In this paper, we present two observations about static spherically symmetric solutions of the Einstein-Klein-Gordon equations. The first is a comment extending the well-known result of the existence of static states (i.e. standing wave solutions) of the Einstein-Klein-Gordon equations. The second more important observ…
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48 results for “Static Spherically Symmetric”
New symmetries found in Riemann-Cartan geometries.
problem Investigating symmetries in geometries with curvature and torsion.
method Mathematical tools to determine symmetries and subclasses of geometries.
result Determined all static and stationary spherically symmetric Riemann-Cartan geometries and subclasses with specific symmetries.
Proves stability of spacetime Penrose inequality for spherical symmetric initial data.
problem Stability of the Penrose inequality for spherical symmetric spacetimes.
method Formulated and proved stability statement using spherical symmetry and asymptotically flat initial data.
result Initial data must arise from an isometric embedding into a static spacetime close to Schwarzschild spacetime.
On the fluid ball conjecturemath.DG
Paper proves a rigidity result for static perfect fluids.
problem Proving a rigidity result for static perfect fluids.
method Robinson's divergence formula and boundary conditions.
result Rigidity result for static perfect fluids.
Static spherically symmetric solutions to the Einstein-Euler equations with prescribed central densities are known to exist, be unique and smooth for reasonable equations of state. Some criteria are also available to decide whether solutions have finite extent (stars with a vacuum exterior) or infinite extent. In the l…
The paper explores how a geometric flow can turn a black hole into a traversable wormhole.
problem The study investigates how a static, spherically symmetric black hole can be transformed into a traversable wormhole.
method The approach involves analyzing almost -Ricci-Yamabe solitons and their geometric coupling with the Hawking temperature.
result The geometric flow successfully transforms the black hole into a traversable wormhole, opening the throat and preserving the exact cosmological spacetime.
The paper characterizes photon surfaces in static spacetimes and proves their uniqueness.
problem Characterizing and proving uniqueness of photon surfaces in static spacetimes.
method Local characterization and proof of uniqueness using specific spacetime properties.
result Static, vacuum, asymptotically isotropic spacetimes with equipotential photon surfaces are isometric to Schwarzschild spacetime.
Proves equality in Minkowski inequality for static, flat manifolds.
problem Proving equality in Minkowski inequality for static, flat manifolds.
method Analyzes quasi-spherical metrics and static manifolds.
result Equality in Minkowski inequality achieved only by Schwarzschild space slices.
Study of caustics in Einstein-dust system, showing spacetime singularities and diverging curvature.
problem Understanding caustics and singularities in the Einstein-dust system.
method Established local existence result for spherically symmetric spacetimes containing caustics, constructed from solutions to a PDE problem.
result Obtained spherically symmetric spacetimes with diverging curvature and singular boundary.
The central object of study of this thesis is inverse mean curvature vector flow of two-dimensional surfaces in four-dimensional spacetimes. Being a system of forward-backward parabolic PDEs, inverse mean curvature vector flow equation lacks a general existence theory. Our main contribution is proving that there exist …
The (twice-contracted) second Bianchi identity is a differential curvature identity that holds on any smooth manifold with a metric. In the case when such a metric is Lorentzian and solves Einstein's equations with an (in this case inevitably smooth) energy-momentum-stress tensor of a "matter field" as the source of sp…
The positive mass theorem is one of the fundamental results in general relativity. It states that, assuming the dominant energy condition, the total mass of an asymptotically flat spacetime is non-negative. The Penrose inequality provides a lower bound on mass by the area of the black hole and is closely related to the…
This paper tackles gauge fixing and regularity for perturbations around spherical backgrounds.
problem Understanding gauge freedom and regularity in perturbation theory for symmetric tensors.
method Analyzing Hodge-type decomposition for axially symmetric and axistationary tensors, showing existence and uniqueness of gauge tensors.
result Stationary and axially symmetric second order perturbations can be rendered in a canonical form with only one degree of differentiability loss near the origin.
The paper classifies Landsberg spherically symmetric Finsler metrics in various dimensions.
problem Investigating compatibility conditions on spherically symmetric Finsler metrics.
method Using the inverse problem of calculus of variations, the paper focuses on Landsberg and Berwald types.
result All Landsberg spherically symmetric manifolds in higher dimensions are either Riemannian or have specific geodesic spray formulas.
The paper classifies spherically symmetric Finsler metrics as Berwaldian or Riemannian.
problem Classifying spherically symmetric Finsler metrics.
method Proving all spherically symmetric Landsberg surfaces are Berwaldian and modifying the classification of spherically symmetric Finsler metrics.
result All Berwald spherically symmetric metrics of dimension are Riemannian or given by a specific formula.
