M. Sharif, Z. Yousaf
We try to find some exact analytical models of spherically symmetric spacetime of collapsing fluid under shearfree condition. We consider two types of solutions: one is to impose a condition on the mass function while the other is to restrict the pressure. We obtain totally of five exact models, and some of them satisfy the Darmois conditions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
We show that shearfree perfect fluids obeying an equation of state p=(gamma -1) mu are non-rotating or non-expanding under the assumption that the spatial divergence of the magnetic part of the Weyl tensor is zero.
Gravitational collapse of anisotropic cylindrical shearfree fluids with new exact interior solutions of GR
本文研究柱对称无剪切引力坍缩，发现轴向和方位角压力流体的新精确内部解，并证明在无限长各向异性圆柱坍缩时可发射引力波，与球对称情形不同。
The implications of shearfree condition on instability range of anisotropic fluid in $f(R,T)$ are studied in this manuscript. A viable $f(R, T)$ model is chosen to arrive at stability criterion, where $R$ is Ricci scalar and $T$ is the trace of energy momentum tensor. The evolution of spherical star is explored by employing perturbation scheme on modified field equations and contracted Bianchi identities in $f(R, T)$. The effect of imposed shearfree condition on collapse equation and adiabatic index $Γ$ is studied in Newtonian and post-Newtonian regimes.
We consider diagonal cylindrically symmetric metrics, with an interior representing a general non-rotating fluid with anisotropic pressures. An exterior vacuum Einstein-Rosen spacetime is matched to this using Darmois matching conditions. We show that the matching conditions can be explicitly solved for the boundary values of metric components and their derivatives, either for the interior or exterior. Specializing to shearfree interiors, a static exterior can only be matched to a static interior, and the evolution in the non-static case is found to be given in general by an elliptic function …
A class of spherically symmetric spacetimes invariantly defined by a zero flux condition is examined first from a purely geometrical point of view and then physically by way of Einstein's equations for a general fluid decomposition of the energy-momentum tensor. The approach, which allows a formal inversion of Einstein's equations, explains, for example, why spherically symmetric perfect fluids with spatially homogeneous energy density must be shearfree.
It is shown that an effective anisotropic spherically symmetric fluid model with heat flow can absorb the addition to a perfect fluid of pressure anisotropy, heat flow, bulk and shear viscosity, electric field and null fluid.
We investigate solutions of Einstein field equations for the non-static spherically symmetric perfect fluid case using different equations of state. The properties of an exact spherically symmetric perfect fluid solutions are obtained which contain shear. We obtain three different solutions out of these one turns out to be an incoherent dust solution and the other two are stiff matter solutions.
This work is concerned with the finiteness problem for static, spherically symmetric perfect fluids in both Newtonian Gravity and General Relativity. We derive criteria on the barotropic equation of state guaranteeing that the corresponding perfect fluid solutions possess finite/infinite extent. In the Newtonian case, for the large class of monotonic equations of state, and in General Relativity we improve earlier results.
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.
In this short note we comment about some criticisms - appeared in a recent paper by Iguchi et al - to our previous works on gravitational collapse of perfect fluids. We show that those criticisms are incorrect on their own.
We study the spherically symmetric collapse of a perfect fluid using area-radial coordinates. We show that analytic mass functions describe a static regular centre in these coordinates. In this case, a central singularity can not be realized without an infinite discontinuity in the central density. We construct mass functions involving fluid dynamics at the centre and investigate the relationship between those and the nature of the singularities.
Einstein's field equations for timelike self-similar spherically symmetric perfect-fluid models are investigated. The field equations are rewritten as a first-order system of autonomous differential equations. Dimensionless variables are chosen in such a way that the number of equations in the coupled system is reduced as far as possible and so that the reduced phase space becomes compact and regular. The system is subsequently analysed qualitatively using the theory of dynamical systems.
