Research Theme
Field Equation
The Einstein Double Field Equation as a proposed field equation of closed-string gravity.
Einstein Double Field Equation
If Double Field Theory is gravity, its variational principle must determine the analogue of Einstein's equation. The proposed field equation is the Einstein Double Field Equation,
The point of this equation is not its formal resemblance to Einstein's equation. The point is that geometry must respond to sources through a covariant field equation.
In a Riemannian sector this equation must reproduce the familiar equations of the universal bosonic supergravity sector.
Complete Closed-String Massless Sector
The Einstein Double Field Equation is proposed as a unified field equation for the complete closed-string massless sector. Its purpose is to test whether the fields \(g_{\mu\nu}\), \(B_{\mu\nu}\), and \(\phi\) can be treated as parts of one gravitational structure rather than as a metric plus auxiliary matter fields.
This proposal remains a working hypothesis. It must be constrained by mathematical coherence, reduction to known Riemannian sectors, coupling to sources, propagation, and empirical tests.
For the technical formulation and coupled Riemannian equations, see the lecture notes.
Related Directions
A field equation becomes meaningful only as part of a larger chain. Geometry supplies the covariant objects. The field equation expresses dynamics. Propagation and matter coupling determine what physical fields see. Phenomenology asks whether the resulting structure can be tested.