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Solutions to the gravitational field equations in curved phase-spaces

Abstract:

After reviewing the basics of the geometry of the cotangent bundle of spacetime, via the introduction of nonlinear connections, we build an action and derive the generalized gravitational field equations in phase spaces. A nontrivial solution generalizing the Hilbert- Schwarzschild black hole metric in spacetime is found. The most relevant physical consequence is that the metric becomes momentum-dependent (observer dependent) which is what one should aim for in trying to quantize geometry (gravity): the observer must play an important role in any measurement (observation) process of the spacetime he/she lives in. To finalize, some comments about modifications of the Weyl-Heisenberg algebra [xi; pj] = ih gij(x, p) and its implications are made.