35 research outputs found
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