Study of isometries in spacetimes without observer horizons.
problem Understanding the symmetries of spacetimes without specific boundaries.
method Analysis of isometry groups in causal spacetimes without observer horizons.
result The group of time orientation-preserving isometries acts properly on the spacetime.
The study defines conditions for Finsler spacetime structures in (α,β)-metrics and identifies their isometries.
problem Conditions for Finsler spacetime structures in (α,β)-metrics. method Established necessary and sufficient conditions for Finsler spacetime structures.
result Identified (α,β)-Finsler spacetimes and determined the relation between isometries of (α,β)-metrics and the underlying pseudo-Riemannian metric. Study classifies metrics on anti-de Sitter spacetime with specific symmetries.
problem Classifying metrics with specific symmetries on anti-de Sitter spacetime.
method Used classification techniques for pseudo-Riemannian and almost contact metric structures.
result Obtained classifications of homogeneous structures on anti-de Sitter spacetime.
Study of convergence in Lorentzian spacetimes using temporal functions.
problem Non-compactness of spacetime isometries and convergence in semi-Riemannian settings.
method Introduced anchored convergence and used Cauchy temporal functions to define convergence for spacetimes.
result Established local and global regularity of Cauchy temporal functions and their properties.
We study the existence of a non-spacelike isometry, ζ, in higher dimensional Kundt spacetimes with constant scalar curvature invariants (CSI). We present the particular forms for the null or timelike Killing vectors and a set of constraints for the metric functions in each case. Within the class of N dimensional CSI Ku…
Reconstruct spacetime from order and number of points.
problem Reconstruct spacetime from chronological relations and i.i.d. samples.
method Relaxing hypotheses of Gromov reconstruction theorem, using random adjacency matrices and chronological relations.
result Spacetime can be recovered by only knowing 'order' and 'number' of its points.
We develop the basics of a theory of almost isometries for spaces endowed with a quasi-metric. The case of non-reversible Finsler (more specifically, Randers) metrics is of particular interest, and it is studied in more detail. The main motivation arises from General Relativity, and more specifically in spacetimes endo…
Given a regular curve in Minkowski spacetime, we describe necessary and sufficient conditions for this curve to admit a family of pairwise-disjoint crooked planes. Using this criterion, we describe crooked foliations along orbit curves of one-parameter groups of Lorentzian isometries.
Researchers extend parametrization of Margulis spacetimes using strip deformations.
problem Parametrize Margulis spacetimes with decorated horoballs.
method Use strip deformations to parametrize complete finite-area hyperbolic surfaces with spikes decorated with horoballs.
result Generalized parametrization of Margulis spacetimes with photons.
This research bridges Killing vectors and Lie algebras through induced vector fields.
problem Understanding the relationship between Killing vector fields and Lie algebras.
method Defining and exploring induced vector fields to connect Killing vector fields with isometry Lie groups.
result Established a new connection between Killing vector fields and Lie algebras.
Study proves rigidity results for analytic spacetimes without boundary or timelike boundary.
problem Determining compact subsets and spacetimes from scattering data.
method Analytic spacetimes, thin exterior layers, non-trapping lightlike geodesics.
result Time separation and scattering relations uniquely determine spacetimes.
Null distance encodes causal structure in spacetimes.
problem Encoding causal structure in Lorentzian manifolds.
method Using null distance defined by Sormani and Vega, and proving causal structure is encoded by null distance.
result Lorentzian isometry between spacetimes with bijective map preserving null distance and cosmological time function.
This paper is the continuation of [8]. We essentially prove that the familly of strongly causal spacetimes defined in [8] associated to generic achronal subsets in Ein contains all the examples of BTZ multi black-holes. It provides new elements for the global description of these multi black-holes. We also prove that a…
Overview of marginally trapped surfaces in various spacetimes.
problem Understanding marginally trapped surfaces in different spacetimes.
method Differential geometric study of marginally trapped surfaces in Minkowski, de Sitter, anti-de Sitter, and Robertson-Walker spacetimes.
result General local descriptions and classifications of these surfaces.
We consider 3+1 rotationally symmetric Lorentzian Einstein spacetime manifolds with Λ>0 and reduce the equations to 2+1 Einstein equations coupled to `shifted' wave maps. Subsequently, we prove various (explicit) positive mass-energy theorems. No smallness is assumed.
New splitting theorem for weighted Finsler spacetimes without Berwald condition.
problem Proving timelike splitting theorems for Finsler spacetimes under weaker conditions.
method Using the p-d'Alembertian and a recently developed strategy. result Established a diffeomorphic splitting for timelike geodesically complete Finsler spacetimes.
