New representation of field equations for QMAG, presenting new solutions.
problem Finding new explicit solutions for quadratic metric-affine gravity.
method Developed a new explicit representation of field equations without assumptions on torsion properties.
result Presented two conjectures on new types of solutions of QMAG.
A classical pp-wave is a 4-dimensional Lorentzian spacetime which admits a nonvanishing parallel spinor field; here the connection is assumed to be Levi-Civita. We generalise this definition to metric compatible spacetimes with torsion and describe basic properties of such spacetimes. We use our generalised pp-waves fo…
In this paper we deal with quadratic metric-affine gravity, which we briefly introduce, explain and give historical and physical reasons for using this particular theory of gravity. Further, we introduce a generalisation of well known spacetimes, namely pp-waves. A classical pp-wave is a 4-dimensional Lorentzian spacet…
We develop the method of anholonomic frames with associated nonlinear connection (in brief, N--connection) structure and show explicitly how geometries with local anisotropy (various type of Finsler--Lagrange--Cartan--Hamilton geometry) can be modeled in the metric--affine spaces. There are formulated the criteria when…
The anholonomic frame method is generalized for non--Riemannian gravity models defined by string corrections to the general relativity and metric-affine gravity (MAG) theories. Such spacetime configurations are modeled as metric-affine spaces provided with generic off-diagonal metrics (which can not be diagonalized by …
A method to derive Lagrangians from field equations in metric-affine theories of gravity.
problem Deriving Lagrangians from field equations in metric-affine theories of gravity.
method Variational completion method to transform field equations into Euler-Lagrange equations and find a Lagrangian.
result Starting from metric equations, full metric equations and Lagrangian can be derived up to metric-independent terms.
The paper develops methods to generate invariant quantities in Metric-Affine Geometry.
problem Developing methods to generate invariant quantities in Metric-Affine Geometry.
method The paper introduces a theorem to generate invariant quantities under transformations of the affine connection, proving invariance conditions.
result Theorem establishing conditions for invariance of functionals under transformations of the affine connection.
A common approach to metric-affine, local Poincaré, special-relativistic and Galilei spacetime geometry is developed. Starting from an affine composite bundle, we introduce local reference frames and their evolution along worldlines and we study both, absolute and relative simultaneity postulates, giving rise to altern…
We consider spacetime to be a connected real 4-manifold equipped with a Lorentzian metric and an affine connection. The 10 independent components of the (symmetric) metric tensor and the 64 connection coefficients are the unknowns of our theory. We introduce an action which is quadratic in curvature and study the resul…
Paper presents an action principle for Einstein-Weyl equations in 3D.
problem Finding an action principle for Einstein-Weyl equations.
method Metric affine f(R) gravity action plus additional terms involving Lagrange multipliers and gravitational Chern-Simons contributions.
result The Weyl vector dynamics is governed by a special case of the generalized monopole equation.
We construct new classes of exact solutions in metric--affine gravity (MAG) with string corrections by the antisymmetric H--field. The solutions are parametrized by generic off--diagonal metrics possessing noncommutative symmetry associated to anholonomy framerelations and related nonlinear connection (N--connection)…
Presented spherical symmetric teleparallel geometry frames and field equations.
problem Teleparallel geometry with spherical symmetry.
method Developed proper and diagonal co-frames, spin connections, and field equations.
result Advantage of diagonal co-frame over proper in f(T) teleparallel gravity.
The book contains a collection of works on Riemann-Cartan and metric-affine manifolds provided with nonlinear connection structure and on generalized Finsler-Lagrange and Cartan-Hamilton geometries and Clifford structures modelled on such manifolds. The choice of material presented has evolved from various applications…
Classifies solutions in multisymplectic field theories using geometric gauge freedom.
problem Classifying solutions in multisymplectic field theories.
method Using the kernel of a premultisymplectic form and equivalence relations.
result Equivalence relations and reduction procedures for sections.
New geometries defined for string models, filling gaps in the literature.
problem Developing mathematical structures for string models.
method Defining E-metric-connection geometries and locality structures.
result Unified framework for metric-affine and generalized geometries.
Study of energy conservation in fourth-order gravity theories.
problem Conservation principles in fourth-order gravitational theories.
method Detailed analysis of energy concepts, focusing on quadratic Lagrangian and solutions.
result Presentation of positive energy theorems in restricted situations.
