Classical scalar fields have been considered as a possible effective description of dark matter. We show that, for any metric theory of gravity, no static, spherically symmetric, regular, spatially localized, attractive, stable spacetime configuration can be sourced by the coherent excitation of a scalar field with positive definite energy density and no Noether charges. In the weak-field regime the result also applies for configurations with a repulsive gravitational potential. This extends Derrick's theorem to the case of a general (non-canonical) scalar field, including the self-gravitational effects. Some possible ways out are briefly discussed.
In this paper we give a complete classification of spherically symmetric static space-times by their Noether symmetries. The determining equations for Noether symmetries are obtained by using the usual Lagrangian of a general spherically symmetric static spacetime which are integrated for each case. In particular we observe that spherically symmetric static spacetimes are categorized into six distinct classes corresponding to Noether algebra of dimensions 5, 6, 7, 9, 11 and 17. Using Noether`s theorem we also write down the first integrals for each class of such spacetimes corresponding to the…
The solutions for the field equations of $f(R)$ gravity are investigated in static cylindrically symmetric space-time. Conserved quantities of the system, as well as unknown functions, can be determined with the help of the Noether symmetry method. In this article, some unknown values of the equations of state parameter (EoS) have emerged as a result of the constraints obtained by analyzing the Noether symmetry equations for the $f(R)=f_0 R$ case. Consequently, several new exact solutions have been found for cases of General Relativity in static cylindrically symmetrical space-time for the non…
In this paper, we analyze static traversable wormholes via Noether symmetry technique in modified Gauss-Bonnet $f(\mathcal{G})$ theory of gravity (where $\mathcal{G}$ represents Gauss-Bonnet term). We assume isotropic matter configuration and spherically symmetric metric. We construct three $f(\mathcal{G})$ models, i.e, linear, quadratic and exponential forms and examine the consistency of these models. The traversable nature of wormhole solutions is discussed via null energy bound of the effective stress-energy tensor while physical behavior is studied through standard energy bounds of isotro…
Noether and Mei symmetries in static spherically symmetric quadratic gravity: variational consistency, constraints, and conserved curvature flux
The British University in Egypt（埃及英国大学）；North-West University（西北大学）；Imam Mohammad Ibn Saud Islamic University (IMSIU)（伊马姆穆罕默德·本·沙特伊斯兰大学）；Fukushima University（福岛大学）
In this paper we describe 4-dimensional gravity coupled to scalar and Maxwell fields by the Einstein-Katz action, that is, the covariant version of the "Gamma-Gamma $-$ Gamma-Gamma" part of the Hilbert action supplemented by the divergence of a generalized "Katz vector". We consider static solutions of Einstein's equations, parametrized by some integration constants, which describe an ensemble of asymptotically AdS black holes. Instead of the usual Dirichlet boundary conditions, which aim at singling out a specific solution within the ensemble, we impose that the variation of the action vanish…
We study a classical many-particle system with an external control represented by a time-dependent extensive parameter in a Lagrangian. We show that thermodynamic entropy of the system is uniquely characterized as the Noether invariant associated with a symmetry for an infinitesimal non-uniform time translation $t\to t+η\hbar β$, where $η$ is a small parameter, $\hbar$ is the Planck constant, $β$ is the inverse temperature that depends on the energy and control parameter, and trajectories in the phase space are restricted to those consistent with quasi-static processes in thermodynamics.
