Author(s)

Alberto Strumia

Istituto Nazionale di Alta Matematica “Francesco Severi”, Rome, Italy.

We present a simple way to approach the hard problem of quantization of the gravitational field in four-dimensional space-time, due to non-linearity of the Einstein equations. The difficulty may be overcome when the cosmological constant is non-null. Treating the cosmological contribution as the energy-momentum of vacuum, and representing the metric tensor onto the tetrad of its eigenvectors, the corresponding energy-momentum and, consequently, the Hamiltonian are easily quantized assuming a correspondence rule according to which the eigenvectors are replaced by creation and annihilation operators for the gravitational field. So the geometric Einstein tensor, which is opposite in sign respect to the vacuum energy-momentum (plus the possible known matter one), is also quantized. Physical examples provided by Schwarzschild-De Sitter, Robertson-Walker-De Sitter and Kerr-De Sitter solutions are examined.

General Relativity, Quantum Gravity, Cosmological Constant

Strumia, A. (2022) A Way to Quantum Gravity. Journal of High Energy Physics, Gravitation and Cosmology, 8, 309-316. doi: 10.4236/jhepgc.2022.82025.