The Einstein-scalar field theory can be used to model gravitational physics with scalar field matter sources. We discuss the initial value formulation of this field theory, and show that the ideas of Leray can be used to show that the Einstein-scalar field system of partial differential equations is well-posed as an ev…
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48 results for “Einstein-scalar field”
Proves global existence and uniqueness of solutions for Einstein-scalar-field equations.
problem Global existence and uniqueness of solutions for specific Einstein-scalar-field equations.
method Proves global existence and uniqueness of classical solutions with small initial data and wake-like decaying null infinity.
result Global existence and uniqueness of solutions for the equations with wake-like decaying null infinity.
We establish new existence and non-existence results for positive solutions of the Einstein-scalar field Lichnerowicz equation on compact manifolds. This equation arises from the Hamiltonian constraint equation for the Einstein-scalar field system in general relativity. Our analysis introduces variational techniques, i…
Proves weak cosmic censorship for a specific Einstein-scalar field system in 2+1 dimensions.
problem Proves the absence of naked singularities in a specific Einstein-scalar field system.
method Establishes a mass gap and shows the presence of infinite blueshift to prove the absence of naked singularities.
result Proves the weak cosmic censorship conjecture for the circularly symmetric Einstein-scalar field system in 2+1 dimensions.
Unique solutions found for wave-like decaying null infinity equations.
problem Wave-like decaying null infinity equations with spherically symmetric Einstein-scalar-field.
method Local and global unique solutions for small initial data.
result Sharp decaying condition for unique solutions.
Unique global solutions found for specific initial data.
problem Einstein-scalar-field equations with specific initial conditions.
method Spherically symmetric analysis of small, slowly decaying data.
result Unique global solutions exist for the equations.
In this paper, we prove a far-from-CMC result similar to the ones obtained by Holst, Nagy, Tsogtgerel and Maxwell for the conformal Einstein-scalar field constraint equations on compact Riemannian manifolds with positive (modified) Yamabe invariant.
We use the conformal method to obtain solutions of the Einstein-scalar field gravitational constraint equations. Handling scalar fields is a bit more challenging than handling matter fields such as fluids, Maxwell fields or Yang-Mills fields, because the scalar field introduces three extra terms into the Lichnerowicz e…
We follow the approach employed by Y. Choquet-Bruhat, J. Isenberg and D. Pollack in the case of closed manifolds and establish existence and non-existence results for the Einstein-scalar field constraint equations on asymptotically hyperbolic manifolds.
Proves existence of solution to Lichnerowicz equation on non-CMC manifolds.
problem Existence of positive solution to Lichnerowicz equation on non-CMC closed manifolds with supercritical terms.
method Employed a fixed-point argument involving sub- and supersolutions, with conditions on coefficients to prevent classical solutions.
result Proves existence of a positive and essentially bounded solution.
Polynomial Blow-up Upper Bounds for the Einstein-scalar field System Under Spherical Symmetrymath.AP
The study finds polynomial upper bounds for singularities in Einstein-scalar field system.
problem Understanding the strength of singularities in gravitational collapse.
method Analyzing geometric quantities, focusing on the Kretschmann scalar.
result Polynomial blow-up upper bounds for the Kretschmann scalar, improving previous bounds.
We study the constraint equations for the Einstein-scalar field system on compact manifolds. Using the conformal method we reformulate these equations as a determined system of nonlinear partial differential equations. By introducing a new conformal invariant, which is sensitive to the presence of the initial data for …
Study of Bondi-Sachs formalism for massless scalar field with zero cosmological constant.
problem Analyzing the Bondi-Sachs formalism for Einstein's massless scalar field equations.
method Asymptotic expansions and peeling property for Bondi-Sachs metrics and scalar fields.
result Positivity of Bondi energy-momentum under specific conditions.
Researchers simplify Einstein-scalar field equations on specific manifolds.
problem Complexity of Einstein-scalar field conformal constraint equations.
method Study under harmonic manifold assumptions, reducing equations to a single nonlinear equation.
result Solutions exist on Euclidean and hyperbolic manifolds, nonexistence on spheres.
Stability proved for open Milne spacetime, showing gravity's long-term behavior.
problem Global stability of open Milne spacetime for Einstein-scalar field equations.
method Gaussian normal coordinates, exploiting expanding geometry of Milne spacetime.
result Spatial metric tends to hyperbolic metric as time goes to infinity.
Study on naked singularities without symmetry, forming incomplete future null infinity and singular inner Cauchy horizon.
problem Formation of naked singularities in Einstein-scalar field system without symmetry assumptions.
method Employing four-type differences and scale-invariant weighted norms to control geometry.
result Global naked singularity structure with incomplete future null infinity and singular inner Cauchy horizon.
