[Paper Review] Gravitational interaction of antimatter

M. Villata|arXiv (Cornell University)|Mar 8, 2010

Relativity and Gravitational Theory5 references3 citations

TL;DR

This paper proposes that matter and antimatter mutually repel gravitationally due to CPT invariance in general relativity, derived by applying CPT transformations to the geodesic equation and Einstein field equations. The key result is that gravitational interaction between matter and antimatter is repulsive, implying effective negative gravitational mass, which offers a theoretical basis for explaining cosmic acceleration without dark energy.

ABSTRACT

Until now, there is no experimental evidence on the gravitational behaviour of antimatter. While we may be confident that antimatter attracts antimatter, we do not know anything on the interaction between matter and antimatter. We investigate this issue on theoretical grounds. Starting from the CPT invariance of physical laws, we transform matter into antimatter in the equations of both electrodynamics and gravitation. In the former case, the result is the well-known change of sign of the electric charge. In the latter, we find that the gravitational interaction between matter and antimatter is a mutual repulsion. This result supports cosmological models attempting to explain the Universe accelerated expansion in terms of a matter-antimatter symmetry.

Motivation & Objective

• To determine the gravitational interaction between matter and antimatter using fundamental symmetries of physics.
• To resolve the long-standing uncertainty about whether matter and antimatter attract or repel gravitationally.
• To explore whether gravitational repulsion between matter and antimatter could explain the observed accelerated expansion of the Universe.
• To provide a theoretical foundation for cosmological models where antimatter resides in large-scale voids, avoiding annihilation through mutual repulsion.

Proposed method

• Applying CPT transformations to the equations of motion in general relativity, treating antimatter as time-reversed matter via the Feynman-Stückelberg interpretation.
• Transforming the energy-momentum tensor $ T^{ ueta} $ under CPT, showing it remains CPT-even due to sign changes in both four-velocity and mass.
• Analyzing the geodesic equation $ \frac{d^2x^\lambda}{d\tau^2} = -\frac{m_{(\rm g)}}{m_{(\rm i)}} \frac{dx^\mu}{d\tau} \Gamma^\lambda_{\mu\nu} \frac{dx^\nu}{d\tau} $ under CPT, revealing that matter-antimatter systems experience reversed acceleration.
• Deriving that the gravitational field $ \Gamma^\lambda_{\mu\nu} $ is CPT-odd, so when applied to an antimatter source, it produces a repulsive force on matter.
• Comparing the CPT-transformed geodesic equation with the original, showing that the sign change leads to gravitational repulsion between matter and antimatter.
• Using the invariance of the Einstein field equation $ R_{\mu\nu} - \frac{1}{2}g_{\mu\nu}R = -8\pi G T_{\mu\nu} $ under CPT, confirming that antimatter generates spacetime curvature identical to matter but with reversed sign in cross-interactions.

Experimental results

Research questions

• RQ1 Does CPT invariance in general relativity imply that matter and antimatter repel gravitationally?
• RQ2 Can gravitational repulsion between matter and antimatter explain the observed accelerated expansion of the Universe?
• RQ3 Is it possible for antimatter to exist in large-scale voids without annihilating with matter, due to gravitational repulsion?
• RQ4 How does the CPT transformation affect the geodesic equation and the energy-momentum tensor in curved spacetime?
• RQ5 What is the role of effective negative gravitational mass in matter-antimatter gravitational interactions?

Key findings

• The gravitational interaction between matter and antimatter is repulsive, as shown by CPT transformation of the geodesic equation, leading to a sign reversal in acceleration.
• Antimatter generates spacetime curvature identical to matter under CPT, but the interaction between matter and antimatter fields results in mutual repulsion.
• The energy-momentum tensor $ T^{\nu\beta} $ is CPT-even, ensuring consistency of the field equations under transformation, while the affine connection $ \Gamma^\lambda_{\mu\nu} $ is CPT-odd, enabling repulsion in cross-interactions.
• The result implies that an anti-apple would be repelled by an Earth, and vice versa, due to the effective negative gravitational mass in matter-antimatter systems.
• This repulsion provides a natural mechanism to prevent annihilation in large-scale matter-antimatter symmetric cosmologies, supporting models where voids host antimatter.
• The theoretical framework offers an alternative to the $\Lambda$CDM model by eliminating the need for dark energy and possibly dark matter, as voids can be explained by primordial negative fluctuations acting as effective negative mass sources.