I review the status of the asymptotic safety program which posits a nonperturbative ultraviolet completion of gravitational quantum field theory. In particular, I put emphasis (i) on systematic extensions of approximation schemes, (ii) on the role of field redefinitions, and (iii) on observable consequences.

The latter naturally connects the asymptotic safety program to an effective field...

The event horizon of a dynamical black hole is generically a non-smooth hypersurface. I shall describe the types of non-smooth structure that can arise on a horizon that is smooth at late time. This includes creases, corners and caustic points.

I shall discuss ``perestroikas'' of these structures, in which they undergo a qualitative change at an instant of time. A crease perestroika gives an...

A characteristic feature of semiclassical theories of gravity involving the backreaction of a quantum matter field is the presence of higher order derivatives in the dynamical equations. Hence, the appearance of pathological "runaway solutions" is often argued, i.e., solutions of the linearized equations around a background spacetime that grow exponentially in time. In this talk, this issue is...

I will show that the repulsive effects associated to the zero-point energies of quantum

fields are capable of supporting ultracompact stars that overcome the compactness

limits present in general relativity for any sphere in hydrostatic equilibrium. These

objects are self-consistent solutions in semiclassical gravity that incorporate

the backreaction of the renormalized stress-energy...

Many results in general relativity rely crucially on classical energy conditions inflicted on the stress-energy tensor. Quantum matter, however, violates these conditions since the energy density can fluctuate and in particular become arbitrarily negative at a point. Nonetheless quantum matter should have some reminiscent notion of stability, which can be captured by so-called quantum (weak)...

Some of the quantum properties of rotating black holes in (3+1)-dimensional spacetimes remain unresolved. However, studying higher-dimensional cases may provide insight into their behaviour. In this talk, we investigate the behaviour of a massive scalar field in a Kerr-AdS (4+1)-dimensional spacetime. Specifically, we focus on the existence of a Hartle-Hawking state, which is a vacuum state...

We review the procedure to construct ground and KMS states, for real scalar fields whose dynamics is dictated by the Klein-Gordon equation, on standard static Lorentzian manifolds with a time-like boundary. We observe that this construction, depending on which boundary condition we fix on the boundary, does not always lead to a bi-distribution $w_2\in \mathcal{D}'(M\times M)$ for the two-point...

It is well-known that the (1+1) dimensional Schwarzschild and spatially flat FLRW spacetimes are conformally flat. This work examines entanglement harvesting from the conformal field vacuums in these spacetimes between two Unruh-DeWitt detectors, moving along outgoing null trajectories. In (1+1) dimensional Schwarzschild spacetime, we considered the Boulware and Unruh vacua for our...

In this talk I will discuss how the algebraic approach to (perturbative) quantum field theory can benefit the search for the theory quantum gravity through several different approaches. I will discuss the problem of constructing gauge invariant observables, the asymptotic safety program and consequences of potential discreteness of spacetime at small scales.