Regular black holes from higher-derivative effective delta sources

Certain approaches to quantum gravity and classical modified gravity theories result in effective field equations in which the original source is substituted by an effective one. In these cases, the occurrence of regular spacetime configurations may be related to the regularity of the effective source, regardless of the specific mechanism behind the regularization. In this chapter, we make an introduction to the effective source formalism applied to higher-derivative gravity. The results presented here, however, can be easily transposed to other frameworks that use similar sources. The generality obtained is also because we consider a general higher-derivative gravity model instead of restricting the analysis to some specific theories. In the first part, we discuss the model in the Newtonian limit, which offers a natural context for introducing effective sources. We show how the regularity properties of the effective sources depend on the behavior of the action's form factor in the ultraviolet regime, which leads to results valid for large families of models (or for families of modified delta sources). Subsequently, we use the general results on the effective sources to construct regular black hole metrics. One of our concerns is the higher-order regularity of the solutions, i.e., the possibility that not only the invariants built with curvature tensors but also the ones with covariant derivatives are regular. In this regard, we present some theorems relating the regularity of sets of curvature-derivative invariants with the regularity properties of the effective sources.Comment: 41 pages, 3 figures. Preprint of the invited chapter for the book "Regular Black Holes: Towards a New Paradigm of the Gravitational Collapse" (Ed. C. Bambi, Springer Singapore, 2023). The final authenticated version is available online at http://doi.org/10.1007/978-981-99-1596-5_

Black holes in non-local gravity

In this chapter we present a status report of black hole-like solutions in non-local theories of gravity in which the Lagrangians are at least quadratic in curvature and contain specific non-polynomial (i.e., non-local) operators. In the absence of exact black hole solutions valid in the whole spacetime, most of the literature on this topic focus on approximate and simplified equations of motion, which could provide insights on the full non-linear solutions. Therefore, the largest part of this chapter is devoted to the linear approximation. We present results on stationary metric solutions (including both static and rotating cases) and dynamical spacetimes describing the formation of non-rotating mini black holes by the collapse of null shells. Non-local effects can regularize the curvature singularities in both scenarios and, in the dynamical case, there exists a mass gap below which the formation of an apparent horizon can be avoided. In the final part we discuss interesting attempts towards finding non-linear black hole solutions in non-local gravity. Throughout this chapter, instead of focusing on a particular non-local model, we present results valid for large classes of theories (to a feasible extent). This more general approach allows the comparison of similarities and differences of the various types of non-local gravity models.Comment: Invited chapter for the Section "Nonlocal Quantum Gravity" of the "Handbook of Quantum Gravity" (Eds. C. Bambi, L. Modesto and I.L. Shapiro, Springer Singapore, expected in 2023). 29 page

On Newtonian singularities in higher derivative gravity models

We consider the problem of Newtonian singularity in the wide class of higher derivative gravity models, including the ones which are renormalizable and super-renormalizable at the quantum level. The simplest version of the singularity-free theory has four derivatives and is pretty well-known. We argue that in all cases of local higher-derivative theories, when the poles of the propagator are real and simple, the singularities disappear due to the cancellation of contributions from scalar and tensor massive modes.Comment: Added comment about the black hole solutions in Conclusions section. Fits published version, plus some misprints corrected in formulas at the end of Sect.

Gauge invariance of the background average effective action

Using the background field method for the functional renormalization group approach in the case of a generic gauge theory, we study the background field symmetry and gauge dependence of the background average effective action, when the regulator action depends on external fields. The final result is that the symmetry of the average effective action can be maintained for a wide class of regulator functions, but in all cases the dependence of the gauge fixing remains on-shell. The Yang-Mills theory is considered as the main particular example.Comment: Fits the version accepted in EPJ

Effective quantum gravity, cosmological constant and the Standard Model of particle physics

The renormalization group in effective quantum gravity can be consistently formulated using the Vilkovisky and DeWitt version of effective action and assuming a non-zero cosmological constant. Taking into account that the vacuum counterpart of the cosmological constant is dramatically different from the observed energy density of vacuum, the running of the last quantity in the late cosmology indicates strong constraints on the physics beyond the minimal Standard Model of particle physics.Comment: 15 pages, no figures. Added discussions concerning the general status of the Vilkovisky-DeWitt effective action, corresponding references, and the new Appendix, illustrating the choice of the metric. Conclusions are unchanged. Fits the version accepted in PR

Vacuum effective actions and mass-dependent renormalization in curved space

We review past and present results on the non-local form-factors of the effective action of semiclassical gravity in two and four dimensions computed by means of a covariant expansion of the heat kernel up to the second order in the curvatures. We discuss the importance of these form-factors in the construction of mass-dependent beta functions for the Newton's constant and the other gravitational couplings.Comment: 26 pages, review prepared for the special issue of Universe collecting the contributions for the workshop "Quantum Fields - from Fundamental Concepts to Phenomenological Questions" (Mainz 26-28 September 2018), covers the results of 1803.06948 and 1812.0046