Classifies connections on Galilei manifolds, generalizing known results.
problem Classifying general affine connections on Galilei manifolds.
method Classification through tensor fields, extending known Galilei connections.
result Additional freedom in connections not metric-compatible, linked to clock form and space metric.
Curve shortening in metric-affine plane shrinks convex curves to points.
problem Shortening curves in non-Euclidean spaces.
method Curve shortening flow in metric-affine plane with geometric conditions.
result Closed convex curves in metric-affine plane shrink to points in finite time.
Integral formulas for metric-affine spaces with specific distributions.
problem Finding geometrical obstructions for distributions and foliations.
method Integral formulas involving Ricci and scalar curvatures, second fundamental forms, and integrability tensors.
result Splitting of manifolds and geometrical obstructions for distributions and foliations.
Researchers found invariant metric connections on Berger spheres that are Einstein with skew torsion.
problem Determining invariant metric affine connections on Berger spheres that are Einstein with skew torsion.
method Explicitly determined and expressed connections in both Riemannian and Lorentzian signatures.
result Every Berger sphere with Lorentzian signature admits invariant metric affine connections Einstein with skew-torsion up to S3. Study on wormholes in modified gravity using generalized geometry.
problem Existence and conditions for thin shell wormholes in F(R)-gravity. method Used Colombeau algebra to define generalized geometry and analyze wormholes.
result Suitable quadratic F can satisfy the null energy condition (NEC). By analyzing the affine Taylor expansion of a non-degenerate plane curve, we obtain characterizations of classes of such curves via curvature properties of the gravity curve. The proof is based on an analysis of the degree parity and leading coefficients of polynomials occurring in the expansion.
Study of Einstein-Hilbert action on metric-affine spaces with connections.
problem Formulating and solving variational problems for mixed Einstein-Hilbert action.
method Developed variational formulas for extrinsic geometry, derived Euler-Lagrange equations, and characterized critical points.
result Derived new equations analogous to Einstein and Cartan equations, with a new Ricci type tensor.
New theory connects string theory to swampland distance conjecture.
problem Connecting string theory to swampland distance conjecture.
method Deformations of the heterotic superpotential, treating separately for large fluxes or large distances, integrating out fields to obtain a new field theory.
result New holomorphic theory defined, connects to swampland distance conjecture.
We call a manifold with torsion and nonmetricity the metric-affine manifold. The nonmetricity leads to a difference between the auto parallel line and the extreme line, and to a change in the expression of the Frenet transport and moving basis. The torsion leads to a change in the Killing equation. We also need to add …
Researchers find conditions for autoparallels to be Finsler geodesics.
problem Existence of a Finsler Lagrangian metrizing autoparallels in metric-affine geometry.
method Determined necessary and sufficient conditions for Finsler metrizability of torsion-free affine connections.
result A broad class of connections is Finsler metrizable, making their autoparallels Finsler geodesics.
Courant algebroid connections help describe string theory equations.
problem Describing equations of motion in string theory.
method Connection on Courant algebroid with curvature tensor.
result Curvature tensor describes string theory equations.
In abstract Yang-Mills theory the standard instanton construction relies on the Hodge star having real eigenvalues which makes it inapplicable in the Lorentzian case. We show that for the affine connection an instanton-type construction can be carried out in the Lorentzian setting. The Lorentzian analogue of an instant…
Contravariant gravity on Poisson manifolds is linked to Einstein gravity.
problem Exploring the relationship between Poisson gravity and Einstein gravity.
method Investigating the compatibility of Poisson and Riemann structures to define a unique connection and derive the contravariant gravity theory.
result The contravariant gravity theory can be described as an equivalent system of Einstein gravity coupled to matter.
Introduces a new relation between BF theory and gravity.
problem Formulating gauge theories based on 2-connections.
method Categorical generalization of BF theory coupled to gravity.
result Alternative relation between BFCG and gravity.
Proposes new conformal parametrizations for modified Einstein gravity.
problem Initial data in modified Einstein gravity theories.
method Proposes conformal parametrizations that lead to conformally covariant systems.
result Some conformal parametrizations give rise to conformally covariant systems.
