An Armenian astrophysicist, Dr. Gagik Ter-Kazarian, has solved a century-old problem in Albert Einstein’s general theory of relativity: how to define and calculate the relative velocity of a test particle with respect to an observer in curved spacetime. Working at the Victor Hambardzumyan Byurakan Astrophysical Observatory in Armenia, Dr. Ter-Kazarian addressed a fundamental issue that had remained unresolved since 1915. His breakthrough includes determining the “kinetic recession velocity” of astronomical objects, demonstrating that these velocities always remain below the speed of light in a vacuum—thereby preserving the principle of causality.
The achievement, announced by the National Academy of Sciences of Armenia, marks a major milestone in theoretical physics and was detailed in two peer-reviewed articles published in the journal Gravitation and Cosmology.
In his 2022 article titled “On the Kinetic Recession Velocities of Astronomical Objects” (Vol. 28, No. 2), Dr. Ter-Kazarian defines and calculates the actual, so-called “kinetic” recession velocity of astronomical bodies. The results confirm that these velocities, regardless of redshift values, do not exceed the speed of light in a vacuum—thus preserving causality, a foundational principle in physics.
He also quantified how much of astronomical objects’ motion is due to cosmic expansion, providing another critical metric for understanding large-scale motion in the universe.
Dr. Ter-Kazarian explained that this astrophysical challenge is one part of a broader and long-unsolved issue in physics: calculating “relative velocity” in curved space. Since 1915, this problem remained unresolved within the framework of Einstein’s general relativity due to the difficulty of performing “parallel transport” of a velocity vector in curved spacetime—an essential requirement for calculating relative motion.
In 2023, he announced that he had overcome this theoretical barrier by solving the problem for any Riemannian space. His findings were published in a second article, “Coordinate-Independent Definition of Relative Velocity in Pseudo-Riemannian Space-Time: Implications for Special Cases” (Vol. 29, No. 1), where he defines and calculates the relative velocity of a test particle along an observer’s worldline for all possible scenarios.
As an application, Dr. Ter-Kazarian computed this velocity in several key contexts, including Minkowski metrics, arbitrary stationary metrics with both particle and observer at rest, homogeneous gravitational fields, rotating coordinate systems, Schwarzschild metrics, Kerr-type metrics, and Robertson–Walker metrics.
This groundbreaking work places Armenia at the forefront of global theoretical physics research and contributes to deepening our understanding of one of the most complex areas in Einstein’s legacy.
