Einstein Gravity Research Articles

A new slow-rotating black hole solution in Chern-Simons axion of Einstein gravity

This research aims to incorporate an axionic field within the context of dynamical Chern-Simons (CS) gravity and investigate the behavior of a slowly rotating black hole (BH) within this theoretical framework. To the best of our knowledge, this is the first instance where such a problem has been tackled within the context of (CS) gravitational theory coupled with the axionic field. The Lagrangian of this theory includes two CS scalar field functions, denoted as ω(ϑ) and U(ϑ), where ϑ represents the CS scalar field. Our investigation involves calculating the equation related to the CS scalar field and demonstrating that deriving a solution necessitates imposing constraints on U and ω, specifically in the form of U′=ω, where U′≡dU(ϑ)dϑ. By utilizing the solution for the CS scalar field in other field equations, we reveal that the enigmatic function U can be expressed explicitly as U=ϑ2p+1, where p represents an integer with unrestricted values. In the instance where p=0, the CS Axion Einstein gravity theory [1] aligns with the study carried out in [2]. Furthermore, our analysis establishes that for positive values of p, the theory is capable of generating a significantly potent CS BH compared to the model derived in [2]. Moreover, our study delves into the geodesics of this BH, deriving its conserved quantities, orbital period, as well as its geodesic precession angle.

Gravito-electromagnetic perturbations and QNMs of regular black holes

In the framework of Einstein’s gravity coupled to nonlinear electromagnetic fields, we study gravito-electromagnetic perturbations of magnetic regular black holes (BHs). The master equations of perturbations are obtained through Chandrasekhar’s formulation, from which it can be seen, different from the electric counterparts, for magnetic BHs gravitational perturbations with odd-parity coupled only to the electromagnetic perturbations with even-parity. We solve the master equations numerically and obtain quasinormal modes (QNMs) for three typical regular BHs. Results show that QNMs of distinct regular BHs differ significantly, and they differ from that of the Reissner–Nordström BH as well. Indications of these results on the stability of these regular BHs are discussed in detail.

Observational constraints on non-minimally coupled curvature–matter models of gravity from the analysis of Pantheon data

We considered non-minimally coupled curvature–matter models of gravity in a Friedmann–Robertson–Walker Universe filled with perfect fluid and investigated its cosmological implications in the light of Pantheon compilation of 1048 supernova Ia (SNe Ia) data points along with 54 data points from observed Hubble data. The non-minimal curvature–matter coupling has been introduced by adding a term to the usual action for Einstein gravity involving the Einstein–Hilbert action and minimally coupled matter action. We investigate the observational constraints on the non-minimal models by choosing two different kinds of parametrisation of fluid-pressure profiles using a dimensionless parameter k. The interplay of the three parameters plays a pivotal role in testing the consistency of non-minimally coupled fluid–curvature scenarios with the observed data. We found there exist large domains in the ()-parameter space for which models with non-minimal curvature–matter mixing stand as viable cosmological models reproducing the observed features of late-time cosmic evolution. We also commented on the possibility of ‘gravitationally induced particle creation’ in the context of SNe Ia data.

Study on the RVB method for calculating the Hawking temperature of black holes

In this work, we study the RVB method for calculating the Hawking temperature of different black holes and find that there is an undetermined integral constant in the temperature expression. We use this method to calculate the Hawking temperature of the black hole in Einstein gravity, and massive gravity, Einstein–Gauss–Bonnet gravity, Scalar–Tensor–Vector modified gravity and [Formula: see text] gravity, respectively. By comparing with the temperature obtained by the Hawking temperature formula, we find that regardless of the gravitational theory from which the black hole solution is obtained, after the black hole metric is reduced to two dimensions, if there is no first-order term of [Formula: see text] in [Formula: see text], the integral constant is 0. If there is a first-order term of [Formula: see text] in [Formula: see text], the integral constant is determined by the coefficient in front of the first-order term of [Formula: see text].

Starobinsky inflation from string theory?

