Quasi-topological Gravity Research Articles

Hairy black holes and naked singularities of quartic quasi-topological gravity within the framework of logarithmic electrodynamics

We establish a new family of hairy black hole solutions of quartic quasi-topological gravity sourced by logarithmic electrodynamics and conformal scalar field. Here, we derive the metric function defining black hole structures and investigate the effects of electric charge, scalar hair, and dimensionality parameters on the location of the event horizon. The corresponding hairy black hole solution of the quartic quasi-topological gravity sourced by Maxwell field is also deduced in this setup. In addition, we also compute thermodynamic quantities for these objects such as temperature, entropy and heat capacity, and check the first law of thermodynamics. Furthermore, the impacts of scalar hair and electric charge on the divergences of heat capacity and extreme black hole’s horizon radius are also investigated. Finally, we also analyze thermodynamic stability and critical behavior of the resultant hairy black holes at the event horizon.

Endowing black holes with beyond-Horndeski primary hair: An exact solution framework for scalarizing in every dimension

This work outlines a straightforward mechanism for endorsing primary hair into Schwarzschild black holes, resulting in a unique modification within the framework of a special scalar-tensor theory, the so-called beyond-Horndeski gravity. The derived solutions are exact, showcase primary hair with a regular scalar field profile everywhere, and continuously connect with the vacuum geometry. Initially devised to introduce primary hair in spherically symmetric solutions within general relativity in any dimension, our investigation explores the conditions under which spherically symmetric black holes in alternative gravitational theories become amenable to the endowment of primary hair through a similar pattern. As a preliminary exploration, we embark on the process of endowing primary hair to the Reissner-Nordström black hole. Subsequently, we extend our analysis to encompass spherically symmetric solutions within Lovelock and cubic quasitopological gravity theories. Published by the American Physical Society 2024

Correlation of horizons and black hole thermodynamics

For black holes with more than one horizon, the existence of a global temperature is not fully understood. This can affect the thermodynamics of these black holes to be unclear. In this paper, using the method of quantum tunneling, we find a global temperature for asymptotically AdS multi-horizon black holes appeared in three-dimensional quasitopological gravities given by [Formula: see text], in which the effective surface gravity is related to the surface gravity of each horizon. We also find a global temperature for the asymptotically warped AdS3 black holes, having the same expression as the AdS multi-horizon black holes. In all of the cases the global temperature differs from the conventional Hawking temperature.

Reissner–Nordström black holes in quintic quasi-topological gravity

This paper investigates charged black holes within the framework of quintic quasi-topological gravity, focusing on their thermodynamics, conserved quantities, and stability. We construct numerical solutions and explore their thermodynamic properties, supplemented by the study of analytically solvable special cases. By verifying the first law of thermodynamics, we validate our approach and compare our findings to those of Einstein gravity. The physical properties of the solutions are examined across anti-de Sitter, de Sitter, and flat spacetime backgrounds. Our analysis reveals that anti-de Sitter solutions demonstrate thermal stability, while de Sitter and flat solutions lack this property. Finally, we discuss the implications of our results and propose potential avenues for future research in this field.

Conformal hairy black holes of quartic quasi-topological gravity with power-Yang–Mills source

We study higher dimensional hairy black holes of quartic quasi-topological gravity in the framework of non-abelian power-Yang–Mills theory. It is shown that real solutions of the gravitational field equations exist only for positive values of quartic quasi-topological coefficient. Depending on the values of the mass, conformal coupling constants, quasi-topological coefficients, Yang–Mills magnetic charge, and nonlinearity parameter, they can be interpreted as black holes with one horizon, at most three horizons and naked singularity. It is also shown that the solution associated with these black holes has an essential curvature singularity at the centre r=0. Thermodynamic and conserved quantities for these hairy black holes are computed and we show that the first law has been verified. We also check thermodynamic stability in both canonical and grand canonical ensembles. In addition to this, we also formulate new power-Yang–Mills hairy black hole solutions in pure quasi-topological gravity. The physical and thermodynamic properties of these black holes are discussed as well. It is concluded that unlike Yang–Mills black holes without scalar hair there exist stability regions for the power-Yang–Mills hairy black holes in grand canonical ensemble. Finally, we discuss the thermodynamics of horizon flat power-Yang–Mills rotating black branes and analyze their thermodynamic and conserved quantities by using the counter-term method inspired by AdS/CFT correspondence.

