions are presented and the validity of the First Law is investigated, and in these cases an expression for the energy is provided.
The requirements are formulated which lead to the existence of the class of globally regular solutions to the minimally coupled GR equations which are asymptotically de Sitter at the center. The brief review of the resulting geometry is presented. The source term, invariant under radial boots, is classified as spherically symmetric vacuum with variable density and pressure, associated with an r-dependent cosmological term, whose asymptotic in the origin, dictated by the weak energy condition, is the Einstein cosmological term. For this class of metrics the ADM mass is related to both de Sitter…
Geometric structure of spherically-symmetric space-time in metric-affine gauge theory of gravity is studied. Restrictions on curvature tensor and Bianchi identities are obtained. By using certain simple gravitational Lagrangian the solution of gravitational equations for vacuum spherically-symmetric gravitational field is obtained.
Using self dual Ashtekar variables, we investigate (at the effective level) the spherically symmetry reduced model of loop quantum gravity, both in vacuum and when coupled to a scalar field. Within the real Ashtekar-Barbero formulation, the system scalar field coupled to spherically symmetric gravity is known to possess a non closed (quantum) algebra of constraints once the holonomy corrections are introduced, which forbids the loop quantization of the model. Moreover, the vacuum case, while not anomalous, introduces modifications which are usually interpreted as an effective signature change …
We extend previous results in spherically symmetric gravitational systems coupled with a massless scalar field within the loop quantum gravity framework. As starting point, we take the Schwarzschild spacetime. The results presented here rely on the uniform discretization method. We are able to minimize the associated discrete master constraint using a variational method. The trial state for the vacuum consists of a direct product of a Fock vacuum for the matter part and a Gaussian centered around the classical Schwarzschild solution. This paper follows the line of research presented by Gambini…
We develop an effective framework for the $\barμ$ scheme of holonomy corrections motivated by loop quantum gravity for vacuum spherically symmetric space-times. This is done by imposing the areal gauge in the classical theory, and then expressing the remaining components of the Ashtekar-Barbero connection in the Hamiltonian constraint in terms of holonomies of physical length $\ell_{\rm Pl}$. The stationary solutions to the effective Hamiltonian constraint can be found exactly, and we give the explicit form of the effective metric in Painlevé-Gullstrand coordinates. This solution has the corre…
We present the static spherically symmetric vacuum solutions of the Jordan, Brans-Dicke field equations. The new solutions are obtained by considering a polar Gaussian, isothermal and radial hyperbolic metrics.
We outline the class of globally regular spherically symmetric solutions to the minimally coupled GR equations asymptotically de Sitter in the origin and asymptotically Schwarzschild at infinity. A source term connects smoothly de Sitter vacuum at the regular center with Minkowski vacuum at infinity and corresponds to anisotropic spherically symmetric vacuum defined macroscopically by the algebraic structure of its stress-energy tensor invariant under boosts in the radial direction. De Sitter-Schwarzschild geometry describes a vacuum nonsingular black hole which evolves, in the course of Hawki…
We prove some theorems characterizing the global properties of static, spherically symmetric configurations of a self-gravitating real scalar field in general relativity (GR) in various dimensions, with an arbitrary potential $V$, not necessarily positive-definite. The results are extended to sigma models, scalar-tensor and curvature-nonlinear theories of gravity. We show that the list of all possible types of space-time causal structure in the models under study is the same as for a constant scalar field, namely, Minkowski (or AdS), Schwarzschild, de Sitter and Schwarzschild - de Sitter, and …
We analyse the vacuum static spherically symmetric space-time for a specific class of non-conservative theories of gravity based on the Rastall's theory. We obtain a new vacuum solution which has the same structure as the Schwarzschild-de Sitter solution in the General Relativity theory obtained with a cosmological constant playing the rôle of source. We further discuss the structure (in particular, the coupling to matter fields) and some cosmological aspects of the underline non-conservative theory
In this paper we investigate spherically symmetric vacuum solutions of $f(R)$ gravity in a higher dimensional spacetime. With this objective we construct a system of non-linear differential equations, whose solutions depend on the explicit form assumed for the function $F(R)=\frac{df(R)}{dR}$. We explicit show that for specific classes of this function exact solutions from the field equations are obtained; also we find approximated results for the metric tensor for more general cases admitting $F(R)$ close to the unity.
In this manuscript, we study the nearly flat approximation of a conformally invariant gravitational theory in metric measure space (MMS). In addition, we investigate the transformation of the energy-momentum tensor in this context and obtain the vacuum solution of MMS and its weak field limit in the spherically symmetric coordinates. We show that while it is already a vacuum solution, it can simulate dark matter when restricted to the framework of general relativity, i.e., a symmetry-broken conformal frame. This is done by employing a density function which is an essential part of MMS. We deri…
In this paper we study properties that the vacuum must possess in the minimal extension to the teleparallel equivalent of general relativity (TEGR) where the action is supplemented with a quadratic torsion term. No assumption is made about the weakness of the quadratic term although in the weak-field regime the validity of our previously derived perturbative solution is confirmed. Regarding the exact nature of the vacuum, it is found that if the center of symmetry is to be regular, the mathematical conditions on the tetrad at the isotropy point mimic those of general relativity. With respect t…
Vacuum Static Spherically Symmetric Spacetimes in Harada's Theory
本文推导了Harada引力理论中最一般的球对称静态真空解，并指出该理论解具有非平凡二阶Killing张量，可用于研究测地线运动。
We prove that, for a given spherically symmetric fluid distribution with tangential pressure on an initial spacelike hypersurface with a timelike boundary, there exists a unique, local in time solution to the Einstein equations in a neighbourhood of the boundary. As an application, we consider a particular elastic fluid interior matched to a vacuum exterior.