Starobinsky inflation is currently one of the best models concerning agreement with cosmological data. Despite this observational success, it is still lacking a robust embedding into a UV complete theory. Previous efforts to derive Starobinsky inflation from string theory have been based on the derivation of higher derivative curvature terms from the low-energy limit of ten-dimensional string theory. This approach is however known to fail due to the difficulty to tame the effect of contributions proportional to the Ricci scalar to a power larger than two. In this paper we investigate an alternative attempt which exploits instead the ubiquitous presence of scalar fields in string compactifications combined with the fact that Starobinsky inflation can be recast as Einstein gravity coupled to a scalar field with a precise potential and conformal coupling to matter fermions. After showing that the dilaton does not feature the right Yukawa coupling to matter, we focus in particular on type IIB Kähler moduli since they have shown to lead to exponential potentials with a Starobinsky-like plateau. We consider three classes of moduli with a different topological origin: the volume modulus, bulk fibre moduli, and blow-up modes. The only modulus with the correct coupling to matter is the volume mode but its potential does not feature any plateau at large field values. Fibre moduli admit instead a potential very similar to Starobinsky inflation with a natural suppression of higher curvature corrections, but they cannot reproduce the correct conformal coupling to matter. Blow-up modes have both a wrong potential and a wrong coupling. Our analysis implies therefore that embedding Starobinsky inflation into string theory seems rather hard. Finally, it provides a detailed derivation of the coupling to matter of fibre moduli which could be used as a way to discriminate Starobinsky from fibre inflation.

The covariant approach to static spacetimes in Einstein and extended gravity theories

We present a covariant study of static space-times, as such and as solutions of gravity theories. By expressing the relevant tensors through the velocity and the acceleration vectors that characterise static space-times, the field equations provide a natural non-redundant set of scalar equations. The same vectors suggest the form of a Faraday tensor, that is studied in itself and in (non)-linear electrodynamics. In spherical symmetry, we evaluate the explicit expressions of the Ricci, the Weyl, the Cotton and the Bach tensors. Simple restrictions on the coefficients yield well known and new solutions in Einstein, f(R), Cotton and Conformal gravity, with or without charges, in vacuo or with fluid source.

The celestial chiral algebra of self-dual gravity on Eguchi-Hanson space

We consider the twistor description of classical self-dual Einstein gravity in the presence of a defect operator wrapping a certain ℂℙ1. The backreaction of this defect deforms the flat twistor space to that of Eguchi-Hanson space. We show that the celestial chiral algebra of self-dual gravity on the Eguchi-Hanson background is likewise deformed to become the loop algebra of a certain scaling limit of the family of W(μ)-algebras, where the scaling limit is controlled by the radius of the Eguchi-Hanson core. We construct this algebra by computing the Poisson algebra of holomorphic functions on the deformed twistor space, and check this result with a space-time calculation of the leading contribution to the gravitational splitting function. The loop algebra of a general W(μ)-algebra (away from the scaling limit) similarly arises as the celestial chiral algebra of Moyal-deformed self-dual gravity on Eguchi-Hanson space. We also obtain corresponding results for self-dual Yang-Mills.

Flows of rotating extremal attractor black holes

We investigate the attractor mechanism of five-dimensional extremal rotating black holes in Einstein gravity minimally coupled with a multiplet complex scalar. By imposing regularity on the horizon, we show that the only possible attractor value of the scalar field is zero in our setup and that the local geometry is determined by the Myers-Perry black hole solution. We numerically obtain the extremal AdS black hole solutions interpolating the near horizon geometry to the asymptotic AdS spacetime under the existence of a bare potential of the scalar field. The black hole energy and the angular momenta are discretized for the usual Dirichlet boundary condition. Under the general boundary condition, we also find hairy extremal AdS black holes in which the energy is smaller than that of the extremal Myers-Perry AdS black hole solution for the same angular momentum.

On the ghost problem of conformal gravity

We study the metric perturbations around the de Sitter and Minkowski backgrounds in Conformal Gravity. We confirm the presence of ghosts in both cases. In the de Sitter case, by applying the Maldacena boundary conditions — the Neumann boundary condition and the positive-frequency mode condition — to the metric, we show that one cannot recover a general solution for the perturbations. In turn, alongside the Neumann boundary condition, we derive an additional condition with which the perturbations of conformal gravity and dS perturbations of Einstein gravity with cosmological constant coincide. We further show that the Neumann boundary condition does not lead to a general solution in Minkowski space. Conversely, we derive the alternative boundary conditions, with which we attain an agreement between the perturbations of conformal and Einstein gravity in full generality, thus removing the ghost of conformal gravity.

