Abstract
We use the theory of teleparallelism equivalent to general relativity based on noncommutative spacetime coordinates. In this context, we write the corrections of the Schwarzschild solution. We propose the existence of a Weitzenböck spacetime that matches the corrected metric tensor. As an important result, we find the corrections of the gravitational energy in the realm of teleparallel gravity due to the noncommutativity of spacetime. Then we interpret such corrections as a manifestation of quantum theory in gravitational field.
Highlights
On Noncommutative Corrections of Gravitational Energy in Teleparallel GravityWe use the theory of teleparallelism equivalent to general relativity based on noncommutative spacetime coordinates
The notion of noncommutative spatial coordinates arose with Heisenberg, who wrote a letter to Peierls, in 1930, about the existence of an uncertain relation between coordinates in space-time as a possible solution to avoid the singularities in the self-energy terms of pontual particles
It is introduced by replacing the normal product between tetrads by the Moyal product, rather than applying such a procedure in lagrangian density
Summary
We use the theory of teleparallelism equivalent to general relativity based on noncommutative spacetime coordinates. In this context, we write the corrections of the Schwarzschild solution. We propose the existence of a Weitzenbock spacetime that matches the corrected metric tensor. We find the corrections of the gravitational energy in the realm of teleparallel gravity due to the noncommutativity of spacetime. We interpret such corrections as a manifestation of quantum theory in gravitational field
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