The paper characterizes spherically symmetric metrics with scalar curvature.
problem Characterizing spherically symmetric metrics with scalar curvature.
method Established a curvature compatibility condition on spherically symmetric Finsler metrics and constructed a Berwald frame.
result Characterized spherically symmetric metrics with scalar curvature.
The class of spherically symmetric Finsler metrics is studied and locally dually flat and projectively flat spherically symmetric Finsler metrics is classified.
In general relativity, spatial light rays of static spherically symmetric spacetimes are geodesics of surfaces in Riemannian optical geometry. In this paper, we apply results on the isoperimetric problem to show that length-minimizing curves subject to an area constraint are circles, and discuss implications for the ph…
Spherically symmetric metrics form a rich and important class of metrics. Many well-known Finsler metrics of constant flag curvature can be locally expressed as a spherically symmetric metric on R^n. In this paper, we study spherically symmetric metrics with constant Ricci curvature and constant flag curvature.
The paper examines properties of spherical Finsler metrics, proving their semi-C-reducibility and conditions for vanishing mean stretch curvature.
problem Analyzing curvature properties of spherical Finsler metrics.
method Proving semi-C-reducibility and finding conditions for vanishing mean stretch curvature.
result Conditions for a general spherically symmetric Finsler metric to have vanishing mean stretch curvature.
This paper completes the classification of S1-symmetric static vacuum black holes.
problem Identifying all S1-symmetric static vacuum black hole solutions.
method Analyzing and constructing known solutions and proving their completeness.
result Proves that the Schwarzschild, Boost, and Weyl-Korotkin-Nicolai families exhaust all S1-symmetric static vacuum black hole solutions.
Characterizes photon surfaces in static spacetimes, proving uniqueness.
problem Understanding photon surfaces in static spacetimes of arbitrary dimension.
method Complete characterization and new insights into spacetime geometry.
result Proves uniqueness of certain electrostatic spacetimes.
The first irreducible solution of the self-duality equations on the Euclidean Schwarzschild (ES) manifold was found by Charap and Duff in 1977, only 2 years later than the famous BPST instantons on were discovered. While soon after, in 1978, the ADHM construction gave a complete descrip…
In the current paper, first we give the correct version of the formula for mean Berwald curvature of a spherically symmetric Finsler metric given in paper \cite{YCheWSon2015}. Further, we establish differential equations characterizing projectively as well as dually flat spherically symmetric Finsler metrics. Finally, …
Study spherically symmetric Finsler metrics with specific curvature properties.
problem Characterize Finsler metrics with scalar and constant flag curvature.
method Analyze spherically symmetric metrics on symmetric spaces with given curvature properties.
result Provide families of Finsler metrics with scalar and constant flag curvature.
The paper studies T-tensor of spherically symmetric Finsler metrics and characterizes metrics satisfying the T-condition.
problem Characterizing spherically symmetric Finsler metrics with vanishing T-tensor.
method Deriving a general expression for the T-tensor and characterizing metrics satisfying the T-condition.
result Characterization of spherically symmetric Finsler metrics with vanishing T-tensor.
We survey many of the important properties of spherically symmetric spacetimes as follows. We present several different ways of describing a spherically symmetric spacetime and the resulting metrics. We then focus our discussion on an especially useful form of the metric of a spherically symmetric spacetime in polar-ar…
Derives a formula for fermion dimensions in spherically symmetric monopole backgrounds.
problem Calculating the dimension of the plane-wave normalizable kernel for massless fermions in spherically symmetric monopole backgrounds.
method Derives a formula for the dimension of the plane-wave normalizable kernel of the Dirac operator for fermions of any representation of SU(N) in the presence of any spherically symmetric monopole background.
result Derives a formula for the dimension of the plane-wave normalizable kernel of the Dirac operator.
The study proves geometric inequalities for static convex domains in static rotationally symmetric spaces.
problem Proving geometric inequalities for static convex domains in static rotationally symmetric spaces.
method Locally constrained curvature flow in a static rotationally symmetric space , proving graphical solutions and static convexity preservation.
result Proves weighted geometric inequalities for static convex domains close to a slice of .
Study wormholes in Einstein-Yang-Mills theory with a phantom field.
problem Existence of wormholes in Einstein-Yang-Mills theory with a phantom scalar field.
method Rigorous mathematical proof and numerical analysis of wormhole solutions.
result Existence of an infinite sequence of symmetric wormhole solutions.
The study proves strong cosmic censorship violation for spherically symmetric dust clouds.
problem Violation of strong cosmic censorship for spherically symmetric dust clouds.
method Derived an ordinary differential equation for light rays and used it to prove strong cosmic censorship violation.
result Generic violation of strong cosmic censorship for spherically symmetric dust clouds.
