Abstract:This work is based on the formalism developed in the study of the thermodynamics of spacetime used to derive Einstein equations from the proportionality of entropy within an area. When low-energy quantum gravity effects are considered, an extra logarithmic term in the area is added to the entropy expression. Here, we present the derivation of the quantum modified gravitational dynamics from this modified entropy expression and discuss its main features. Furthermore, we outline the application of the modified d… Show more
“…However, the resulting dynamics is consistent with unimodular gravity, which is invariant only under transverse diffeomorphisms [19,20]. Furthermore, gravitational dynamics derived from thermodynamics is invariant under Weyl transformations [21] and, thus, has exactly the same symmetries as WTG. In this way, starting with Wald entropy obtained from the Diff invariant Lagrangian of GR one arrives at equations of gravitational dynamics consistent with WTDiff invariant WTG.…”
Weyl transverse gravity is a gravitational theory that is invariant under transverse diffeomorphisms and Weyl transformations. It is characterised by having the same classical solutions as general relativity while solving some of its issues with the cosmological constant. In this work, we first find the Noether currents and charges corresponding to local symmetries of Weyl transverse gravity as well as a prescription for the symplectic form. We then employ these results to derive the first law of black hole mechanics in Weyl transverse gravity (both in vacuum and in the presence of a perfect fluid), identifying the total energy, the total angular momentum, and the Wald entropy of black holes. We further obtain the first law and Smarr formula for Schwarzschild-anti-de Sitter and pure de Sitter spacetimes, discussing the contributions of the varying cosmological constant, which naturally appear in Weyl transverse gravity. Lastly, we derive the first law of causal diamonds in vacuum.
“…However, the resulting dynamics is consistent with unimodular gravity, which is invariant only under transverse diffeomorphisms [19,20]. Furthermore, gravitational dynamics derived from thermodynamics is invariant under Weyl transformations [21] and, thus, has exactly the same symmetries as WTG. In this way, starting with Wald entropy obtained from the Diff invariant Lagrangian of GR one arrives at equations of gravitational dynamics consistent with WTDiff invariant WTG.…”
Weyl transverse gravity is a gravitational theory that is invariant under transverse diffeomorphisms and Weyl transformations. It is characterised by having the same classical solutions as general relativity while solving some of its issues with the cosmological constant. In this work, we first find the Noether currents and charges corresponding to local symmetries of Weyl transverse gravity as well as a prescription for the symplectic form. We then employ these results to derive the first law of black hole mechanics in Weyl transverse gravity (both in vacuum and in the presence of a perfect fluid), identifying the total energy, the total angular momentum, and the Wald entropy of black holes. We further obtain the first law and Smarr formula for Schwarzschild-anti-de Sitter and pure de Sitter spacetimes, discussing the contributions of the varying cosmological constant, which naturally appear in Weyl transverse gravity. Lastly, we derive the first law of causal diamonds in vacuum.
“…A large literature has been produced to calculate those semiclassical properties of different modified black holes spacetimes [68]. The properties investigated by those works were the variations, caused by the metric modifications, in the Hawking radiation spectrum of every test field and in the temperature and entropy of the black holes.…”
Section: The Hawking Radiation and The Greybody Factormentioning
We consider perturbations of the massless Dirac field in the background of a black hole solution found by Bodendorfer, Mele, and Münch (BMM), using a polymerization technique that furnishes contributions inspired by Loop Quantum Gravity (LQG) Theory. Using the sixth order WKB method, we analyzed its quasinormal modes for several modes, multipole numbers and the two classes of BMM black holes. We also considered the potential that governs these perturbations to analyze the bound on the Greybody Factor (GF) due the emission rates of particles. As results, we found that the Loop Quantum Gravity parameters are responsible for raising the potential and the real and imaginary parts of the quasinormal frequencies and decrease the bound on the Greybody Factor for the two classes of black holes (with more more prominent effects for the de-amplification case, which is compatible with previous analyses done for other fields).
“…A large literature has been produced to calculate those semiclassical properties of different modified black holes spacetimes [64]. The properties investigated by those works were the variations, caused by the metric modifications, in the Hawking radiation spectrum of every test field and in the temperature and entropy of the black holes.…”
Section: The Hawking Radiation and The Gfmentioning
We consider perturbations of the massless Dirac field in the background of a black hole solution found by Bodendorfer, Mele, and Münch (BMM), using a polymerization technique that furnishes contributions inspired by Loop Quantum Gravity (LQG) Theory. Using the sixth order WKB method, we analyzed its quasinormal modes for several modes, multipole numbers and the two classes of BMM black holes. We also considered the potential that governs these perturbations to analyze the bound on the Greybody Factor (GF) due the emission rates of particles. As results, we found that the Loop Quantum Gravity parameters are responsible for raising the potential and the real and imaginary parts of the quasinormal frequencies and decrease the bound on the Greybody Factor for the two classes of black holes (with more prominent effects for the de-amplification case, which is compatible with previous analyses done for other fields).
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