Past lightcones of certain points in globally hyperbolic spacetimes determine the entire spacetime.
problem Determining the entire spacetime from the past lightcone of a point.
method Analyzing properties of globally hyperbolic spacetimes and using null lines and observer horizons.
result Past lightcones of certain points in globally hyperbolic spacetimes determine the entire spacetime (up to isometry).
In 1900, Macfarlane proposed a hyperbolic variation on Hamilton's quaternions that closely resembles Minkowski spacetime. Viewing this in a modern context, we expand upon Macfarlane's idea and develop a model for real hyperbolic 3-space in which both points and isometries are expressed as complex quaternions, analogous…
The paper proves uniform Temple charts and applies them to null distance metrics.
problem Proving the existence of uniform Temple charts and their applications to null distance metrics.
method Constructing uniform Temple charts and estimating gradients of optical functions; applying these charts to study spacetime metrics.
result Proves (N,d^τ) is a rectifiable metric space and applies a Lorentzian isometry theorem. It is of interest to study supergravity solutions preserving a non-minimal fraction of supersymmetries. A necessary condition for supersymmetry to be preserved is that the spacetime admits a Killing spinor and hence a null or timelike Killing vector field. Any spacetime admitting a covariantly constant null vector fiel…
We study the causality relation in the 3-dimensional anti-de Sitter space AdS and its conformal boundary Ein. To any closed achronal subset Λ in Ein_2 we associate the invisible domain E(Λ) from Λ in AdS. We show that if Γ is a torsion-free discrete group of isometries of AdS preserving Λ and is non-elem…
In general relativity, an IDEAL (Intrinsic, Deductive, Explicit, ALgorithmic) characterization of a reference spacetime metric g0 consists of a set of tensorial equations T[g]=0, constructed covariantly out of the metric g, its Riemann curvature and their derivatives, that are satisfied if and only if g is loc…
The paper analyzes null infinity's geometry without restrictions.
problem Understanding null infinity's geometry without constraints.
method Coordinate-free approach, treating conformal factor as dynamical.
result Isometric spacetimes with identical free data at null infinity.
"Ends of hyperbolic 3-manifolds should support canonical Wick Rotations, so they realize effective interactions of their ending globally hyperbolic spacetimes of constant curvature." We develop a consistent sector of WR-rescaling theory in 3D gravity, that, in particular, concretizes the above guess for many geometrica…
We examine the existence of one parameter groups of diffeomorphisms whose infinitesimal generators annihilate all scalar polynomial curvature invariants through the application of the Lie derivative, known as I-preserving diffeomorphisms. Such mappings are a generalization of isometries and appear to be rel…
Study reveals how boundary wave operator determines metric properties on anti-de Sitter spacetimes.
problem Determining metric properties on anti-de Sitter spacetimes.
method Analysis of Klein-Gordon equation and Dirichlet-to-Neumann map.
result Determines the Taylor series of the bulk metric at the boundary.
Inverse problem solved for relativistic Boltzmann equation on spacetime.
problem Determining spacetime from causal measurements.
method Using the nonlinearity of the Boltzmann equation to uniquely determine the spacetime.
result The spacetime is uniquely determined up to isometry in the causal set I+(x−)∩I−(x+). Study of spacelike submanifolds with umbilical lightlike normals in Lorentzian spacetimes.
problem Geometric and topological constraints on codimension-two spacelike submanifolds.
method Analysis of submanifolds with umbilical lightlike normal directions, using geometric and topological constraints.
result Any such submanifold is contained in a lightlike hypersurface, which is totally umbilical if the lightlike normal direction is umbilical.
Extending BTZ models to complete hyperbolic surfaces.
problem Extending BTZ models to complete hyperbolic surfaces.
method Proving a parametrization result for globally hyperbolic Cauchy-maximal and Cauchy-compact locally Minkowski manifolds with extreme BTZ.
result The tangent bundle of the Teichmüller space parametrizes globally hyperbolic Cauchy-maximal and Cauchy-compact locally Minkowski manifolds with extreme BTZ.
Classical Kleinian groups are discrete subgroups of isometries of H n. The well-known theory of Kleinian groups starts with the definition of their associated limit set in the boundary of H n , and includes the geometric properties of the quotient hyperbolic space. This approach, naively applied, fails in the Lorentzia…
The paper constructs a new Ricci-flat metric on almost abelian Lie groups.
problem Finding Lorentzian homogeneous Ricci-flat metrics on almost abelian Lie groups.
method Constructing left-invariant metrics on almost abelian Lie groups, focusing on dimensions four or higher.
result A new Ricci-flat metric that generalizes the Petrov solution to higher dimensions.
Anosov representations are linked to specific spacetimes.
problem Understanding representations of groups into Lie groups.
method Holonomy of Anosov representations into O0(2, n) and spatial compactness of spacetimes.
result Anosov representations are the holonomy of CGHM conformally flat spacetimes.
