WHY GRAVITATIONAL RADIATION IS BELIEVED TO HAVE NEGATIVE MASS

by

Edmond S. Miksch

ed_miksch@yahoo.com

Copyright: March 21, 2007

Abstract

It is believed that gravitational radiation has negative mass. A gravitional radiator, such as a pair of closely-orbiting black holes or a pair of closely-orbiting neutron stars is expected to gain energy as a result of gravitational radiation, although it may be losing energy by other mechanisms. In particular, the black holes may be imparting a stirring motion to dark matter in the vicinity, which would cause the black holes to lose energy.

Prequisites

An understanding of basic physics including electromagnetism, and an understanding of the basic principles of special and general relativity, will be helpful for understanding the following.

Terminology and Conventions

We use the term "mass" to refer to to the conserved quantity, and never use it for the rest mass of a particle, since rest mass is not conserved. Mass has gravitational properties and inertial properties. We see no reason for questioning the equivalence of gravitational and inertial mass. Energy is viewed as comprising mass in any volatile form.

Vector quantities, which have both direction and magnitude, are denoted by bold face characters. When the syimbol for a vector quantity is not in boldface, it denoteds the magnitude of the vector quantity. Asterisks are sometimes used to denote multiplication. Weight is considered to be a real force, as is centrifugal force and the Coriolis force. In this, we rely on the relativistic principle that we may view the universe from any coordinate frame we choose.

We do not, however, question purists who prefer to consider geodesics in Minkowsky space, rather than considering gravitational forces as contributing to the acceleration of a mass. Our attempt is to stay as close as possible to everyday experience. SI units are employed. These include the meter, second, kilogram, Joule, Newton, Volt, Ampere, Coulomb, etc.

Introduction to Gravitational Radiation

In the home page, negative-mass.com, it was shown that the gravitational field has a negative mass density. Likewise, on the page, Calculation of the Mass Density of the Coriolis Field , the Coriolis field is shown to have a negative mass density. These negative densities can be used in one of the arguments showing that gravitational radiation carries negative energy and hence negative mass. Another approach is to examine the equations relating the gravitational and Coriolis fields in a gravitational wave, and employ the gravitational equivalent of the Poynting vector of electromagnetism to determine the direction in which energy flow occurs. One finds that the direction of the energy flow is opposite to the direction of propagation of the gravitational wave. Thus, the gravitational wave carries negative energy and hence, negative mass.

This shouldn't be too surprising. After all, a bicycle chain in tension carries negative energy. Energy flows from the front sprocket (driven by the pedals) to the rear sprocket (attached to the rear wheel), but the tense chain moves from the rear sprocket to the front sprocket.

One might ask how a wave which carries negative energy would be able to move any component, such as a mirror, of a graviatational wave detector. The answer is that if the gravitational wave gives positive energy to the mirror to move the mirror, then the negative energy of the gravitational radiation is increased. Coherent amplification of the gravitational wave may occur, or a gravitational wave in a direction different from that of the incoming wave may be created. Thus, energy is conserved.

We understand that observations have been made of closely-orbiting black holes, and that the period of rotation is seen to decrease, indicating a loss of energy. We question whether that loss of energy is due to gravitational radiation having positive energy because the theoretical indications are so strong that gravitational radiation has negative energy. Perhaps some other mechanism causes loss of energy. For example, the black holes may introduce stirring motions in nearby dark matter, and thus lose energy.

Theory of Gravitational Radiation

The reader is encouraged to develop the theory, following the approaches suggested in the introduction, and to determine whether the energy carried by a gravitational wave is negative or positive. A particular suggestion is to calculate the gravitational equivalent of the Poynting vector and determine whether energy flow is parallel or antiparallel to the direction of the gravitational wave.

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