Einstein's field equations for spatially self-similar spherically symmetric perfect-fluid models are investigated. The field equations are rewritten as a first-order system of autonomous differential equations. Dimensionless variables are chosen in such a way that the number of equations in the coupled system is reduced as far as possible and so that the reduced phase space becomes compact and regular. The system is subsequently analysed qualitatively with the theory of dynamical systems.
We construct conformastat spherically symmetric spacetimes representing anisotropic fluid matter distributions from given solutions of the Poisson's equation of Newtonian gravity and its corresponding circular speed profile. As simple examples, we present three families of spherically symmetric spacetimes which we apply in constructing new models of relativistic anisotropic thick spherical shells, and of relativistic galaxy models composite by a central spherical bulge, the thick disk and the dark matter halo, writing in this case the metric in cylindrical coordinates. Moreover, the geodesic m…
By a choice of new variables the pressure isotropy condition for spherically symmetric static perfect fluid spacetimes can be made a quadratic algebraic equation in one of the two functions appearing in it. Using the other variable as a generating function, the pressure and the density of the fluid can be expressed algebraically by the function and its derivatives. One of the functions in the metric can also be expressed similarly, but to obtain the other function, related to the redshift factor, one has to perform an integral. Conditions on the generating function ensuring regularity and phys…
The present work investigates the gravitational collapse of a perfect fluid in $f(R)$ gravity models. For a general $f(R)$ theory, it is shown analytically that a collapse is quite possible. The singularity formed as a result of the collapse is found to be a curvature singularity of shell focusing type. The possibility of the formation of an apparent horizon hiding the central singularity depends on the initial conditions.
We consider the self-similar solutions associated with the critical behavior observed in the gravitational collapse of spherically symmetric perfect fluids with equation of state $p=αμ$. We identify for the first time the global nature of these solutions and show that it is sensitive to the value of $α$. In particular, for $α>0.28$, we show that the critical solution is associated with a new class of asymptotically Minkowski self-similar spacetimes. We discuss some of the implications of this for critical phenomena.
We classify all spherically symmetric and homothetic spacetimes that are allowed kinematically by constructing them from a small number of building blocks. We then restrict attention to a particular dynamics, namely perfect fluid matter with the scale-free barotropic equation of state p = alpha mu where 0<alpha<1 is a constant. We assign conformal diagrams to all solutions in the complete classification of Carr and Coley, and so establish which of the kinematic possibilities are realized for these dynamics. We pay particular attention to those solutions which arise as critical solutions during…
Sonic point/photon sphere (SP/PS) correspondence is a theoretical phenomenon which appears in fluid dynamics on curved spacetime and its existence has been recently proved in quite wide situations as theorems. The theorems state that a sonic point (SP) of radiation fluid flow must be on an unstable photon sphere (PS) when the fluid flows radially or rotationally on an equatorial plane in spherically symmetric spacetime of arbitrary dimensions. In this paper, we investigate SP/PS correspondence in spherically, planarly and hyperbolically symmetric spacetime. As the corresponding objects of phot…
Formulating a perfect fluid filled spherically symmetric metric utilizing the 3+1 formalism for general relativity, we show that the metric coefficients are completely determined by the mass-energy distribution, and its time rate of change on an initial spacelike hypersurface. Rather than specifying Schwarzschild coordinates for the exterior of the collapsing region, we let the interior dictate the form of the solution in the exterior, and thus both regions are found to be written in one coordinate patch. This not only alleviates the need for complicated matching schemes at the interface, but …
We classify all spherically symmetric spacetimes admitting a kinematic self-similar vector of the second, zeroth or infinite kind. We assume that the perfect fluid obeys either a polytropic equation of state or an equation of state of the form $p=Kμ$, where $p$ and $μ$ are the pressure and the energy density, respectively, and $K$ is a constant. We study the cases in which the kinematic self-similar vector is not only ``tilted'' but also parallel or orthogonal to the fluid flow. We find that, in contrast to Newtonian gravity, the polytropic perfect-fluid solutions compatible with the kinematic…
The Riemann, Ricci and Einstein tensors for N-dimensional spherically symmetric spacetimes in various systems of coordinates are studied, and the general metric for conformally flat spacetimes is given. As an application, all the Friedmann-Robertson-Walker-like solutions for a perfect fluid with an equation of state $p = k ρ$ are found. Then, these solutions are used to model the gravitational collapse of a compact ball, by first cutting them along a timelike hypersurface and then joining them with asymptotically flat Vaidya solutions. It is found that when the collapse has continuous self-sim…
Conformally flat spherically symmetric cosmological models representing a charged perfect fluid as well as a bulk viscous fluid distribution have been obtained. The cosmological constant Λis found positive and is a decreasing function of time which is consistent with the recent supernovae observations. The physical and geometrical properties of the models are discussed.
