Black holes and covariance in effective quantum gravity: A solution without Cauchy horizons

The issue of general covariance in effective quantum gravity models within the Hamiltonian framework is addressed. The previously proposed equations for the covariance condition in spherically symmetric models are explicitly derived. By solving this equation, a new effective Hamiltonian constraint is obtained, incorporating free functions that can account for quantum gravity effects. The resulting spacetime structure is analyzed by specifying the free functions. Remarkably, in this model, the classical singularity is replaced by a region where the metric asymptotically approaches a Schwarzschild-de Sitter one with negative mass. Thus, this new quantum-corrected black hole model avoids the Cauchy horizons presented typically in previously studied models. The covariant approach is also applicable to matter coupling in the models.

💡 Research Summary

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The paper tackles a long‑standing problem in effective quantum gravity (EQG): how to incorporate quantum corrections into a spherically symmetric Hamiltonian formulation while preserving general covariance. Starting from the classical Ashtekar‑Barbero variables for spherically symmetric vacuum general relativity, the authors keep the diffeomorphism constraint unchanged (it continues to generate spatial diffeomorphisms) and focus all quantum modifications on the Hamiltonian constraint. They assume that the constraint algebra remains first‑class but allow a deformation factor μ, depending on the phase‑space variables, to appear in the Poisson bracket of two Hamiltonian constraints: \