# Theory of Relativity revisited: New force at large distances

## Is there something missing from Einstein’s equations? Daniel Grumiller from the Vienna University of Technology is proposing a new model of gravity which could reconcile the theory of relativity with astronomical observation.

Vienna (VUT). – Einstein revolutionized our understanding of the universe – but until today, some important questions in gravitational physics remain unanswered. While the motion of Planets around the Sun can be predicted with great accuracy, the speed of the stars circling the center of galaxies can still not be explained satisfactorily. The existence of invisible “dark matter” has been proposed, to explain these phenomena. At the Institute for Theoretical Physics, Daniel Grumiller is doing research on the theory of gravitation. His calculations show that an extension of the theory of relativity could answer open questions. His ideas have been published in this week’s edition of “Physical Review Letters”.

Could gravity at large distances have additional components, which so far have not been taken into account? On the quest for yet unknown factors which affect the force of gravity, Grumiller went back to the very foundations of the theory. He started out with the question: Which kind of equations that could describe gravity, are allowed by mathematics? Only specific kinds of mathematical expressions can be included into the physics of gravitation without violating the symmetries of the universe or clearly contradicting physical observations we make every day.**An unknown additional force**

Daniel Grumiller simplified the theory of gravitation by first of all looking at spherically symmetric cases – such as the gravitational field of a planet or a star or of an approximately spherical galaxy. “We can show mathematically, which factors affect the force of gravity”, Grumiller explains. Some of these factors are well known: The classical Newtonian force of gravity and Einstein’s relativistic corrections – both of which decrease at large distances. Also, Einstein’s “cosmological constant”, which plays a role at extremely large distances, appears quite naturally in the equations. In addition to that, however, another contribution to gravity is found: A constant force, acting between two objects regardless of their distance. Grumiller calls it “Rindler force”, after the Viennese gravitational physicist Wolfgang Rindler. This force is so small that it cannot be observed in everyday phenomena. “It does not contradict the theory of relativity, it is rather an extension which fits in seamlessly in the structure of the theory of relativity”, Grumiller says.

In a first attempt to estimate the magnitude of this force, Grumiller calculated the rotational velocity of stars orbiting the center of a galaxy. After all, the newfound Rindler force should play a decisive role at galactically large distances, at which the classical force of gravity becomes very small. And indeed, remarkably large rotational velocities of stars have been observed, and Grumiller’s equations turn out to describe them much better than previous calculation. “This is a strong indication of the Rindler force not only being mathematically possible, but also being present in nature”, Grumiller believes.**The mystery of the Pioneer spacecraft**

Applying the same method, Grumiller investigated another one of the mysteries of gravitational physics: The pioneer-anomaly. For years, it has been observed that the spacecraft Pioneer 10 and Pioneer 11, travelling far away from sun and earth, do not exactly follow the trajectories predicted by the theory of relativity. “The observed trajectories can be correctly described by taking into account a small additional force, acting in the direction of the sun – such as the Rindler foce”, Grumiller explains.

Despite this remarkable success, a lot remains to be done in this research project. “It will be very exciting to include this simplified model in a more general way into the framework of the four-dimensional theory of relativity”, Grumiller says. From that, he hopes to get a better understanding of what determines the strength of the Rindler force, as well as some insight into its connection to “dark matter”. Up until now, Grumiller points out, his model still remains agnostic as to whether or not dark matter exists at all.**Downloadlink: http://tuweb.tuwien.ac.at/index.php?id=10703** **Further information:**

Dr. Daniel Grumiller

Institute of Theoretical Physics

Vienna University of Technology

Wiedner Hauptstraße 8-10, 1040 Vienna

T: +43-1-58801-13634

daniel.grumiller@tuwien.ac.at