Gravity of Negative Mass: Some Subtle Aspects and Implications


  • Chandra Sivaram Indian Institute of Astrophysics, Bengaluru.
  • Kenath Arun CHRIST (Deemed to be University), Bengaluru
  • Avijeet Prasad University of Oslo, Oslo, Norway.



Negative mass, early Universe, inflation, dark matter, dark energy


The gravitational interaction has mass of only one sign as the source that is conventionally taken to be positive. The existence of negative mass is not precluded in either Newtonian gravity or general relativity. Negative masses have been invoked in many recent papers to understand the dominance of repulsive dark energy that is accelerating the universe. Here we discuss the various gravitating properties of negative mass particles and their implications for black holes, cosmology, and fundamental physics. Inconsistencies in the earlier works are also discussed. We study the possibility of such negative mass particles accounting for the accelerated expansion of the universe. We set constraints on the density of these negative mass particles based on astrophysical observations.

Author Biographies

Chandra Sivaram, Indian Institute of Astrophysics, Bengaluru.

Indian Institute of Astrophysics, Bengaluru, Karnataka, India.

Kenath Arun, CHRIST (Deemed to be University), Bengaluru

Department of Physics and Electronics, CHRIST (Deemed to be University), Bengaluru, Karnataka, India.

Avijeet Prasad, University of Oslo, Oslo, Norway.

Institute of Theoretical Astrophysics, University of Oslo, Oslo, Norway.


Jammer, M.: Concepts of Mass in Classical and Modern Physics. Harvard Univ. Press, Cambridge (1961)

Bondi, H.: Negative mass in general relativity. Rev. Mod. Phys. 29, 423 (1957)

Terletsky,Ya.P.: Positive, negative and imaginary rest masses. J. Phys. Radium, 23, 910 (1963)

Farnes, J.S.: A unifying theory of dark energy and dark matter: Negative masses and matter creation within a modified ΛCDM framework. Astron. Astrophys. 620, A92 (2018)

Petit, J.P., d’Agostini, G.: Negative mass hypothesis in cosmology and the nature of dark energy. Astrophys. Space Sci. 354, 611 (2014)

Benoit-Lévy, A., Chardin, G.:Introducing the Dirac-Milne universe. Astron. Astrophys. 537, A78 (2012)

Einstein, A.: Comment on Schrödinger’s Note “On a System of Solutions for the Generally Covariant Gravitational Field Equations”. Physikalische Zeitschrift, 19, 165 (1918). Translated by Engel A. in The Collected Papers of Albert Einstein, Vol. 7, The Berlin Years: Writings, 1918–1921 (Princeton University Press).

Messiah, A.: Quantum mechanics. Interscience Publishers, New York (1961)

Sakurai, J.J.: Mass reversal and weak interactions. Il Nuovo Cimento. 7, 649 (1958)

Ashcroft, N.W., Mermin, N.D.: Solid State Physics. Harcourt, New York (1976)

Morris, M.S. et al.:Wormholes, time machines, and the weak energy condition. Phys. Rev. Lett. 61, 1446 (1988)

Hawking, S.W.:Particle creation by black holes. Comm. Math. Phys. 43, 199 (1975)

Caldwell, R.R.:A phantom menace? Cosmological consequences of a dark energy component with super-negative equation of state. Phys. Lett. B. 545, 23 (2002)

Winterberg, F.:Remark concerning the gravitational interaction of matter and anti-matter. Il Nuovo Cimento. 19, 186 (1961)

Forward, R.L.:Negative matter propulsion. J. Propul. Power. 6, 28 (1990)

Buchdahl, H.A.:General relativistic fluid spheres. Phys. Rev. 116, 1027 (1959)

de Sabbata, V., Sivaram, C.: Spin and Torsion in Gravitation. World Scientific, Singapore, (1994)

Sivaram, C., Arun, K.:Some enigmatic aspects of the early universe. Astrophys. Space Sci. 334, 225 (2011)

Sivaram, C., Arun, K.:Primordial rotation of the universe, hydrodynamics, vortices and angular momenta of celestial objects. Open Astron. J. 5, 7 (2012)

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