arXiv research

Proves global existence and uniqueness of solutions for Einstein-scalar-field equations.

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…

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…

Unique solutions found for wave-like decaying null infinity equations.

Unique global solutions found for specific initial data.

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 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.

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 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 …

Researchers simplify Einstein-scalar field equations on specific manifolds.

Stability proved for open Milne spacetime, showing gravity's long-term behavior.

Proves weak cosmic censorship for a specific Einstein-scalar field system in 2+1 dimensions.

Study of Bondi-Sachs formalism for massless scalar field with zero cosmological constant.

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 …

The study finds polynomial upper bounds for singularities in Einstein-scalar field system.

Study of naked singularities in Einstein vacuum equations using new self-similarity.

Study on naked singularities without symmetry, forming incomplete future null infinity and singular inner Cauchy horizon.

New method proves instability of naked singularity and censors it.

Study shows instability of naked singularities in scalar field models.

Second paper in series solves Einstein vacuum equations for three impulsive waves.

The paper challenges the smooth null infinity model by constructing counter-examples and showing non-smoothness of null infinity.

Paper proves trapped surface formation for Einstein-Maxwell-charged scalar field system.

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 $π$ 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…

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 $V(φ)$, and provide full global geometric estimates when the soluti…

Study proves stability of big bang singularity in complex system.

The paper proves the existence of finite-energy solutions to a specific elliptic equation on Riemannian manifolds.

New black hole models with both null and spacelike singularities.

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 on curvature blow-up rates in black hole interiors from gravitational collapse.

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…

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 $(\mathcal{S},D,ω)$ defined over the scalar manifold $\mathcal{M}$. The cons…

The paper proves conditions for curvature blow-up in quiescent big bang 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…

Data-driven approach learns effective equations for phase field interfaces.

A 5D manifold's rigidity proven for k=3 with constant scalar curvature.

Geometrically describes Jacobi equations for field theories with dissipation.

The paper studies a new vacuum field equation and its solutions.

The paper generalizes Bach and Einstein equations with a field.

Three types of equations of mathematical physics, namely, the equations, which describe any physical processes, the equations of mechanics and physics of continuous media, and field-theory equations are studied in this paper. In the first and second case the investigation is reduced to the analysis of the nonidentical …

Develops higher-order Euler-Poincaré field equations for principal G-bundles.

Researchers solve field equations for special gravitational instantons.

In this article we present a natural generalization of Newton's Second Law valid in field theory, i.e., when the parameterized curves are replaced by parameterized submanifolds of higher dimension. For it we introduce what we have called the geodesic $k$-vector field, analogous to the ordinary geodesic field and which …

The reduction problem of the chiral field equation on symmetric spaces is studied. It is shown that the symmetric chiral field has infinitely many local conservation laws. A recursive formula for these conservation laws is derived and the first associated integral of motion are given explicitly. Furthermore, the Zakhar…

Study rigidifies non-compact manifolds with specific curvature conditions.

Solves inverse problem for Maxwell equations using vector fields.

Let $X$be a complex hyperelliptic curve of genus two equipped with the canonical metric $ds^2$. We study mean field equations on complex hyperelliptic curves and show that the Gaussian curvature function of $(X,ds^2)$ determines an explicit solution to a mean field equation.