We consider spherically symmetric linear perturbations of static spherically symmetric spacetimes where the matter content is ellectrically counterpoised dust. We show that the evolution equation for the fluid perturbation implies that the fluid elements move with constant velocities. Therefore there are neither oscillations nor exponential departure from the background solution. We present an explicit example that shows that the perturbation could lead to the formation of a black hole.
No-go theorem for static spherically symmetric configurations composed of two charged pressureless fluid species
本研究提出两种带电无压尘埃球对称平衡构型的不可行定理，证明仅当二者荷质比相同时平衡才可能，该结论在牛顿力学、狭义与广义相对论中均成立，为黑洞模拟体的构建条件提供了理论约束。
In this paper, we examine static spherically symmetric wormhole solutions in generalized $f(R,ϕ)$ gravity. To do this, we consider three different kinds of fluids: anisotropic, barotropic and isotropic. We explore different $f(R,ϕ)$ models and inspect the energy conditions for all of those three fluids. It is found that under some models in this theory, it is possible to obtain wormhole solutions without requiring exotic matter. The discussion about the conditions where the standard energy conditions (WEC and NEC) are valid for the fluids is discussed in details. From our results and for our c…
We consider the subject of self--binding in static, spherically symmetric objects consisting of a charged fluid. We have shown previously that in the case of a perfect fluid, only the localized part of the mass contributes to gravitational self--binding of such objects and that in the limiting case of objects comprised purely of electromagnetic mass, there is no gravitational binding. Here, we extend this result to the more general case of an anisotropic fluid. Our inspection of the Oppenheimer--Volkov equation allows tracking of both gravitational and non-gravitational contributions to bindin…
Exact solutions for static spherically symmetric spacetime with a perfect fluid in Rastall theory
该研究将广义相对论中理想流体静态球对称时空的精确解拓展至Rastall理论，推导得出对应广义相对论已知情形的解，且w≠1/3、-1时解的行为随常数选择变化。
We carry out numerical simulations of the gravitational collapse of a perfect fluid with the ultrarelativistic equation of state $P=κρ$, in spherical symmetry in $2+1$ spacetime dimensions with $Λ<0$. At the threshold of prompt collapse, we find type II critical phenomena (apparent horizon mass and maximum curvature scale as powers of distance from the threshold) for $κ\gtrsim 0.43$, and type I critical phenomena (lifetime scales as logarithm of distance from the threshold) for $κ\lesssim 0.42$. The type I critical solution is static, while the type II critical solution is not self-similar (as…
Self-similar, spherically symmetric cosmological models with a perfect fluid and a scalar field with an exponential potential are investigated. New variables are defined which lead to a compact state space, and dynamical systems methods are utilised to analyse the models. Due to the existence of monotone functions global dynamical results can be deduced. In particular, all of the future and past attractors for these models are obtained and the global results are discussed. The essential physical results are that initially expanding models always evolve away from a massless scalar field model w…
We express Einstein's field equations for a spherically symmetric ball of general fluid such that they are conducive to an initial value problem. We show how the equations reduce to the Vaidya spacetime in a non-null coordinate frame, simply by designating specific equations of state. Furthermore, this reduces to the Schwarzschild spacetime when all matter variables vanish. We then describe the formulation of an initial value problem, whereby a general fluid ball with vacuum exterior is established on an initial spacelike slice. As the system evolves, the fluid ball collapses and emanates null…
Physical interpretation of spherically symmetric perfect fluid solutions to Einstein's equations
本研究探讨球对称完美流体解的物理可行性，通过流体动力学方法分析其与理想气体的兼容性，并开发了xIdeal工具用于精确解分析。
An algorithm presented by K. Lake to obtain all static spherically symmetric perfect fluid solutions was recently extended by L. Herrera to the interesting case of locally anisotropic fluids (principal stresses unequal). In this work we develop an algorithm to construct all static spherically symmetric anisotropic solutions for general relativistic polytropes. Again the formalism requires the knowledge of only one function (instead of two) to generate all possible solutions. To illustrate the method some known cases are recovered.