PhD dissertation on Finsler geometry and gravity, focusing on Berwald spaces and exact solutions.
problem Characterizing and solving Finsler gravity equations.
method Analysis of Berwald spaces, (α,β)-metrics, and exact solutions to Finsler gravity equations. result Exact vacuum solutions in Finsler gravity.
We present new classes of exact solutions with noncommutative symmetries constructed in vacuum Einstein gravity (in general, with nonzero cosmological constant), five dimensional (5D) gravity and (anti) de Sitter gauge gravity. Such solutions are generated by anholonomic frame transforms and parametrized by generic off…
A differential calculus, differential geometry and the E-R Gravity theory are studied on noncommutative spaces. Noncommutativity is formulated in the star product formalism. The basis for the gravity theory is the infinitesimal algebra of diffeomorphisms. Considering the corresponding Hopf algebra we find that the defo…
We argue that Horava-Lifshitz (HL) gravity provides the minimal holographic dual for Lifshitz-type field theories with anisotropic scaling and dynamical exponent z. First we show that Lifshitz spacetimes are vacuum solutions of HL gravity, without need for additional matter. Then we perform holographic renormalization …
We use conformal, but ghostful, Weyl gravity to study its ghost-free, second derivative, partially massless (PM) spin 2 component in presence of Einstein gravity with positive cosmological constant. Specifically, we consider both gravitational- and self- interactions of PM via the fully non-linear factorization of conf…
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.
A theory of gravitation is proposed, modeled after the notion of a Ricci flow. In addition to the metric an independent volume enters as a fundamental geometric structure. Einstein gravity is included as a limiting case. Despite being a scalar-tensor theory the coupling to matter is different from Jordan-Brans-Dicke gr…
A new geometric flow K-flow on 3-manifolds shrinks or preserves homogeneous spheres.
problem Analyzing the behavior of Thurston's model geometries under the K-flow. method Defining and studying the K-flow on 3-dimensional Riemannian manifolds, using a DeTurck-type argument for short-time existence. result The K-flow shrinks or preserves homogeneous spheres, showing short-time existence. De Donder form for gravity is globally defined.
problem Defining a globally defined De Donder form for second order gravity.
method Using Ostrogradski's Legendre transformation and diffeomorphism invariance.
result De Donder form is globally defined by local coordinate descriptions.
We simplify and extend a 6D conformal gravity theory to 8D, linking it to Q-curvature.
problem Constructing and understanding conformal gravity actions in different dimensions.
method Streamlined construction of 6D action, proving existence of 8D action, relating to Q-curvature.
result A unique 8D conformal gravity action exists with Einstein metrics as solutions.
Analyzing static solutions in Finsler gravity, extending known results.
problem Extending the analyticity of static vacuum solutions to Finsler spacetimes.
method Examining Finsler spacetimes with properties similar to static Lorentzian spacetimes.
result Finsler spacetimes with vanishing Ricci scalar are analytic.
Identifies null hypersurfaces with constant surface gravity.
problem Understanding null hypersurfaces in spacetimes.
method Analyzes spacetimes satisfying null convergence condition.
result Null hypersurfaces admit null sections with constant surface gravity.
Explains non-lorentzian theories and their dynamics.
problem Understanding non-lorentzian kinematics and dynamics.
method Review of kinematical spacetimes, construction of particle dynamics actions, discussion of gravity theories and field theories.
result Introduction and analysis of non-lorentzian gravity and field theories.
HR in 8D encodes unique conformal gravity with negative curvature.
problem Holographic Renormalisation in 8D Einstein Gravity.
method Relating HR to Topological Regularisation and adding the Euler term.
result The unique conformal gravity theory reproduces the polynomial and cancels divergent terms.
Special issue honors Stanley Deser, focusing on advanced physics topics.
problem None explicitly stated in the abstract.
method Collection of articles in memory of Stanley Deser.
result No specific key result mentioned in the abstract.
Projective connection explains gravity dynamics in 2D.
problem Understanding dynamics in 2D gravity with projective connection.
method Using projective connection over affine connections, defining action with curvature invariants.
result Projective connection naturally describes metric interaction in 2D gravity.
Study Codazzi tensors in space-times, linking to Cotton gravity.
problem Understanding Codazzi tensors and their role in space-times.
method Analyzing geometric properties and proving conditions for Codazzi tensors.
result Codazzi tensors restrict space-times, influencing energy-momentum tensors in Cotton gravity.