Classification of generalized quasitopological gravities

Classification of generalized quasitopological gravities

Slowly rotating black holes in quartic generalized quasi-topological gravity

We study slowly rotating black hole solutions in the six independent theories of Quartic Generalized Quasi-topological Gravity in four dimensions. Unlike in the static case for which all six theories yield the same solution, for rotating black holes we obtain distinct results for five out of the six theories. Working to leading order in the rotation parameter, we find that the equations characterizing these black holes can be reduced to second order for each theory, similar to what has already been done for Einstein Cubic Gravity. We construct approximate and numerical solutions to these equations, and study how physical properties of the solutions such as the angular velocity, photon sphere, black hole shadow, and innermost stable circular orbit are modified, working to leading order in the coupling constant.

Electromagnetic quasinormal modes of dyonic AdS black holes with quasitopological electromagnetism in a Horndeski gravity theory mimicking EGB gravity at D → 4

We investigate some properties of a black hole in a Horndeski gravity theory mimicking EGB gravity at [Formula: see text]. Borrowing ideas from quasitopological gravities provide a matter source of dyonic fields, in which the black hole solution carries two charges, electric and magnetic, in the context of the Einstein–Gauss–Bonnet (EGB) gravity. However, due to several limitations of the EGB gravity in [Formula: see text], we consider a Horndeski gravity theory which can mimic EGB gravity in [Formula: see text]. The essential practice used in this paper is the electromagnetic quasinormal modes process, with the goal of discovering the spectrum of such an electromagnetic perturbation over the black hole spacetime. The Wentzel–Kramer–Brillouin (WKB) approximation is used to achieve the desired results. The study shows that both the charges have similar impacts on the quasinormal modes.

Electromagnetic generalized quasitopological gravities in ( 2+1 ) dimensions

The construction of quasitopological gravities in three-dimensions requires coupling a scalar field to the metric. As shown in [arXiv:2104.10172], the resulting ``electromagnetic'' quasitopological (EQT) theories admit charged black hole solutions characterized by a single-function for the metric, $\ensuremath{-}{g}_{tt}={g}_{rr}^{\ensuremath{-}1}\ensuremath{\equiv}f(r)$, and a simple azimuthal form for the scalar. Such black holes, whose metric can be determined fully analytically, generalize the Ba\~nados-Teiteilboim-Zanelli black hole (BTZ) solution in various ways, including singularity-free black holes without any fine-tuning of couplings or parameters. In this paper we extend the family of EQT theories to general curvature orders. We show that, beyond linear order, $f(r)$ satisfies a second-order differential equation rather than an algebraic one, making the corresponding theories belong to the electromagnetic generalized quasitopological (EGQT) class. We prove that at each curvature order, the most general EGQT density is given by a single term which contributes nontrivially to the equation of $f(r)$ plus densities which do not contribute at all to such equation. The proof relies on the counting of the exact number of independent order-$n$ densities of the form $\mathcal{L}({R}_{ab},{\ensuremath{\partial}}_{a}\ensuremath{\phi})$, which we carry out. We study some general aspects of the new families of EGQT black-hole solutions, including their thermodynamic properties and the fulfillment of the first law, and explicitly construct a few of them numerically.

Quasi-topological gravities on general spherically symmetric metric

In this work we study a more restricted class of quasi-topological gravity theories where the higher curvature terms have no contribution to the equation of motion on general static spherically symmetric metric where gttgrr ≠ constant. We construct such theories up to quintic order in Riemann tensor and observe an important property of these theories: the higher order term in the Lagrangian vanishes identically when evaluated on the most general non-stationary spherically symmetric metric ansatz. This not only signals the higher terms could only have non-trivial effects when considering perturbations, but also makes the theories quasi-topological on a much wider range of metrics. As an example of the holographic effects of such theories, we consider a general Einstein-scalar theory and calculate it’s holographic shear viscosity.

Generalized quasi-topological gravities: the whole shebang

Generalized quasi-topological gravities (GQTGs) are higher-curvature extensions of Einstein gravity in D-dimensions. Their defining properties include possessing second-order linearized equations of motion around maximally symmetric backgrounds as well as non-hairy generalizations of Schwarzschild’s black hole characterized by a single function, , which satisfies a second-order differential equation. In (Bueno et al 2020 Class. Quantum Grav. 37 015002) GQTGs were shown to exist at all orders in curvature and for general D. In this paper we prove that, in fact, n − 1 inequivalent classes (as far as static and spherically symmetric solutions are concerned) of order-n GQTGs exist for . Amongst these, we show that one—and only one—type of densities is of the quasi-topological kind, namely, such that the equation for f(r) is algebraic. Our arguments do not work for D = 4, in which case there seems to be a single unique GQT density at each order which is not of the quasi-topological kind. We compute the thermodynamic charges of the most general D-dimensional order-n GQTG, verify that they satisfy the first law and provide evidence that they can be entirely written in terms of the embedding function which determines the maximally symmetric vacua of the theory.

