ECO-spotting: looking for extremely compact objects with bosonic fields

Black holes are thought to describe the geometry of massive, dark compact objects in the universe. To further support and quantify this long-held belief requires knowledge of possible, if exotic alternatives. Here, we wish to understand how compact can self-gravitating solutions be. We discuss theories with a well-posed initial value problem, consisting in either a single self-interacting scalar, vector or both. We focus on spherically symmetric solutions, investigating the influence of self-interacting potentials into the compactness of the solutions, in particular those that allow for flat-spacetime solutions. We are able to connect such stars to hairy black hole solutions, which emerge as a zero-mass black hole. We show that such stars can have light rings, but their compactness is never parametrically close to that of black holes. The challenge of finding black hole mimickers to investigate full numerical-relativity binary setups remains open.

Charged black holes in the infinite derivative theory of gravity

The infinite derivative theory of gravity is a generalization of Einstein gravity with many interesting properties, but the black hole solutions in this theory are still not fully understood. In the paper, we concentrate on studying the charged black holes in such a theory. Adding the electromagnetic field part to the effective action, we show how the black hole solutions around the Reissner-Nordstr{\"o}m metric can be solved perturbatively and iteratively. We further calculate the corresponding temperature, entropy and electrostatic potential of the black holes and verify the first law of thermodynamics.

Scalarized black holes

Black holes represent outstanding astrophysical laboratories to test the strong gravity regime, since alternative theories of gravity may predict black hole solutions whose properties may differ distinctly from those of general relativity. When higher curvature terms are included in the gravitational action as, for instance, in the form of the Gauss–Bonnet term coupled to a scalar field, scalarized black holes result. Here we discuss several types of scalarized black holes and some of their properties.

Spherically symmetric charged black holes with wavy scalar hair

We study standard Einstein-Maxwell theory minimally coupled to a complex valued and self-interacting scalar field. We demonstrate that new, previously unnoticed spherically symmetric, charged black hole solutions with scalar hair exist in this model for sufficiently large gravitational coupling and sufficiently small electromagnetic coupling. The novel scalar hair has the form of a spatially oscillating “wave packet” and back-reacts on the space-time such that both the Ricci and the Kretschmann scalar, respectively, possess qualitatively similar oscillations.

Scalarized Einstein–Maxwell-scalar black holes in a cavity

In this paper, we study the spontaneous scalarization of Reissner–Nordström (RN) black holes enclosed by a cavity in an Einstein–Maxwell-scalar (EMS) model with non-minimal couplings between the scalar and Maxwell fields. In this model, scalar-free RN black holes in a cavity may induce scalarized black holes due to the presence of a tachyonic instability of the scalar field near the event horizon. We calculate numerically the black hole solutions, and investigate the domain of existence, perturbative stability against spherical perturbations and phase structure. The scalarized solutions are always thermodynamically preferred over RN black holes in a cavity. In addition, a reentrant phase transition, composed of a zeroth-order phase transition and a second-order one, occurs for large enough electric charge Q.

Topological black holes in mimetic gravity

In this paper, we construct some new classes of topological black hole solutions in the context of mimetic gravity and investigate their properties. We study the uncharged and charged black holes, separately. We find the following novel results: (i) In the absence of a potential for the mimetic field, black hole solutions can address the flat rotation curves of spiral galaxies and alleviate the dark matter problem without invoking particle dark matter. Thus, mimetic gravity can provide a theoretical background for understanding flat galactic rotation curves through modifying Schwarzschild space–time. (ii) We also investigate the casual structure and physical properties of the solutions. We observe that in the absence of a potential, our solutions are not asymptotically flat, while in the presence of a negative constant potential for the mimetic field, the solutions are asymptotically anti-de Sitter (AdS). (iii) Finally, we explore the motion of massless and massive particles and give a list of the types of orbits. We study the differences of geodesic motion in the Einstein gravity and in mimetic gravity. In contrast to the Einstein gravity, massive particles always move on bound orbits and cannot escape the black hole in mimetic gravity. Furthermore, we find stable bound orbits for massless particles.