We consider the role of the type-A trace anomaly in static black hole solutions to semiclassical Einstein equation in four dimensions. Via Wald's Noether charge formalism, we compute the contribution to the entropy coming from the anomaly induced effective action and unveil a logarithmic correction to the Bekenstein-Hawking area law. The corrected entropy is given by a seemingly universal formula involving the coefficient of the type-A trace anomaly, the Euler characteristic of the horizon and the value at the horizon of the solution to the uniformization problem for Q-curvature. Two instances…
We use Noether symmetry approach to find spherically symmetric static solutions of the non-minimally coupled electromagnetic fields to gravity. We construct the point-like Lagrangian under the spherical symmetry assumption. Then we determine Noether symmetry and the corresponding conserved charge. We derive Euler-Lagrange equations from this point-like Lagrangian and show that these equations are same with the differential equations derived from the field equations of the model. Also we give two new exact asymptotically flat solutions to these equations and investigate some thermodynamic prope…
We consider the static, spherically symmetric black hole solutions in bigravity theory for minimal model with a condition $f_{μν} = C^{2} g_{μν}$ and evaluate the entropy for black holes. In this condition, we show that there exists the Schwarzschild solution for $C^{2} = 1$, which is unique consistent solution. We examine how the massive spin-2 field contributes and affects to the Bekenstein-Hawking entropy corresponding to Einstein gravity. In order to obtain the black hole entropy, we use a recently proposed approach which use Virasoro algebra and central charge corresponding to surface ter…
We calculate the Noether currents and charges for Einstein-Maxwell theory using a version of the Wald approach. In spherical symmetry, the choice of time can be taken as the Kodama vector. For the static case, the resulting combined Einstein-Maxwell charge is just the mass of the black hole. Using either a classically defined entropy or the Iyer-Wald selection rules, the entropy is found to be just a quarter of the area of the trapping horizon. We propose identifying the combined Noether charge as an energy associated with the Kodama time. For the extremal black hole case, we discuss the probl…
The $f(R)$ theory is considered for static cylindrically symmetric and plane-symmetric spacetimes. In order to find solutions to the field equations of these models, the Noether symmetry method is used. First, we examine the GR case for cylindrically symmetrical space-time with the $w=-1$ dark energy state. Then, with the assumption of $f(R) = f_0R^n$, cases with matter and non-matter are examined and general solutions are determined for both space-times. Thus, it is shown that inclusive new solutions are obtained, considering the Noether symmetric conditions. In addition, the GR limit for eac…
Gravitational radiation reaction around a static black hole surrounded by a Dehnen type dark matter halo
The Institute for Research in Fundamental Sciences (IPM)（伊朗基础科学研究所）；Dipartimento di Fisica e Astronomia, Alma Mater Università di Bologna（博洛尼亚大学物理与天文学系）；Istituto Nazionale di Fisica Nucleare, I.S. FLaG, Sezione di Bologna（意大利国家核物理研究所博洛尼亚分部）；Alma Mater Research Center on Applied Mathematics (AM 2 )（阿尔玛·mater应用数学研究中心）；Università di Camerino, Divisione di Fisica（卡梅里诺大学物理系）；Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Perugia（意大利国家核物理研究所佩鲁贾分部）；INAF - Osservatorio Astronomico di Brera（意大利国家天体物理研究所布雷拉天文台）；Al-Farabi Kazakh National University（法拉比哈萨克国立大学）
We have studied the Hawking radiation from {\it generalized} rotating and static $(2+1)$-dimensional BTZ black holes. In this regard, we have benefited the quantum tunneling approach with WKB approximation and obtained the tunneling rate of outgoing scalar and spinor particles across the horizons. We have also obtained the Hawking temperature at the horizons corresponding to the emission of these particles. It is shown that the tunneling rate and Hawking temperature of generalized $(2+1)$-dimensional BTZ black holes are different from ordinary $(2+1)$-dimensional BTZ black holes due to the Noe…
New analytical model of static black hole with a dark matter halo and parametric constraints through quasiperiodic oscillations
Harbin Institute of Technology（哈尔滨工业大学）；Tashkent State Technical University（塔什干国立技术大学）；National Research University TIIAME（塔吉克斯坦国立研究大学TIIAME）；Zhejiang University of Technology（浙江工业大学）；Tashkent University of Applied Sciences（塔什干应用科学大学）；New Uzbekistan University（新乌兹别克斯坦大学）；National University of Uzbekistan（乌兹别克斯坦国立大学）
Two new families of exact solutions to the Einstein equations for a conformastatic spacetime with axial symmetry are presented which describe thin disks of dust immersed in a spheroidal halo. The solutions are obtained by expressing the metric function in terms of an auxiliary function which satisfies the Laplace equation, a characteristic property of the conformastatic spacetimes. The first family of solutions is obtained from the displacement, cut and reflexion method, which introduces a discontinuity in the first $z$-derivate of the metric tensor across the plane of the disk. The second fam…
We consider a generic scalar-tensor theory involving a shift-symmetric scalar field and minimally coupled matter fields. We prove that the Noether current associated with shift-symmetry vanishes in regular, spherically symmetric and static spacetimes. We use this fact to prove the absence of scalar hair for spherically symmetric and static stars in Horndeski and beyond theories. We carefully detail the validity of this no-hair theorem.
We investigate the static and spherically symmetric solutions of Einstein's equations for a scalar field with non-canonical kinetic term, assumed to provide both the dark matter and dark energy components of the Universe. In particular, we give a prescription to obtain solutions (dark halos) whose rotation curve v_c(r) is in good agreement with observational data. We show that there exist suitable scalar field Lagrangians that allow to describe the cosmological background evolution and the static solutions with a single dark fluid.
In the framework of the unimodular metagravity, with the scalar graviton/graviscalar dark matter, a regular anomalous one-parameter solution to the static spherically symmetric metagravity equations in empty space is found. The solution presents a smooth graviscalar halo, with a finite central density profile, qualitatively reproducing the asymptotically flat rotation curves of galaxies. To refine the description studying the axisymmetric case in the presence of luminous matter is in order.