New method proves instability of naked singularity and censors it.
problem Proving instability and censoring naked singularity.
method Einstein-scalar field system, hyperbolic short-pulse method, non-perturbative elliptic arguments.
result Tiny anisotropic perturbation leads to anisotropic apparent horizon censoring the naked singularity.
Paper proves trapped surface formation for Einstein-Maxwell-charged scalar field system.
problem Formation of trapped surfaces in Einstein-Maxwell-charged scalar field system.
method Generalized Christodoulou's approach for spherical symmetry and improved for Minkowskian data.
result Improved bound on trapped surface formation for Minkowskian data.
Lichnerowicz-type equations with sign-changing nonlinearities on complete manifolds with boundarymath.AP
We prove an existence theorem for positive solutions to Lichnerowicz-type equations on complete manifolds with boundary and nonlinear Neumann conditions. This kind of nonlinear problems arise quite naturally in the study of solutions for the Einstein-scalar field equations of General Relativity in the framework of the …
We give the global mathematical formulation of a class of generalized four-dimensional theories of gravity coupled to scalar matter and to Abelian gauge fields. In such theories, the scalar fields are described by a section of a surjective pseudo-Riemannian submersion over space-time, whose total space carries a Lo…
We summarize the global geometric formulation of Einstein-Scalar-Maxwell theories twisted by flat symplectic vector bundle which encodes the duality structure of the theory. We describe the scalar-electromagnetic symmetry group of such models, which consists of flat unbased symplectic automorphisms of the flat symplect…
Study proves stability of big bang singularity in complex system.
problem Stability of Kasner solutions in Einstein-Maxwell-scalar field-Vlasov system.
method Detailed mathematical structures and new delicate arguments.
result Nonlinear stability with Kasner exponents in full strong sub-critical regime.
B List has recently studied a geometric flow whose fixed points correspond to static Ricci flat spacetimes. It is now known that this flow is in fact Ricci flow modulo pullback by a certain diffeomorphism. We use this observation to associate to each static Ricci flat spacetime a local Ricci soliton in one higher dimen…
Study shows instability of naked singularities in scalar field models.
problem Stability of naked singularities in spherically symmetric Einstein-Scalar field systems.
method Analysis of a family of incoming null cones becoming increasingly singular.
result Naked singularities are unstable to black hole formation under certain perturbations.
Study on curvature blow-up rates in black hole interiors from gravitational collapse.
problem Understanding curvature blow-up rates in black hole interiors during gravitational collapse.
method Investigation of spherically symmetric Einstein-scalar field spacetimes, focusing on blow-up rates of curvature and mass.
result Kretschmann scalar blows up faster than in Schwarzschild setting, indicating a new blow-up phenomenon.
The strong unique continuation property for Einstein metrics can be concluded from the well-known fact that Einstein metrics are analytic in geodesic normal coordinates. Here we give a proof of the same result that given two Einstein metrics with the same Ricci curvature on a fixed manifold, if they agree to infinite o…
The paper challenges the smooth null infinity model by constructing counter-examples and showing non-smoothness of null infinity.
problem The structure of gravitational radiation near infinity, particularly at smooth null infinity.
method Constructing solutions to the spherically symmetric Einstein-Scalar field equations and analyzing asymptotic behavior.
result The asymptotic expansion of the derivative of the scalar field near null infinity contains logarithmic terms, indicating non-smoothness.
Second paper in series solves Einstein vacuum equations for three impulsive waves.
problem Solving local Cauchy problem for impulsive gravitational waves.
method Geometric commutators for energy estimates, fractional-derivative regularity, anisotropic Sobolev embedding.
result Scalar field becomes everywhere Lipschitz and away from singular region.
In this article we study self-gravitating static solutions of the Einstein-ScalarField system in arbitrary dimensions. We discuss the existence and the non-existence of geodesically complete solutions depending on the form of the scalar field potential , and provide full global geometric estimates when the soluti…
Study of naked singularities in Einstein vacuum equations using new self-similarity.
problem Mathematical study of naked singularities in the Einstein vacuum equations.
method Introduction of new self-similarity and geometric twisting for singularity formation.
result Construction of solutions corresponding to the exterior region of a naked singularity.
New black hole models with both null and spacelike singularities.
problem Understanding singularities in black hole spacetimes.
method Developed a new spacelike-characteristic gluing method to construct black hole spacetimes.
result First examples of black holes with coexisting null and spacelike singularities.