Proves existence and uniqueness of vacuum black hole solutions in higher dimensions.
problem Existence and uniqueness of solutions to Einstein equations in higher-dimensional spacetimes.
method Develops a generalized plumbing construction and analyzes singular harmonic maps.
result Establishes existence and uniqueness for black hole solutions in (n+3)-dimensional spacetimes. New derivation shows spacetime interval is quadratic without light.
problem Deriving spacetime geometry from fundamental principles.
method Formalizing axioms of smoothness, homogeneity, isotropy, and determinism.
result Invariant spacetime interval is quadratic, independent of light.
We first show that the intrinsic, geometrical structure of a dynamical horizon is unique. A number of physically interesting constraints are then established on the location of trapped and marginally trapped surfaces in the vicinity of any dynamical horizon. These restrictions are used to prove several uniqueness theor…
Mathematical treatment of plane waves, proving their inextendibility and completeness.
problem Completeness and inextendibility of homogeneous plane waves.
method Cohomogeneity one Heisenberg actions, isometry group analysis.
result Proof of C2-inextendibility and geodesic completeness of non-flat homogeneous plane waves. Study shows how 3+1D cosmologies can evolve to de Sitter space under certain conditions.
problem Understanding the evolution of 3+1D cosmologies with specific symmetry constraints.
method Mean Curvature Flow methods applied to cosmologies with positive cosmological constant and specific symmetry groups.
result Asymptotically, 3+1D cosmologies evolve to de Sitter space under certain conditions.
The paper extends Hawking--Page solutions to various spacetimes with singularities.
problem Understanding the extensions of Hawking--Page solutions with different types of singularities.
method Kaluza--Klein reduction and Christodoulou's methods.
result Extensions of Lorentzian Hawking--Page solutions with null, spacelike singularities, and Cauchy horizons of Taub--NUT type are proven.
Proves symmetries of extremal horizons in spacetimes.
problem Proving symmetries of extremal horizons in arbitrary dimensions.
method Analyzes Killing vector fields and near-horizon geometry.
result Enhanced isometry groups and shifted Aretakis instability.
We solve Bartnik's stationary extension problem near Schwarzschild spheres.
problem Existence and uniqueness of asymptotically flat stationary vacuum spacetimes.
method Developed a double geodesic gauge, reducing equations to elliptic and transport-type problems.
result Local well-posedness for Bartnik stationary metric extension problem near Schwarzschild spheres.
Starting from the recent classification of quotients of Freund--Rubin backgrounds in string theory of the type AdS_{p+1} x S^q by one-parameter subgroups of isometries, we investigate the physical interpretation of the associated quotients by discrete cyclic subgroups. We establish which quotients have well-behaved cau…
Paper defines and proves geometric uniqueness of Einstein field equations.
problem Einstein field equations characteristic Cauchy problem
method Covariant definition of double null data, proving geometric uniqueness
result Double null data fully covariant and geometrically unique
New insights into black hole horizons from asymptotic expansions.
problem Understanding the geometry of black hole horizons.
method Proving the asymptotic expansion of spacetime metrics at non-degenerate Killing horizons.
result The full asymptotic expansion of smooth vacuum metrics at non-degenerate Killing horizons is determined by the horizon geometry.
Develops a foundational argument for Lorentzian or Euclidean spacetime geometry without light or electromagnetic phenomena.
problem Relativity without light
method Formalizing physical principles as axioms about an invariant interval function D result Invariant interval functions are powers of nondegenerate quadratic forms
This article propounds, in the wake of influential work of Fefferman and Graham about Poincaré extensions of conformal structures, a definition of a (Poincaré-)Schrödinger manifold whose boundary is endowed with a conformal Bargmann structure above a non-relativistic Newton-Cartan spacetime. Examples of such manifolds …
The model integrates Standard Model bosons into a higher-dimensional spacetime.
problem Integrating Standard Model bosons into a higher-dimensional spacetime.
method Considered a spacetime of the form P=M4imesK with K=SU(3), integrating the Einstein-Hilbert Lagrangian density over K. result Encodes not only Yang-Mills terms but also a kinetic term for the Higgs field and potential for gauge bosons.
New method proves Alexandrov theorem for curved spacetimes.
problem Proving Alexandrov theorem for curved surfaces with conical singularities.
method Adapting Volkov's variational method to handle Lorentzian angles.
result Existence of a locally Minkowski 3-manifold with conical singularities isometric to a given surface.
The paper strengthens a singularity theorem in General Relativity.
problem Proving conditions under which spacetime is incomplete or has specific geometric structures.
method Improving a previous theorem by Galloway and Ling, the paper introduces new conditions for spacetime properties.
result Conditions for spacetime to be past null geodesically incomplete, or have specific geometric structures.