# An Approach for Modelling Tachyons with Gravitation

## TL;DR

This paper develops a Hamiltonian framework within classical relativity to model tachyons and their gravitational effects, potentially explaining dark matter phenomena through tachyonic neutrinos.

## Contribution

It introduces a Hamiltonian model for tachyons in gravitational fields using linearized Einstein equations and a static metric approximation.

## Key findings

- Provides a formula for tachyon-gravity interactions
- Suggests tachyonic neutrinos could account for dark matter effects
- Enables future testing of tachyonic particles in cosmology

## Abstract

This work expands previous efforts, within the classical theories of Special and General Relativity, to include tachyons (faster-than-light particles) along with ordinary (slower-than-light) particles at any energy. The objective here is to construct a Hamiltonian that includes both the particles and the gravitational field that they produce. We do this with a linear approximation for the Einstein field equations; and we also assume a time-independent gravitational metric implied by a static picture of the particles' motion. The resulting formula will allow serious modelling to test the idea that cosmic background neutrinos may be tachyons, which can produce the observed gravitational effects now ascribed to some mysterious Dark Matter.