In theoretical physics, negative mass is a hypothetical type of exotic matter whose mass is of opposite sign to the mass of normal matter, e.g. −1 kg. Such matter would violate one or more energy conditions and exhibit strange properties such as the oppositely oriented acceleration for an applied force orientation. It is used in certain speculative hypothetical technologies such as time travel to the past and future, construction of traversable artificial wormholes, which may also allow for time travel, Krasnikov tubes, the Alcubierre drive, and potentially other types of faster-than-light warp drives. Currently, the closest known real representative of such exotic matter is a region of negative pressure density produced by the Casimir effect.
In cosmology In December 2018, astrophysicist Jamie Farnes from the University of Oxford proposed a "dark fluid" theory, related, in part, to notions of gravitationally repulsive negative masses, presented earlier by Albert Einstein, that may help better understand, in a testable manner, the considerable amounts of unknown dark matter and dark energy in the cosmos.
In general relativity Negative mass is any region of space in which for some observers the mass density is measured to be negative. This may occur due to a region of space in which the sum of the three normal stress components (pressure on each of three axes) of the Einstein stress–energy tensor is larger in magnitude than the mass density. All of these are violations of one or another variant of the positive energy condition of Einstein's general theory of relativity; however, the positive energy condition is not a required condition for the mathematical consistency of the theory.
Inertial versus gravitational mass In considering negative mass, it is important to consider which of these concepts of mass are negative. Ever since Newton first formulated his theory of gravity, there have been at least three conceptually distinct quantities called mass:
inertial mass – the mass m that appears in Newton's second law of motion, F = m a "active" gravitational mass – the mass that produces a gravitational field that other masses respond to "passive" gravitational mass – the mass that responds to an external gravitational field by accelerating. The law of conservation of momentum requires that active and passive gravitational mass be identical. Einstein's equivalence principle postulates that inertial mass must equal passive gravitational mass, and all experimental evidence to date has found these are, indeed, always the same. In most analyses of negative mass, it is assumed that the equivalence principle and conservation of momentum continue to apply without using any matter in the process, and therefore all three forms of mass are still the same, leading to the study of "negative mass". But the equivalence principle is simply an observational fact, and is not necessarily valid. If such a distinction is made, a "negative mass" can be of three kinds: whether the inertial mass is negative, the gravitational mass, or both. In his 4th-prize essay for the 1951 Gravity Research Foundation competition, Joaquin Mazdak Luttinger considered the possibility of negative mass and how it would behave under gravitational and other forces. In 1957, following Luttinger's idea, Hermann Bondi suggested in a paper in Reviews of Modern Physics that mass might be negative as well as positive. He pointed out that this does not entail a logical contradiction, as long as all three forms of mass are negative, but that the assumption of negative mass involves some counter-intuitive form of motion. For example, an object with negative inertial mass would be expected to accelerate in the opposite direction to that in which it was pushed (non-gravitationally). There have been several other analyses of negative mass, such as the studies conducted by R. M. Price, though none addressed the question of what kind of energy and momentum would be necessary to describe non-singular negative mass. Indeed, the Schwarzschild solution for negative mass parameter has a naked singularity at a fixed spatial position. The question that immediately comes up is, would it not be possible to smooth out the singularity with some kind of negative mass density. The answer is yes, but not with energy and momentum that satisfies the dominant energy condition. This is because if the energy and momentum satisfies the dominant energy condition within a spacetime that is asymptotically flat, which would be the case of smoothing out the singular negative mass Schwarzschild solution, then it must satisfy the positive energy theorem, i.e. its ADM mass must be positive, which is of course not the case. However, it was noticed by Belletête and Paranjape that since the positive energy theorem does not apply to asymptotic de Sitter spacetime, it would actually be possible to smooth out, with energy–momentum that does satisfy the dominant energy condition, the singularity of the corresponding exact solution of negative mass Schwarzschild–de Sitter, which is the singular, exact solution of Einstein's equations with cosmological constant. In a subsequent article, Mbarek and Paranjape showed that it is in fact possible to obtain the required deformation through the introduction of the energy–momentum of a perfect fluid.
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