We investigate here the locally naked singularity formed due to a spherically symmetric inhomogeneous collapsing cloud having non-zero isotropic pressure, in terms of its strength. Sufficient condition provided by Clarke and Krolak for it to be Tipler strong has been used to restrict the parameters that represent the non-linear relation between the physical radius and the radial coordinate of the outgoing radial null geodesic at the singular center. Studying end state of a collapsing cloud requires information about the dynamics of collapse, which is unknown in a general scenario. Hence we stu…
An exact solution of the Einstein field equations is found under the assumption of spherically symmetry and the existence of one-parameter group of homothetic motions. This solution has a singularity at $r = 0$, and has non-vanishing expansion, acceleration and shear. Tidal forces in radial direction will not stretch an observer falling in this fluid. If the material is represented by perfect fluid, we can verify that the solution coincides with stiff matter case. In this case, the solution has zero expansion. Tidal forces in radial direction will not stretch an observer falling in this fluid …
We study the complete gravitational collapse of a class of spherically symmetric inhomogeneous perfect fluid models obtained by introducing small radial perturbations in an otherwise homogeneous matter cloud. Our aim here is to study the genericity and stability of the formation of black holes and locally naked singularities in collapse. While the occurrence of naked singularities is known for many models of collapse, the key issue now in focus is genericity and stability of these outcomes. Towards this purpose, we study how the introduction of a somewhat general class of small inhomogeneities…
Analytic spherically symmetric solutions of the Einstein field equations coupled with a perfect fluid and with self-similarities of the zeroth, first and second kinds, found recently by Benoit and Coley [Class. Quantum Grav. {\bf 15}, 2397 (1998)], are studied, and found that some of them represent gravitational collapse. When the solutions have self-similarity of the first (homothetic) kind, some of the solutions may represent critical collapse but in the sense that now the "critical" solution separates the collapse that forms black holes from the collapse that forms naked singularities. The …
The purpose of this paper is to further investigate the solution space of self-similar spherically symmetric perfect-fluid models and gain deeper understanding of the physical aspects of these solutions. We achieve this by combining the state space description of the homothetic approach with the use of the physically interesting quantities arising in the comoving approach. We focus on three types of models. First, we consider models that are natural inhomogeneous generalizations of the Friedmann Universe; such models are asymptotically Friedmann in their past and evolve fluctuations in the ene…
We present two classes of inhomogeneous, spherically symmetric solutions of the Einstein-Maxwell-Perfect Fluid field equations with cosmological constant generalizing the Vaidya-Shah solution. Some special limits of our solution reduce to the known inhomogeneous charged perfect fluid solutions of the Einstein field equations and under some other limits we obtain new charged and uncharged solutions with cosmological constant. Uncharged solutions in particular represent cosmological models where the universe may undergo a topology change and in between is a mixture of two different Friedmann-Rob…
The Einstein equations are integrated in the presence of two (incoming and outgoing) streams of null dust, under the assumptions of spherical symmetry and staticity. The solution is also written in double null and radiation coordinates and it is reinterpreted as an anisotropic fluid. Interior matching with a static fluid and exterior matching with the Vaidya solution along null hypersurfaces is discussed. The connection with two-dimensional dilaton gravity is established.
