# Relativistic gravity fields and electromagnetic fields generated by flows of matter

## TL;DR

This paper derives a relativistic gravity field from moving matter, completing Feynman's electromagnetic formulas, and expresses electromagnetic and charge-current fields in terms of generalized functions within Maxwell's framework.

## Contribution

It presents a relativistic gravity field generated by matter flows and amends Feynman's electromagnetic potential formulas for mathematical completeness.

## Key findings

- Derived a relativistic gravity field from matter flows.
- Amended Feynman's electromagnetic potential formulas.
- Expressed charge and current densities as generalized functions.

## Abstract

One of the highlight of this note is that the author presents the relativistic gravity field that Einstein was looking for. The field is a byproduct of the matter in motion. This field can include both the discrete and continuous components. In free space the waves produced in this field propagate with velocity of light. Another highlight is the proof of amended Feynman's formulas for electromagnetic potentials. This makes the formulas mathematically complete and precise. The main result can be stated as follows. In a fixed Lorentzian frame given is a trajectory $r_2(t,r_0)$ of flow of matter. The parameter $r_0$ changes in a compact set $F$ representing the position of the matter at some initial time $t_0.$ The flow must satisfy certain conditions of regularity. Given any signed measure $q(Q)$ of finite variation defined on Borel subsets of $F,$ representing total charge contained in the set $Q\subset F,$ such a flow determines the scalar $\phi$ and the vector $A$ potentials for a pair $(E,B)$ of fields satisfying Maxwell's equations and as a byproduct the field $\varrho,$ representing density of charges, and the field $j,$ representing the density of currents. All these fields are represented in terms of generalized functions.