We study a multiply warped products manifold associated with the Reissner-Nordstrom metric to investigate the physical properties inside the black hole event horizons. It is shown that, different from the uncharged Schwarzschild metric, the Ricci curvature components inside the Reissner-Nordstrom black hole horizons ar…
A 5D manifold's rigidity proven for k=3 with constant scalar curvature.
problem Proving rigidity for a specific case of a quasi-Einstein manifold.
method Analyzing a 5D quasi-Einstein manifold with constant scalar curvature and boundary conditions.
result The case k=3 is rigid, with a specific scalar curvature formula.
The paper proves the existence of finite-energy solutions to a specific elliptic equation on Riemannian manifolds.
problem Existence of finite-energy solutions to a singular elliptic equation on Riemannian manifolds.
method ε-regularized problems, mountain pass arguments, and limiting procedures.
result Existence of nonnegative finite-energy supersolutions under certain conditions.
We give a global formulation of the coupling of four-dimensional scalar sigma models to Abelian gauge fields for the generalized situation when the "duality structure" of the Abelian gauge theory is described by a flat symplectic vector bundle defined over the scalar manifold . The cons…
Study rigidifies non-compact manifolds with specific curvature conditions.
problem Analyzing non-compact generalized m-quasi-Einstein manifolds with constant scalar curvature and soliton function.
method Introduced a weighted function and proved its subharmonicity to derive rigidity results.
result Proves manifolds are Euclidean under specific conditions, with constant μ essential.
New estimates quantify blow-up rates of spacelike singularities in gravitational collapse.
problem Quantifying the blow-up rates of spacelike singularities in gravitational collapse.
method Deriving new quantitative estimates using spherical symmetry and double-null coordinates.
result Polynomial blow-up rates for various quantities, with improved estimates for and .
The paper proves conditions for curvature blow-up in quiescent big bang singularities.
problem Understanding the nature of big bang singularities in cosmological models.
method Analyzing initial data sets with positive mean curvature and proving curvature blow-up conditions.
result Proves the formation of quiescent big bang singularities under certain conditions.
A new framework for hyperbolic neural networks using the Klein model is introduced.
problem Previous works focused on Poincaré and hyperboloid models, neglecting the Klein model.
method Formulation of operations using the Klein model, study of the Klein linear layer, and comparison with Poincaré ball model.
result The Klein HNN performs similarly to the Poincaré ball model, offering a third option.
Braided vector fields on spatial subdomains homeomorphic to the cylinder play a crucial role in applications such as solar and plasma physics, relativistic astrophysics, fluid and vortex dynamics, elasticity, and bio-elasticity. Often the vector field's topology -- the entanglement of its field lines -- is non-trivial,…
Spinor fields depending on tensor fields and other spinor fields are considered. The concept of extended spinor fields is introduced and the theory of differentiation for such fields is developed.
Flux Quantizationhep-th
The paper explores how fields in higher dimensions are quantized.
problem Understanding non-perturbative completions of higher gauge fields.
method Generalizes the Chern-Dold character map to higher-dimensional supergravity theories.
result Flux and charge quantization laws for higher gauge fields are understood via non-linear Bianchi identities.
Paper transforms torse-forming vector fields into simpler forms.
problem Generalizing vector fields and their transformations.
method Present techniques to transform torse-forming vector fields into simpler cases.
result Concrete examples of transformations are provided.
Researchers found indecomposable Killing tensor fields on quaternionic projective spaces.
problem Characterizing Killing tensor fields on projective spaces.
method Analyzing Killing tensor fields on quaternionic and complex projective spaces, proving algebraic properties.
result Generated algebras of Killing tensor fields on quaternionic and complex projective spaces.
Conformal vector fields on LCP manifolds are orthogonal and Killing.
problem Understanding conformal vector fields on specific geometric manifolds.
method Analyzing properties of conformal vector fields on compact locally conformally product manifolds.
result Conformal vector fields are orthogonal to the flat distribution and Killing.
Paper describes holomorphic polyvector fields on toric varieties.
problem No specific problem stated; general description of fields.
method Explicit description of holomorphic polyvector fields on smooth compact toric varieties.
result Generalizes Demazure's result of holomorphic vector fields on toric varieties.
Tensor fields depending on other tensor fields are considered. The concept of extended tensor fields is introduced and the theory of differentiation for such fields is developed.
The paper proves that certain modified conformal vector fields are trivial on compact and non-compact manifolds.
problem Proving triviality of modified conformal vector fields on Riemannian manifolds.
method Analyzing properties of homothetic, conformal, and gradient vector fields on compact and non-compact manifolds.
result Established conditions under which -modified conformal vector fields are trivial.