Loop Quantum Gravity (LQG) is a theory that proposes a way to model the behavior of the spacetime in situations where its atomic characteristic arises. Among these situations, the spacetime behavior near the Big Bang or black hole's singularity. The detection of gravitational waves, on the other hand, has opened the way to new perspectives in the investigation of the spacetime structure. In this work, by the use of a WKB method introduced by Schutz and Will [1], and after improved by Iyer and Will [2], we study the gravitational wave spectrum emitted by loop quantum black holes, which correspond to a quantized version of the Schwarzschild spacetime by LQG techniques. From the results obtained, loop quantum black holes have been shown stable under axial gravitational perturbations.

In this work, we obtain the loop quantum cosmology dynamical equations, plus a positive cosmological constant, from the Bekenstein-Hawking entropy-area relation given by Loop Quantum Black Holes, by the use of the Jacobson formalism (Phys Rev Lett 75:1260. The results found out may set a still absent connection between holography and the description of the cosmos given by loop quantum cosmology.

One proposal by Verlinde [1] is that gravity is not a fundamental, but an entropic force. In this way, Verlinde has provide us with a way to derive the Newton's law of gravitation from the Bekenstein-Hawking entropy-area formula. On the other hand, since it has been demonstrated that this formula is susceptible to quantum gravity corrections, one may hope that these corrections could be inherited by the Newton's law. In this way, the entropic interpretation of Newton's law could be a prolific way in order to get verifiable or falsifiable quantum corrections to ordinary gravity in an observationally accessible regimes. Loop quantum gravity is a theory that provide a way to approach the quantum properties of spacetime. From this theory, emerges a quantum corrected semiclassical black hole solution called loop quantum black holes or self-dual black holes. Among the interesting features of loop quantum black holes is the fact that they give rise to a modified entropy-area relation where quantum gravity corrections are present. In this work, we obtain the quantum corrected Newton's law from the entropy-area relation given by loop quantum black holes. In order to relate our results with the recent experimental activity, we consider the quantum mechanical properties of a huge gravitational atom consisting in a light neutral elementary particle in the presence of a loop quantum black hole.

Abstract:In this work, we present some results relating to the issue of the Loop Quantum Black Holes (LQBH) thermodynamics by the use of the tunneling radiation formalism. The information loss paradox is also discussed in this context, and we have considered the influence of back reaction effects.

Non-commutative corrections to the classical expression for the fuzzy sphere area are found out through the asymptotic expansion for its heat kernel trace. As an important consequence, some quantum gravity deviations in the luminosity of black holes must appear. We calculate these deviations for a static, spherically symmetric, black-hole with a horizon modeled by a fuzzy sphere. The results obtained could be verified through the radiation of black holes formed in the Large Hadron Collider (LHC).