Are there Einsteinian gravities involving covariant derivatives of the Riemann tensor?

We study the particle content of higher derivative theories of gravity built with contractions of the Riemann tensor and its covariant derivatives. In the absence of the latter, there is a family of theories exhibiting an Einsteinian spectrum known as generalized quasi-topological gravities. In turn, we present a no-go result for the construction of Einsteinian gravities involving covariant derivatives of the Riemann tensor. We find evidences suggesting that (truncated series) finite order Lagrangians with covariant derivatives of the Riemann tensor generically present ghosts in their spectrum. This might be interpreted as a hint of non-locality in any healthy UV completion of General Relativity.

Higher-derivative holography with a chemical potential

We carry out an extensive study of the holographic aspects of any-dimensional higher-derivative Einstein-Maxwell theories in a fully analytic and non-perturbative fashion. We achieve this by introducing the d-dimensional version of Electromagnetic Quasitopological gravities: higher-derivative theories of gravity and electromagnetism that propagate no additional degrees of freedom and that allow one to study charged black hole solutions analytically. These theories contain non-minimal couplings, that in the holographic context give rise to a modified 〈JJ〉 correlator as well as to a general 〈TJJ〉 structure whose coefficients we compute. We constrain the couplings of the theory by imposing CFT unitarity and positivity of energy (which we show to be equivalent to causality in the bulk) as well as positive-entropy bounds from the weak gravity conjecture. The thermodynamic properties of the dual plasma at finite chemical potential are studied in detail, and we find that exotic zeroth-order phase transitions may appear, but that many of them are ruled out by the physical constraints. We further compute the shear viscosity to entropy density ratio, and we show that it can be taken to zero while respecting all the constraints, providing that the chemical potential is large enough. We also obtain the charged Rényi entropies and we observe that the chemical potential always increases the amount of entanglement and that the usual properties of Rényi entropies are preserved if the physical constraints are met. Finally, we compute the scaling dimension and magnetic response of twist operators and we provide a holographic derivation of the universal relations between the expansion of these quantities and the coefficients of 〈JJ〉 and 〈TJJ〉.

Surface terms of quintic quasitopological gravity and thermodynamics of quasi-topological magnetic brane coupled to nonlinear electrodynamics

For the the quintic quasitopological action which has no well-defined variational principle, we introduced a surface term that for a spacetime with flat boundaries make the action well-defined. Moreover, we investigated the numerical solutions of the above-mentioned gravity coupled to the nonlinear logarithmic and exponential electrodynamics. It has no horizon and curvature except one conical singularity at r=0 with a deficit angle delta phi . Also we found the counterterm which removes non-logarithmic divergences for the static quintic quasitopological gravity. Using this counterterm one can calculate a finite action and conserved quantities for the quintic quasitopological gravity.

Yang\u2013Mills black holes in quasitopological gravity

In this paper, we formulate two new classes of black hole solutions in higher curvature quartic quasitopological gravity with nonabelian Yang–Mills theory. At first step, we consider the SO(n) and SO(n-1,1) semisimple gauge groups. We obtain the analytic quartic quasitopological Yang–Mills black hole solutions. Real solutions are only accessible for the positive value of the redefined quartic quasitopological gravity coefficient, mu _{4}. These solutions have a finite value and an essential singularity at the origin, r=0 for space dimension higher than 8. We also probe the thermodynamic and critical behavior of the quasitopological Yang–Mills black hole. The obtained solutions may be thermally stable only in the canonical ensemble. They may also show a first order phase transition from a small to a large black hole. In the second step, we obtain the pure quasitopological Yang–Mills black hole solutions. For the positive cosmological constant and the space dimensions greater than eight, the pure quasitopological Yang–Mills solutions have the ability to produce both the asymptotically AdS and dS black holes for respectively the negative and positive constant curvatures, k=-1 and k=+1. This is unlike the quasitopological Yang–Mills theory which can lead to just the asymptotically dS solutions for Lambda >0. The pure quasitopological Yang–Mills black hole is not thermally stable.