Self-Dual Gravity and Color-Kinematics Duality in AdS_{4}.

We show that self-dual gravity in Euclidean four-dimensional anti-de Sitter space (AdS_{4}) can be described by a scalar field with a cubic interaction written in terms of a deformed Poisson bracket, providing a remarkably simple generalization of the Plebanski action for self-dual gravity in flat space. This implies a novel symmetry algebra in self-dual gravity, notably an AdS_{4} version of the so-called kinematic algebra. We also obtain the three-point interaction vertex of self-dual gravity in AdS_{4} from that of self-dual Yang-Mills by replacing the structure constants of the Lie group with the structure constants of the new kinematic algebra, implying that self-dual gravity in AdS_{4} can be derived from self-dual Yang-Mills in this background via a double copy. This provides a concrete starting point for defining the double copy for Einstein gravity in AdS_{4} by expanding around the self-dual sector. Moreover, we show that the new kinematic Lie algebra can be lifted to a deformed version of the w_{1+∞} algebra, which plays a prominent role in celestial holography.

C-functions in higher-derivative flows across dimensions

In the context of gravitational theories describing renormalization group flows across dimensions via AdS/CFT, we study the role of higher-derivative corrections to Einstein gravity. We use the Null Energy Condition to derive monotonicity properties of candidate holographic central charges formed by combinations of metric functions. We also implement an entropic approach to the characterization of the four-derivative flows using the Jacobson-Myers functional and demonstrate, under reasonable conditions, monotonicity of certain terms in the entanglement entropy via the appropriate generalization of the Ryu-Takayanagi prescription. In particular, we show that any flow from a higher dimensional theory to a holographic CFT2 satisfies a type of monotonicity. We also uncover direct relations between NEC-motivated and entropic central charges.

Chains of mini-boson stars

In this paper, we re-investigate the static, soliton-like solutions in the model of the Einstein gravity coupled to a free and complex scalar field, which have been known as mini-boson stars. With the numerical methods, we have discovered a new family of solutions in addition to the typical single mini-boson star solution. These solutions can be interpreted as chains of boson stars, consisting of multiple boson stars along the symmetry axis. We demonstrate the configuration of two types of chains, one with an even number of constituents and the other with an odd number of constituents. Furthermore, we also study the effect of the frequency of the complex scalar field on the ADM mass M and the U(1) scalar charge Q. It is noteworthy that the existence of chains of boson stars does not require the introduction of a complex scalar field with self-interacting potential.

Anisotropic Scaling Non-Relativistic Holography: A Symmetry Perspective

We study the holographic dual of the two-dimensional non-relativistic field theory with anisotropic scaling from a symmetry perspective. We construct a new four-dimensional metric with two-dimensional global anisotropic scaling isometry. The four-dimensional spacetime is homogeneous and is a solution of Einstein gravity with quadratic-curvature extension. We consider this spacetime dual to the vacuum of the boundary field theory. By introducing a proper solution phase space, we find that the asymptotic symmetry of the gravity theory is the two-dimensional local anisotropic conformal symmetry, which recovers precisely the results from the dual non-relativistic field theory side.

Encoded information of mixed correlations: the views from one dimension higher

After reviewing the JT gravity, we discuss the four saddles in the mixed correlation measures of black holes Hawking radiation in the setup of geometric evaporation of [1]. By looking from 1d higher point of view and partial dimensional reduction, we examine the phase structures and the universalities for these four saddles. We also discuss the behavior of quantum error correction codes for each of these four phases, reaching to consistent results. Then, instead of dimension reduction between Einstein gravity and JT, we try to explore the connections between partition functions and saddles of 3d Chern-Simons and 2d BF theories, 2d Liouville and 2d Wess-Zumino-Witten models, and also the dimensionally reduced 1d Schwarzian and 1d particles on group. We specifically sketch on the connections between these theories in the setup of mixed correlations and island formulation.