Spatially homogeneous black hole solutions in $$z=4$$ Hořava–Lifshitz gravity in $$(4+1)$$ dimensions with Nil geometry and $$H^2\times R$$ horizons

In this paper, we present two new families of spatially homogeneous black hole solution for $$z=4$$ z = 4 Hořava–Lifshitz Gravity equations in $$(4+1)$$ ( 4 + 1 ) dimensions with general coupling constant $$\lambda $$ λ and the especial case $$\lambda =1$$ λ = 1 , considering $$\beta =-1/3$$ β = - 1 / 3 . The three-dimensional horizons are considered to have Bianchi types II and III symmetries, and hence the horizons are modeled on two types of Thurston 3-geometries, namely the Nil geometry and $$H^2\times R$$ H 2 × R . Being foliated by compact 3-manifolds, the horizons are neither spherical, hyperbolic, nor toroidal, and therefore are not of the previously studied topological black hole solutions in Hořava–Lifshitz gravity. Using the Hamiltonian formalism, we establish the conventional thermodynamics of the solutions defining the mass and entropy of the black hole solutions for several classes of solutions. It turned out that for both horizon geometries the area term in the entropy receives two non-logarithmic negative corrections proportional to Hořava–Lifshitz parameters. Also, we show that choosing some proper set of parameters the solutions can exhibit locally stable or unstable behavior.

Exact black hole solutions with a conformally coupled scalar field and dynamic Ricci curvature in f(R) gravity theories

We report exact black hole solutions in asymptotically flat or (A)dS four-dimensional spacetime with a conformally coupled self-interacting scalar field in f(R) gravity. We first consider the asymptotically flat model $$f(R) = R -2\alpha \sqrt{R}$$ f ( R ) = R - 2 α R and derive an exact black hole solution. Then, we consider the asymptotically (A)dS model $$f(R) =R -2 \Lambda -2 \alpha \sqrt{R-4 \Lambda }$$ f ( R ) = R - 2 Λ - 2 α R - 4 Λ and derive an exact black hole solution. In both cases the modified gravity parameter $$\alpha $$ α , which has the dimension of the inverse mass, cannot be set to zero and the self-interacting potential is determined from the Klein–Gordon equation, preserving the conformal invariance. The thermodynamics of the solutions is also studied.

Holographic stress tensor of colored Lifshitz spacetimes and hairy black holes

We compute the holographic stress tensor of colored Lifshitz spacetimes following the proposal by Ross-Saremi for gravity duals of non-relativistic theories. For a well-defined variational principle, we first construct a finite on-shell action for the Einstein-Yang-Mills model in four dimensions with Lifshitz spacetime as a solution. We then solve the linearised equations of motion and identify the modes that preserve the asymptotically Lifshitz condition. Employing these modes, we also show that the stress tensor is finite, obeying the scaling and the diffeomorphism Ward identities, i.e., conservations laws. As a final application, we evaluate the energy density and the spatial stress tensor of the previously found numerical black hole solutions with various dynamical exponents z. The alternative Smarr relation that has been used in Lifshitz black holes and the first law of thermodynamics are shown to hold without a global Yang-Mills charge, indicating the black holes in question are hairy.

Scalarized Einstein–Maxwell-scalar black holes in anti-de Sitter spacetime

In this paper, we study spontaneous scalarization of asymptotically anti-de Sitter charged black holes in an Einstein–Maxwell-scalar model with a non-minimal coupling between the scalar and Maxwell fields. In this model, Reissner–Nordström-AdS (RNAdS) black holes are scalar-free black hole solutions, and may induce scalarized black holes due to the presence of a tachyonic instability of the scalar field near the event horizon. For RNAdS and scalarized black hole solutions, we investigate the domain of existence, perturbative stability against spherical perturbations and phase structure. In a micro-canonical ensemble, scalarized solutions are always thermodynamically preferred over RNAdS black holes. However, the system has much richer phase structure and phase transitions in a canonical ensemble. In particular, we report a RNAdS BH/scalarized BH/RNAdS BH reentrant phase transition, which is composed of a zeroth-order phase transition and a second-order one.