Gravitational Mass Dependence on Velocity and the Conservation of Energy in General Relativity

Jaroslav Hynecek

doi:10.5539/apr.v10n2p26

Abstract

This paper investigates by simple means the relativistic accelerated motion of a small test body in a simulated uniform gravitational like field and compares the predictions of energy loss, perhaps by radiation, obtained from the General Relativity Theory (GRT) and from the Metric Theory of Gravity (MTG). The study is first conducted in a flat Minkowski space-time with simulated constant gravitational like force and later in a true curved space-time with a metric, which, however, is not derived from the GRT. It is found that the gravitational mass dependence on velocity in GRT is not correct, because it predicts a negative loss of energy while the MTG predicts correctly a positive loss. The energy is conserved in a curved space-time free fall where the gravitational mass does not depend on velocity. There can be no energy radiation during the test body free fall in a uniform gravitational field.

Highlights

The theories describing the accelerated motion are well understood in both; the General Relativity Theory (GRT) and the Metric Theory of Gravity (MTG)
The curved space-time, the GRT like theory, will be discussed later for a comparison. It is simple for both theories and the curved space-time theory to derive equations describing the simulated free fall like velocities and from that the energy loss of a small test body that moves under a uniform acceleration force
It was shown that the loss derived according to the GRT mass dependence on velocity is negative

Summary

Introduction

The theories describing the accelerated motion are well understood in both; the GRT and the MTG. In the GRT the inertial mass and the gravitational mass are assumed identical with identical dependencies on velocity. In the MTG, on the other hand, the gravitational mass depends on velocity differently than the inertial mass (Hynecek, 2005, 2017). The curved space-time, the GRT like theory, will be discussed later for a comparison. It is simple for both theories and the curved space-time theory to derive equations describing the simulated free fall like velocities and from that the energy loss of a small test body that moves under a uniform acceleration force

Theories

Conclusions