The question that immediately comes up is, would it not be possible to smooth out the singularity with some kind of negative mass density. Indeed, the Schwarzschild solution for negative mass parameter has a naked singularity at a fixed spatial position. Price, though none addressed the question of what kind of energy and momentum would be necessary to describe non-singular negative mass. There have been several other analyses of negative mass, such as the studies conducted by R. 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). 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. 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. 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. 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. But the equivalence principle is simply an observational fact, and is not necessarily valid. In most analyses of negative mass, it is assumed that the equivalence principle and conservation of momentum continue to apply, and therefore all three forms of mass are still the same, leading to the study of "negative mass". 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. The law of conservation of momentum requires that active and passive gravitational mass be identical. "passive" gravitational mass – the mass that responds to an external gravitational field by accelerating."active" gravitational mass – the mass that produces a gravitational field that other masses respond to. inertial mass – the mass m that appears in Newton's second law of motion, F = m a.Ever since Newton first formulated his theory of gravity, there have been at least three conceptually distinct quantities called mass: In considering negative mass, it is important to consider which of these concepts of mass are negative. 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. This could occur due to a region of space in which the stress component of the Einstein stress–energy tensor is larger in magnitude than the mass density. Negative mass is any region of space in which for some observers the mass density is measured to be negative. 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. Currently, the closest known real representative of such exotic matter is a region of negative pressure density produced by the Casimir effect. 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. Such matter would violate one or more energy conditions and show some strange properties such as the oppositely oriented acceleration for negative mass. In theoretical physics, negative mass is a type of exotic matter whose mass is of opposite sign to the mass of normal matter, e.g.
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