It is well known that in general theories of gravity with the diffeomorphism symmetry, the black hole entropy is a Noether charge. But what will happen if the symmetry is explicitly broken? By investigating the covariant first law of black hole mechanics with background fields, we show that the Noether entropy is still applicable due to the local nature of the black hole entropy. Moreover, motivated by the proposal that the cosmological constant behaves as a thermodynamic variable, we allow the non-dynamical background fields to be varied. To illustrate this general formalism, we study a gener…
We consider Einstein gravity with a negative cosmological constant endowed with distinct matter sources. The different models analyzed here share the following two properties: (i) they admit static symmetric solutions with planar base manifold characterized by their mass and some additional Noetherian charges, and (ii) the contribution of these latter in the metric has a slower falloff to zero than the mass term, and this slowness is of logarithmic order. Under these hypothesis, it is shown that, for suitable bounds between the mass and the additional Noetherian charges, the solutions can repr…
The crucial role played by pressure in general relativity is explored in the mathematically simple context of a static spherically symmetric geometry. By keeping all pressure terms, the standard formalisms of rotation curve and gravitational lensing observations are extended to a first post-Newtonian order. It turns out that both post-Newtonian formalisms encode the gravitational field differently. Therefore, combined observations of rotation curves and gravitational lensing of the same galaxy can in principle be used to infer both the density and pressure profile of the galactic fluid. The ne…
The gravitational frequency shift of light signals from the center of a spherically symmetric non-static matter distribution is considered. Explicit formulas for the ratio of the emitted and received frequencies are obtained in the case of the oscillating scalar dark matter with logarithmic potential.
In the present work, the Brans-Dicke (BD) theory of gravity is taken as a possible theory of k-essence. Then starting with the (already known) Brans-Dicke-Schwarzschild solution which can represent the gravitationally bound static configurations of the BD scalar k-essence, issues like whether these configurations can reproduce the observed properties of galactic dark matter haloes have been addressed. It has been realized that indeed the BD scalar k-essence can cluster into dark matter halo-like objects with flattened rotation curves while exhibiting a dark energy-like negative pressure on lar…
We find spherically symmetric and static black holes in shift-symmetric Horndeski and beyond Horndeski theories. They are asymptotically flat and sourced by a non trivial static scalar field. The first class of solutions is constructed in such a way that the Noether current associated with shift symmetry vanishes, while the scalar field cannot be trivial. This in certain cases leads to hairy black hole solutions (for the quartic Horndeski Lagrangian), and in others to singular solutions (for a Gauss-Bonnet term). Additionally, we find the general spherically symmetric and static solutions for …
It is shown that an Einstein cluster of WIMPs, WIMPs on stable circular geodesic orbits generating the static spherically symmetric gravitational field of a galactic halo, can exactly reproduce the rotation curve of any galaxy simply by adjusting the local angular momentum distribution and consequent number distribution of the WIMPs. No new physics is involved (assuming the forthcoming discovery of WIMPs). Further, stability of the orbits can require an inner truncation of the halo and an explicit example of this is given. There is no exact Newtonian counterpart to the model presented since pu…
We propose a novel mechanism which explains cored dark matter density profile in recently observed dark matter rich dwarf spheroidal galaxies. In our scenario, dark matter particle mass decreases gradually as function of distance towards the center of a dwarf galaxy due to its interaction with a chameleon scalar. At closer distance towards galactic center the strength of attractive scalar fifth force becomes much stronger than gravity and is balanced by the Fermi pressure of dark matter cloud, thus an equilibrium static configuration of dark matter halo is obtained. Like the case of soliton st…
We consider static spherically symmetric solutions of a general scalar field theory with non-standard kinetic energy coupled to gravity with a view to explain dark matter halos as a coherent state of the scalar field. Consistent solutions are found with a smooth scalar profile which can describe observed rotation curves. Some of the solutions have negative scalar energy density near the origin though the total energy is positive definite. The solutions with positive energy density everywhere have a steeper rotation curve near the origin than those that don't. We also reconsider the no scalar h…
Square-torsion gravity is applied to the long standing dark matter problem. In this context the theory reduces to General Relativity complemented by a dark stress-energy tensor due to the torsion of spacetime and is studied under the simplifying assumption of spherical symmetry. The dark stress-energy tensor is found to satisfy an anisotropic structure equation. In vacuum this is shown to be equivalent to a wave equation with sources. A natural class of exact solutions is found which explicitly perturbs any seed spacetime metric by a conformal factor satisfying a (1+1)-dimensional wave equatio…