The paper explores centroids and static equilibrium points in non-Euclidean geometries.
problem Investigating centroids and static equilibrium points in spherical, hyperbolic, and normed spaces.
method Extending Gal'perin's work, the paper examines convex bodies in these spaces and analyzes the minimum number of equilibrium points.
result Every plane convex body in any of these spaces has at least four equilibrium points, and there are mono-monostatic convex bodies in 3D spherical, hyperbolic, and certain normed spaces.
Locally classifies 4D spherical symmetric Finsler spaces.
problem Classifying 4D spherical symmetric Finsler spaces.
method Local classification of pseudo-Finsler Berwald structures.
result Six classes of non-Riemannian SO(3)-symmetric pseudo-Finsler Berwald functions.
Using generating functional and replica techniques, respectively, we study the dynamics and statics of a spherical Minority Game (MG), which in contrast with a spherical MG previously presented in J.Phys A: Math. Gen. 36 11159 (2003) displays a phase with broken ergodicity and dependence of the macroscopic stationary s…
In this paper we classify the simply connected, spherical pseudohermitian manifolds whose Webster metric is CR-symmetric.
In this paper, we classify the spherically symmetric Berwald metrics in . For the spherically symmetric Landsberg metrics, we prove that there do not exist any non-Berwald metrics among the regular case. The partial differential equation systems which can respectively characterize the spherically symmetri…
Characterizes spherical Finsler metrics satisfying a specific condition.
problem Spherically symmetric Finsler metrics satisfying the -condition.
method Complete characterization and subclass investigation within Landsberg category.
result Identifies precise conditions for metrics satisfying the -condition.
Study compares eigenvalues on spherically symmetric manifolds to Euclidean balls.
problem Comparing eigenvalues on spherically symmetric manifolds to Euclidean balls.
method Examines Dirichlet Laplace eigenvalues on balls of spherically symmetric manifolds and Euclidean space.
result Eigenvalues on spherically symmetric manifolds are smaller for small radii, but larger for hyperbolic spaces.
We develop a solution theory for a generalized electro-magneto static Maxwell system in an exterior domain with anisotropic coefficients converging at infinity with a certain rate towards the identity. Our main goal is to treat right hand side data from some polynomially weighted Sobolev spaces and obtain solutions whi…
We formulate certain inequalities for the geometric quantities characterizing causal diamonds in curved and Minkowski spacetimes. These inequalities involve the red-shift factor which, as we show explicitly in the spherically symmetric case, is monotonic in the radial direction and it takes its maximal value at the cen…
New exact spherically symmetric vacuum solutions found in Finsler gravity.
problem Finding exact vacuum solutions in Finsler gravity.
method Spherically symmetric, asymptotically flat Berwald spacetimes solved for Finsler gravity vacuum equation.
result Only one class of spherically symmetric Berwald spacetimes is compatible with asymptotic flatness and a well-defined causal structure.
We give lower and upper bounds for the first eigenvalue of geodesic balls in spherically symmetric manifolds. These lower and upper bounds are -dependent on the metric coefficients. It gives better lower bounds for the first eigenvalue of spherical caps than those from Betz-Camera-Gzyl.
The paper proves stability of the positive mass theorem in spherical symmetry.
problem The stability of the positive mass theorem in spherical symmetry when mass is small.
method Formulated a conjecture and proved it under spherical symmetry assumption.
result A sequence of asymptotically flat initial data converging to Minkowski space.
The paper classifies spherically symmetric sprays and their curvature properties.
problem Understanding spherically symmetric sprays and their curvature.
method Established a canonical form and derived classification for projectively flat sprays.
result Derived explicit forms for sprays with isotropic and zero curvature.
In this paper, we give the general form of spherically symmetric Finsler metrics in and surprisedly find that many well-known Finsler metrics belong to this class. Then we explicitly express projective metrics of this type. The necessary and sufficient conditions that projective Finsler metrics with spherical sym…
We prove that M. Kramer's classification of list of spherical pairs coincides with that for weakly symmetric spaces by examining the linear isotropy representation of the corresponding homogeneous space associated to each pair.
In this paper, we show that small spherical soap bubbles in irreducible simply connected symmetric spaces of rank greater than one are constructed from the limits of a certain kind of modified mean curvature flows starting from small spheres in the Euclidean space of dimension equal to the rank of the symmetric space, …
Lower bounds for the first Laplacian eigenvalue of geodesic balls of spherically symmetric manifoldsmath.DG
We obtain lower bounds for the first Laplacian eigenvalues of geodesic balls of spherically symmetric manifolds. These lower bounds are only dependent on the metric coefficients.