Dynamic behaviours of black hole phase transitions near quadruple points

Treating the horizon radius as an order parameter in a thermal fluctuation, the free energy landscape model sheds light on the dynamic behaviour of black hole phase transitions. Here we carry out the first investigation of the dynamics of the recently discovered multicriticality in black holes. We specifically consider black hole quadruple points in D = 4 Einstein gravity coupled to non-linear electrodynamics. We observe thermodynamic phase transitions between the four stable phases at a quadruple point as well as weak and strong oscillatory phenomena by numerically solving the Smoluchowski equation describing the evolution of the probability distribution function. We analyze the dynamic evolution of the different phases at various ensemble temperatures and find that the probability distribution of a final stationary state is closely tied to the structure of its off-shell Gibbs free energy.

The null geodesics of charged and non–charged black hole in mimetic gravity

The null geodesics around the charged black hole spacetimes are investigated in the mimetic gravity framework when Einstein's gravity is coupled to a nonlinear electromagnetic field. The photon paths in nonlinear electrodynamics are geodesics of the effective metric which is determined by the background metric and the particular nonlinear theory considered. The nonlinear effects are represented by a quadruple moment and appear as a correction term to Reissner Nordstrom (RN) metric and Reissner Nordstrom-anti-de Sitter (RN–(A)dS) in cylindrical metric. Remarkably, the nonlinear effects prevent the circular orbits around black holes, and the presence of the mimetic field can change the repulsive character of dS space to the attractive one. Also, the effect of the mimetic parameter manifests itself in the stronger or weaker gravity of the black hole.

Bondi-Hoyle-Lyttleton accretion onto a rotating black hole with ultralight scalar hair

We present a numerical study of relativistic Bondi-Hoyle-Lyttleton (BHL) accretion onto an asymptotically flat black hole with synchronized hair. The hair is sourced by an ultralight, complex scalar field, minimally coupled to Einstein's gravity. Our simulations consider a supersonic flow parametrized by the asymptotic values of the fluid quantities and a sample of hairy black holes with different masses, angular momenta, and amount of scalar hair. For all models, steady-state BHL accretion solutions are attained that are characterized by the presence of a shock-cone and a stagnation point downstream. For the models of the sample with the largest component of scalar field, the shock-cone envelops fully the black hole, transitioning into a bow-shock, and the stagnation points move further away downstream. Analytical expressions for the mass accretion rates are obtained after fitting the numerical results, which can be used to analyze black-hole formation scenarios in the presence of ultralight scalar fields. The formation of a shock-cone leads to regions where sound waves can be trapped and resonant oscillations excited. We measure the frequencies of such quasi-periodic oscillations and point out a possible association with quasi-periodic oscillations in the X-ray light curve of Sgr A* and microquasars.

The thermodynamical properties of dS black holes in Einstein gravity with torsion induced by the spinor

The thermodynamical properties of dS black holes in Einstein gravity with torsion induced by the spinor

Entropy of causal diamond ensembles

We define a canonical ensemble for a gravitational causal diamond by introducing an artificial York boundary inside the diamond with a fixed induced metric and temperature, and evaluate the partition function using a saddle point approximation. For Einstein gravity with zero cosmological constant there is no exact saddle with a horizon, however the portion of the Euclidean diamond enclosed by the boundary arises as an approximate saddle in the high-temperature regime, in which the saddle horizon approaches the boundary. This high-temperature partition function provides a statistical interpretation of the recent calculation of Banks, Draper and Farkas, in which the entropy of causal diamonds is recovered from a boundary term in the on-shell Euclidean action. In contrast, with a positive cosmological constant, as well as in Jackiw-Teitelboim gravity with or without a cosmological constant, an exact saddle exists with a finite boundary temperature, but in these cases the causal diamond is determined by the saddle rather than being selected a priori.

Restricted phase space thermodynamics of charged AdS black holes in conformal gravity* *Supported by the National Natural Science Foundation of China (12275138)

The thermodynamics of charged spherically symmetric AdS black holes in conformal gravity is revisited using the recently proposed restricted phase space (RPS) formalism. This formalism avoids all the bizarreness arising in the extended phase space formalism for this model. It is found that the charged AdS black holes in this model may belong to a new universality class that is different from all previously studied cases under the RPS formalism. Besides the distinguished isocharge and isothermal behaviors, the absence of the Hawking-Page transition is another notable feature. However, in the high temperature limit, the thermodynamic behavior of the present model becomes exactly the same as that of the Einstein gravity and black hole scan models, which adds further evidence for the universality of the recently reported correspondence between high temperature AdS black holes and low temperature quantum phonon gases in nonmetallic crystals.