Thermodynamic acceptability of spherically symmetric perfect-fluid solutions in general relativity
本文基于热力学考虑扩展了物理可接受性的概念，提出了一套适用于广义相对论恒星模型的热力学可接受条件，并以Tolman IV解为例展示了其热力学一致性。
A phase space is built that allows to study, classify and compare easily large classes of static spherically symmetric wormholes solutions, sustained by an isotropic perfect fluid in General Relativity. We determine the possible locations of equilibrium points, throats and curvature singularities in this phase space. Throats locations show that the spatial variation of the gravitational redshift at the throat of a static spherically symmetric wormhole sustained by an isotropic perfect fluid is always diverging, generalising the result that there is no such wormhole with zero-tidal force. Sever…
We study some properties of static spherically symmetric elastic bodies in general relativity using both analytical and numerical tools. The materials considered belong to the class of John elastic materials and reduce to perfect fluids when the rigidity parameter is set to zero. We find numerical support that such elastic bodies exist with different possible shapes (balls, single shells and multiple shells) and that their gravitational redshift can be very large ($z\approx 2.8$) without violating the dominant energy condition. Moreover we show that the elastic body has finite radius even in t…
We study spherically symmetric timelike thin-shells in $3+1-$dimensional bulk spacetime with a variable equation of state for the fluid presented on the shell. In such a fluid the angular pressure $p$ is a function of both surface energy density $σ$ and the radius $R$ of the thin-shell. Explicit cases of the thin shells connecting two non-identical cloud of strings spacetimes and a flat Minkowski spacetime to the Schwarzschild metric are investigated.
Interpretation of complexity for spherically symmetric fluid composition within the context of modified gravity theory
本文在f(R,L_m,T)修正引力理论中，利用曲率张量正交分解推导复杂性因子，分析球对称各向异性流体的复杂性，发现暗源项可消除复杂性表现。
A solution of the linearized Einstein's equations for a spherically symmetric perturbation of the ultrarelativistic fluid in the homogeneous and isotropic universe is obtained. Conditions on the boundary of the perturbation are discussed. The examples of particle-like and wave-like solutions are given.
The asymptotic properties of self-similar spherically symmetric perfect fluid solutions with equation of state p=alpha mu (-1<alpha<1) are described. We prove that for large and small values of the similarity variable, z=r/t, all such solutions must have an asymptotic power-law form. Some of them are associated with an exact power-law solution, in which case they are asymptotically Friedmann or asymptotically Kantowski-Sachs for 1>alpha >-1 or asymptotically static for 1>alpha >0. Others are associated with an approximate power-law solution, in which case they are asymptotically quasi-static f…
Spherically symmetric electrically counterpoised dust either collapses or disperses
本研究分析广义相对论中球对称电平衡尘埃的动力学，证明任何微小速度扰动都会使其坍缩为极端 Reissner-Nordström 黑洞或发生弥散，否定其中性平衡与黑洞模拟体可行性。
Considering the standard "static" spherically symmetric ansatz ds2 = -B(r) dt2 + A(r) dr2 + r2 dOmega2 for Einstein's Equations with perfect fluid source, we ask how we can interpret solutions where A(r) and B(r) are not positive, as they must be for the static matter source interpretation to be valid. Noting that the requirement of Lorentzian signature implies A(r) B(r) >0, we find two possible interpretations: (i) The nonzero component of the source four-velocity does not have to be u0. This provides a connection from the above ansatz to the Kantowski-Sachs (KS) spacetimes. (ii) Regions with…
We study spherically-symmetric solutions in Massive Gravity generated by matter sources with polytropic equation of state. We concentrate in the non-perturbative regime where the mass term non-linearities are important, and present the main features of the solutions.
