Abstract
In general relativity, inertia and gravitation are both included in the Levi-Civita connection. As a consequence, the gravitational action, as well as the corresponding energy-momentum density, are in general contaminated by spurious contributions coming from inertial effects. In teleparallel gravity, on the other hand, because the spin connection represents inertial effects only, it is possible to separate inertia from gravitation. Relying on this property, it is shown that to each tetrad there is naturally associated a spin connection that locally removes the inertial effects from the action. The use of the appropriate spin connection can be viewed as a renormalization process in the sense that the computation of energy and momentum naturally yields the physically relevant values. A self-consistent method for solving field equations and determining the appropriate spin connection is presented.
Highlights
The search for a local energy–momentum density for gravity is one of the oldest problem of general relativity
Inertial and gravitational effects are both included in the Levi–Civita connection, and cannot be separated
This means that the gravitational action necessarily includes both gravitational and inertial effects
Summary
The search for a local energy–momentum density for gravity is one of the oldest problem of general relativity. It is not always possible to construct an open family of the embeddings of the reference space–time around a given solution For this reason, the variational principle associated to the renormalized gravitational action (1.2) is not always well defined [7]. On the other hand, owing to the fact that in teleparallel gravity [8] the spin connection represents inertial effects only, it becomes possible to locally separate inertial and gravitational effects – something impossible to achieve in general relativity. Working in the context of teleparallel gravity, the purpose of this paper is to investigate the problem of defining a purely gravitational action, to the exclusion of inertial effects, which will be free of divergences. 5 we show that associating the appropriate spin connection to a given tetrad removes the inertial effects from the action.
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