Effective dynamics of the Schwarzschild black hole interior with inverse triad corrections

Highlights: • Systematic derivation of effective Hamiltonian in LQG using path integrals. • Inverse triad corrections appear in the effective theory using this systematic method. • Prescriptions are introduced to resolve issues when such new corrections are present. • Singularity resolution and black-to-white hole bounce hold with new corrections. • New larger minimum radius-at-bounce for the interior of the Schwarzschild black hole. We reconsider the study of the interior of the Schwarzschild black hole now including inverse triad quantum corrections within loop quantization. We derive these corrections and show that they are related to two parameters ${\delta }_b,{\delta }_c$ associated to the minimum length in the radial and angular directions, that enter Thiemann's trick for quantum inverse triads. Introduction of such corrections may lead to non-invariance of physical results under rescaling of the fiducial volume needed to compute the dynamics, due to noncompact topology of the model. So, we put forward two prescriptions to resolve this issue. These prescriptions amount to interchange ${\delta }_b,{\delta }_c$ in classical computations in Thiemann's trick. By implementing the inverse triad corrections we found, previous results such as singularity resolution and black-to-white hole bounce hold with different values for the minimum radius-at-bounce, and the mass of the white hole.