We show that Schwarzschild geometry remains as a vacuum solution for those four-dimensional f(T) gravitational theories behaving as ultraviolet deformations of general relativity. In the gentler context of three-dimensional gravity, we also find that the infrared-deformed f(T) gravities, like the ones used to describe the late cosmic speed up of the Universe, have as the circularly symmetric vacuum solution a Deser-de Sitter or a BTZ-like spacetime with an effective cosmological constant depending on the infrared scale present in the function f(T).
We study gravity coupled to a scalar field in spherical symmetry using loop quantum gravity techniques. Since this model has local degrees of freedom, one has to face ``the problem of dynamics'', that is, diffeomorphism and Hamiltonian constraints that do not form a Lie algebra. We tackle the problem using the ``uniform discretization'' technique. We study the expectation value of the master constraint and argue that among the states that minimize the master constraint is one that incorporates the usual Fock vacuum for the matter content of the theory.
Particle dynamics in spherically symmetric electro-vacuum instantons
该文研究球对称电真空欧几里得解中的测地线运动，推导ERN与BR时空的运动方程与解析解，发现欧几里得史瓦西时空轨道偏转可正可负，还开发了绘制轨道与阴影的Python代码。
We prove a new global existence result for the asymptotically flat, spherically symmetric Einstein-Vlasov system which describes in the framework of general relativity an ensemble of particles which interact by gravity. The data are such that initially all the particles are moving radially outward and that this property can be bootstrapped. The resulting non-vacuum spacetime is future geodesically complete.
Starting from a spherically symmetric tetrad with three unknown functions of the radial coordinate, a general solution of Møller's field equations in case of spherical symmetry nonsingular black hole is derived. The previously obtained solutions are verified as special cases of the general solution. The general solution is characterized by an arbitrary function and two constants of integration. The general solution gives no more than the spherically symmetric nonsingular black hole solution. The energy content of the general solution depends on the asymptotic behavior of the arbitrary function…
The vacuum solutions around a spherically symmetric and static object in the Starobinsky model are studied with a perturbative approach. The differential equations for the components of the metric and the Ricci scalar are obtained and solved by using the method of matched asymptotic expansions. The presence of higher order terms in this gravity model leads to the formation of a boundary layer near the surface of the star allowing the accommodation of the extra boundary conditions on the Ricci scalar. Accordingly, the metric can be different from the Schwarzschild solution near the star dependi…
A class of static spherically symmetric solutions in $f(Q)$-gravity
本文分析了$f(Q)$-引力中的拓扑静态球对称真空解，通过引入特定Ansatz确保在非度规标量为常数时解满足场方程，并提供了黑洞和可穿越虫洞形式的局部解。
The field equations of a special class of tetrad theory of gravitation have been applied to tetrad space having three unknown functions of radial coordinate. The spherically symmetric vacuum stress-energy momentum tensor with one assumption concerning its specific form generates two non-trivial different exact analytic solutions for these field equations. For large $r$, the exact analytic solutions coincide with the Schwarzschild solution, while for small $r$, they behave in a manner similar to the de Sitter solution and describe a spherically symmetric black hole singularity free everywhere. …
Exotic spherically-symmetric Lambda-vacuum in the four-dimensional Starobinsky model
该研究在四维Starobinsky模型中发现了一个精确的球对称Λ真空解家族，揭示了其物理病态及极端脆弱性。
The general structure of the spherically symmetric solutions in the Weyl conformal gravity is described. The corresponding Bach equations are derived for the special type of metrics, which can be considered as the representative of the general class. The complete set of the pure vacuum solutions is found. It consists of two classes. The first one contains the solutions with constant two-dimensional curvature scalar of our specific metrics, and the representatives are the famous Robertson--Walker metrics. One of them we called the "gravitational bubbles", which is compact and with zero Weyl ten…
A canonical formalism for spherical symmetry, originally developed by Kuchař to describe vacuum Schwarzschild black holes, is extended to include a spherically symmetric, massless, scalar field source. By introducing the ADM mass as a canonical coordinate on phase space, one finds that the super-Hamiltonian and supermomentum constraints for the coupled system simplify considerably. Yet, despite this simplification, it is difficult to find a functional time formalism for the theory. First, the configuration variable that played the role of time for the vacuum theory is no longer a spacetime sca…
A non-diagonal spherically symmetric tetrad field, involving four unknown functions of radial coordinate $r$, is applied to the equations of motion of f(T) gravity theory. A special exact vacuum solution with one constant of integration is obtained. The scalar torsion related to this special solution vanishes. To understand the physical meaning of the constant of integration we calculate the energy associated with this solution and show how it is related to the gravitational mass of the system.
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