We study gravitationally bound static and spherically symmetric configurations of k-essence fields. In particular, we investigate whether these configurations can reproduce the properties of dark matter haloes. The classes of Lagrangians we consider lead to non-isotropic fluids with barotropic and polytropic equations of state. The latter include microscopic realizations of the often-considered Chaplygin gases, which we find can cluster into dark matter halo-like objects with flat rotation curves, while exhibiting a dark energy-like negative pressure on cosmological scales. We complement our s…
In the framework of Einstein-Maxwell-axion theory we consider a static field configuration in the outer zone of a magnetic star. We assume that this field configuration is formed by the following interacting quartet: a spherically symmetric gravitational field of the Reissner-Nordström type, pseudoscalar field, associated with an axionic dark matter, strong intrinsic magnetic field, and axionically induced electric field. Based on the analysis of the solutions to the master equations of the model, we show that the structure of the formed field configuration reveals the following triple effect.…
We examine various methods of constructing conserved quantities in the Teleparallel Equivalent of General Relativity (TEGR). We demonstrate that in the covariant formulation the preferred method are the Noether charges that are true invariant quantities. The Noether charges depend on the vector field $ξ$ and we consider two different options where $ξ$ is chosen as either a Killing vector or a four-velocity of the observer. We discuss the physical meaning of each choice on the example of the Schwarzschild solution in different frames: static, freely falling Lemaitre frame, and a newly obtained …
We study the possibility that a generalised real scalar field minimally coupled to gravity could explain both the galactic and the cosmological dark components of the universe. Within the framework of Einstein's Relativity we model static galactic halos by considering the most general action built from the scalar field and its first derivatives. Although the gravitational configuration is static, the scalar field may be either static, or homogeneous and linear in time. In the case of the static scalar field, the models we look at inevitably posses unphysical negative energies, and we are led t…
The simplistic model of the classical spacetime foam is considered, which consists of static wormholes embedded in Minkowski spacetime. We explicitly demonstrate that such a foam structure leads to a topological bias of point-like sources which can equally be interpreted as the presence of a dark halo around any point source. It is shown that a non-trivial halo appears on scales where the topological structure possesses a local inhomogeneity, while the homogeneous structure reduces to a constant renormalization of the intensity of sources. We also show that in general dark halos possess both (…
We study equations of a non-gauge vector field in a spherically symmetric static metric. The constant vector field with a scale arrangement of components: the time component about the Planck mass m_{Pl} and the radial component about M suppressed with respect to the Planck mass, serves as a source of metric reproducing flat rotation curves in dark halos of spiral galaxies, so that the velocity of rotation v_0 is determined by the hierarchy of scales: \sqrt{2} v_0^2= M/m_{Pl}, and M\sim 10^{12} GeV. A natural estimate of Milgrom's acceleration about the Hubble rate is obtained.
We considered a vacuum polarization inside a galaxy in the eikonal approximation and found that two possible types of polarization exist. The first type is described by the equation of state $p=ρ/3$, similar to radiation. Using the conformally-unimodular metric allows constructing a nonsingular solution for this vacuum ``substance'', if a compact astrophysical object exists in the galaxy's center. As a result, a ``dark'' galactical halo appears that increases the rotation velocity of a test particle as a function of the distance from a galactic center. The second type of vacuum polarization ha…
In the context of scalar tensor theories for gravity, there is a universally adopted hypothesis when running N-body simulations that time derivatives in the equation of motion for the scalar field are negligible. In this work we propose to test this assumption for one specific scalar-tensor model with a gravity screening mechanism: the symmetron. To this end, we implemented the necessary modifications to include the non-static terms in the N-body code Ramses. We present test cases and results from cosmological simulations. Our main finding when comparing static vs. non-static simulations is th…
We have investigated the tidal forces and geodesic deviation motion in the spacetime of a black hole in the galaxy with dark matter halo. Our results show that the tidal force and geodesic deviation motion depend on the dark matter halo mass and the typical lengthscale of galaxy. The effect of the typical lengthscale of galaxy on tidal force is opposite to that of dark matter mass. For the radial tidal force, with the increasing mass of dark matter, it increases in the region far from the black hole, but decreases in the region near black hole. For the angular tidal force, its absolute value o…
There are two observations of galaxies that can offer some insight into the nature of the dark matter (DM), namely the rotation curves and the gravitational lensing. While the first one can be studied using the Newtonian limit, the second one is completely relativistic. Each one separately can not determine the nature of DM, but both together give us key information about this open problem. In this work we use a static and spherically symmetric metric to model the DM halo in a galaxy or in a galaxy cluster. The metric contains two free functions, one associated with the distribution of mass an…