We analyze the isothermal property in static fluid spheres within the framework of the modified $f(R, T)$ theory of gravitation. The equation of pressure isotropy of the standard Einstein theory is preserved however, the energy density and pressure are expressed in terms of both gravitational potentials. Invoking the isothermal prescription requires that the isotropy condition assumes the role of a consistency condition and an exact model generalizing that of general relativity is found. Moreover it is found that the Einstein model is unstable and acausal while the $f(R, T)$ counterpart is wel…
In this paper, we investigate spherically symmetric perfect fluid gravitational collapse in metric $f(R)$ gravity. We take non-static spherically symmetric metric in the interior region and static spherically symmetric metric in the exterior region of a star. The junction conditions between interior and exterior spacetimes are derived. The field equations in f(R) theory are solved using the assumption of constant Ricci scalar. Inserting their solution into junction conditions, the gravitational mass is found. Further, the apparent horizons and their time of formation is discussed. We conclude …
For static fluid spheres, the condition of hydrostatic equilibrium is given by the generalized Tolman--Oppenheimer--Volkoff (TOV) equation, a Riccati equation in the radial pressure. For a perfect fluid source, it is known that finding a new solution from an existing solution requires solving a Bernoulli equation, if the density profile is kept the same. In this paper, we consider maps between static (an)isotropic fluid spheres with the same (arbitrary) density profile and present solution-generating techniques to find new solutions from existing ones. The maps, in general, require solving an …
An algorithm based on the choice of a single monotone function (subject to boundary conditions) is presented which generates all regular static spherically symmetric perfect fluid solutions of Einstein's equations. For physically relevant solutions the generating functions must be restricted by non-trivial integral-differential inequalities. Nonetheless, the algorithm is demonstrated here by the construction of an infinite number of previously unknown physically interesting exact solutions.
Test particle motion around a black hole dressed with a spherically symmetric stationary fluid
本文研究球对称稳态流体吸积对黑洞周围检验粒子轨道的影响，通过微扰史瓦西背景和多种状态方程参数求解测地线，并结合密切轨道根数与红移观测揭示吸积造成的轨道差异。
We give a classification of spherically symmetric kinematic self-similar solutions. This classification is complementary to that given in a previous work by the present authors [Prog. Theor. Phys. 108, 819 (2002)]. Dust solutions of the second, zeroth and infinite kinds, perfect-fluid solutions and vacuum solutions of the first kind are treated. The kinematic self-similarity vector is either parallel or orthogonal to the fluid flow in the perfect-fluid and vacuum cases, while the `tilted' case, i.e., neither parallel nor orthogonal case, is also treated in the dust case. In the parallel case, …
In this work, we explore wormhole solutions in $f(R,T)$ theory of gravity, where $R$ is the scalar curvature and $T$ is the trace of stress-energy tensor of matter. To investigate this, we consider static spherically symmetric geometry with matter contents as anisotropic, isotropic and barotropic fluids in three separate cases. By taking into account Starobinsky $f(R)$ model , we analyze the behavior of energy conditions for these different kind of fluids. It is shown that the wormhole solutions can be constructed without exotic matter in few regions of spacetime. We also give the graphical il…
The aim of the present letter is to explain the `critical behaviour' observed in numerical studies of spherically symmetric gravitational collaps of a perfect fluid. A simple expression results for the critical index $γ$ of the black hole mass considered as an order parameter. $γ$ turns out to vary strongly with the parameter $k$ of the assumed equation of state $p=kρ$.
In Newton's and in Einstein's theory we give criteria on the equation of state of a barotropic perfect fluid which guarantee that the corresponding one-parameter family of static, spherically symmetric solutions has finite extent. These criteria are closely related to ones which are known to ensure finite or infinite extent of the fluid region if the assumption of spherical symmetry is replaced by certain asymptotic falloff conditions on the solutions. We improve this result by relaxing the asymptotic asumptions. Our conditions on the equation of state are also related to (but less restrictive…
Spherically Symmetric, Static Solutions in Presence of Matter-Curvature Coupling
本研究在含物质-曲率非最小耦合（NMC）的引力理论中提出球对称静态时空解，给出多种修正场方程求解方法，分析NMC对应力-能量张量及能量条件的影响。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。