Slowly rotating black holes in quasitopological gravity

While cubic Quasi-topological gravity is unique, there is a family of quartic Quasi-topological gravities in five dimensions. These theories are defined by leading to a first order equation on spherically symmetric spacetimes, resembling the structure of the equations of Lovelock theories in higher-dimensions, and are also ghost free around AdS. Here we construct slowly rotating black holes in these theories, and show that the equations for the off-diagonal components of the metric in the cubic theory are automatically of second order, while imposing this as a restriction on the quartic theories allows to partially remove the degeneracy of these theories, leading to a three-parameter family of Lagrangians of order four in the Riemann tensor. This shows that the parallel with Lovelock theory observed on spherical symmetry, extends to the realm of slowly rotating solutions. In the quartic case, the equations for the slowly rotating black hole are obtained from a consistent, reduced action principle. These functions admit a simple integration in terms of quadratures. Finally, in order to go beyond the slowly rotating regime, we explore the consistency of the Kerr-Schild ansatz in cubic Quasi-topological gravity. Requiring the spacetime to asymptotically match with the rotating black hole in GR, for equal oblateness parameters, the Kerr-Schild deformation of an AdS vacuum, does not lead to a solution for generic values of the coupling. This result suggests that in order to have solutions with finite rotation in Quasi-topological gravity, one must go beyond the Kerr-Schild ansatz.

Electromagnetic quasitopological gravities

We identify a set of higher-derivative extensions of Einstein-Maxwell theory that allow for spherically symmetric charged solutions characterized by a single metric function f (r) = −gtt = 1/grr. These theories are a non-minimally coupled version of the recently constructed Generalized Quasitopological gravities and they satisfy a number of properties that we establish. We study magnetically-charged black hole solutions in these new theories and we find that for some of them the equations of motion can be fully integrated, enabling us to obtain analytic solutions. In those cases we show that, quite generally, the singularity at the core of the black hole is removed by the higher-derivative corrections and that the solution describes a globally regular geometry. In other cases, the equations are reduced to a second order equation for f (r). Nevertheless, for all the theories it is possible to study the thermodynamic properties of charged black holes analytically. We show that the first law of thermodynamics holds exactly and that the Euclidean and Noether-charge methods provide equivalent results. We then study extremal black holes, focusing on the corrections to the extremal charge-to-mass ratio at a non-perturbative level. We observe that in some theories there are no extremal black holes below certain mass. We also show the existence of theories for which extremal black holes do not represent the minimal mass state for a given charge. The implications of these findings for the evaporation process of black holes are discussed.

Einstein quartic gravity: Shadows, signals, and stability

Using a continued fraction ansatz we obtain an analytic approximation for a spherically symmetric black hole solution to Einsteinian Quartic Gravity (EQG), the next simplest Generalized Quasi-Topological Gravity (GQTG) after Einsteinian Cubic Gravity (ECG). This approximate solution is valid everywhere outside of the horizon and we use it to investigate the orbit of massive test bodies near a black hole, specifically computing the innermost stable circular orbit. Using Shapiro time delay we calculate the constraints on the EQG coupling parameter. Finally we compute the shadow of an EQG black hole and figure out it to be larger than its Einsteinian counterpart in general relativity for the same value of the mass. By applying our results to Sagittarius A* (Sgr A*) at the center of Milky Way we find, similar to ECG black holes, that departures from general relativity are small but distinguishable for EQG black holes.

On four-dimensional Einsteinian gravity, quasitopological gravity, cosmology and black holes

We show that the combination of cubic invariants defining five-dimensional quasitopological gravity, when written in four dimensions, reduce to the version of four-dimensional Einsteinian gravity recently proposed by Arciniega, Edelstein & Jaime, that produces second order equations of motion in a FLRW ansatz, with a purely geometrical inflationary period. We introduce a quartic version of the four-dimensional Einsteinian theory with similar properties, and study its consequences. In particular we found that there exists a region on the space of parameters which allows for thermodynamically stable black holes, as well as a well-defined cosmology with geometrically driven inflation. We briefly discuss the cosmological inhomogeneities in this setup. We also provide a combination of quintic invariants with those properties.

Partition functions on slightly squashed spheres and flux parameters

We argue that the conjectural relation between the subleading term in the small-squashing expansion of the free energy of general three-dimensional CFTs on squashed spheres and the stress-tensor three-point charge t4 proposed in arXiv:1808.02052: {F}_{{mathbbm{S}}_{varepsilon}^3}^{(3)}(0)=frac{1}{630}{pi}^4{C}_T{t}_4 , holds for an infinite family of holographic higher-curvature theories. Using holographic calculations for quartic and quintic Generalized Quasi-topological gravities and general-order Quasi-topological gravities, we identify an analogous analytic relation between such term and the charges t2 and t4 valid for five-dimensional theories: {F}_{{mathbbm{S}}_{varepsilon}^5}^{(3)}(0)=frac{2}{15}{pi}^6{C}_Tleft[1+frac{3}{40}{t}_2+frac{23}{630}{t}_4right] . We test both conjectures using new analytic and numerical results for conformally-coupled scalars and free fermions, finding perfect agreement.