$$a_{1}$$ meson-nucleon coupling constant at finite temperature from the soft-wall AdS/QCD model

We study the temperature dependence of the $$a_1$$ a 1 meson-nucleon coupling constant in the framework of the soft-wall AdS/QCD model with thermal dilaton field. Profile functions for the axial-vector and fermion fields in the AdS-Schwarzschild metric are presented. It is constructed an interaction Lagrangian for the fermion-axial-vector-thermal dilaton fields system in the bulk of space-time. From this Lagrangian integral representation for the $$g_{a_1NN}$$ g a 1 N N coupling constant is derived. The temperature dependence of this coupling constant is numerically analyzed.

On the inverse hoop conjecture of Hod

Recently, Hod has shown that Thorne’s hoop conjecture ($$\frac{C(R)}{4\pi M(r\le R)} \le 1\Rightarrow $$ C ( R ) 4 π M ( r ≤ R ) ≤ 1 ⇒ horizon) is violated by stationary black holes and so he proposed a new inverse hoop conjecture characterizing such black holes (that is, horizon $$\Rightarrow \mathcal {H =} \frac{\pi \mathcal {A} }{\mathcal {C}_{{eq} }^{2}} \le 1$$ ⇒ H = π A C eq 2 ≤ 1 ). In this paper, it is exemplified that stationary hairy black holes, endowed with Lorentz symmetry violating Bumblebee vector field related to quantum gravity and dilaton field of string theory, also respect the inverse conjecture. It is shown that stationary hairy singularity, recently derived by Bogush and Galt’sov, does not respect the conjecture thereby protecting it. However, curiously, there are two horizonless stationary wormholes that can also respect the conjecture. Thus one may also state that throat $$\Rightarrow \mathcal {H \le }1$$ ⇒ H ≤ 1 , suggesting that the inverse conjecture may be a necessary but not sufficient proposition.

New class of exact solutions to Einstein–Maxwell-dilaton theory on four-dimensional Bianchi type IX geometry

We construct new classes of cosmological solution to the five dimensional Einstein–Maxwell-dilaton theory, that are non-stationary and almost conformally regular everywhere. The base geometry for the solutions is the four-dimensional Bianchi type IX geometry. In the theory, the dilaton field is coupled to the electromagnetic field and the cosmological constant term, with two different coupling constants. We consider all possible solutions with different values of the coupling constants, where the cosmological constant takes any positive, negative or zero values. In the ansatzes for the metric, dilaton and electromagnetic fields, we consider dependence on time and two spatial directions. We also consider a special case of the Bianchi type IX geometry, in which the geometry reduces to that of Eguchi–Hanson type II geometry and find a more general solution to the theory.

Holographic anisotropic model for light quarks with confinement-deconfinement phase transition

We present a five-dimensional anisotropic holographic model for light quarks supported by Einstein-dilaton-two-Maxwell action. This model generalizing isotropic holographic model with light quarks is characterized by a Van der Waals-like phase transition between small and large black holes. We compare the location of the phase transition for Wilson loops with the positions of the phase transition related to the background instability and describe the QCD phase diagram in the thermodynamic plane — temperature T and chemical potential μ. The Cornell potential behavior in this anisotropic model is also studied. The asymptotics of the Cornell potential at large distances strongly depend on the parameter of anisotropy and orientation. There is also a nontrivial dependence of the Cornell potential on the boundary conditions of the dilaton field and parameter of anisotropy. With the help of the boundary conditions for the dilaton field one fits the results of the lattice calculations for the string tension as a function of temperature in isotropic case and then generalize to the anisotropic one.

Quasilocal Smarr relation for an asymptotically flat spacetime

We investigate the thermodynamics of Einstein–Maxwell (-dilaton) theory for an asymptotically flat spacetime in a quasilocal frame. We firstly define a quasilocal thermodynamic potential via the Euclidean on-shell action and formulate a quasilocal Smarr relation from Euler’s theorem. Then we calculate the quasilocal energy and surface pressure by employing a Brown–York quasilocal method along with Mann–Marolf counterterm and find entropy from the quasilocal thermodynamic potential. These quasilocal variables are consistent with the Tolman temperature and the entropy in a quasilocal frame turns out to be same as the Bekenstein–Hawking entropy. As a result, we found that a surface pressure term and its conjugate variable, a quasilocal area, do not participate in a quasilocal thermodynamic potential, but should be present in a quasilocal Smarr relation and the quasilocal first law of black hole thermodynamics. For dyonic black hole solutions having dynamic dilaton field, a non-trivial dilaton contribution should occur in the quasilocal first law but not in the quasilocal Smarr relation.

Real classical geometry with arbitrary deficit parameter(s) $$\alpha (_{I})$$ in deformed Jackiw–Teitelboim gravity

An interesting deformation of Jackiw–Teitelboim (JT) gravity has been proposed by Witten by adding a potential term $$U(\phi )$$ U ( ϕ ) as a self-coupling of the scalar dilaton field. During calculating the path integral over fields, a constraint comes from integration over $$\phi $$ ϕ as $$R(x)+2=2\alpha \delta (\vec {x}-\vec {x}')$$ R ( x ) + 2 = 2 α δ ( x → - x → ′ ) . The resulting Euclidean metric suffered from a conical singularity at $$\vec {x}=\vec {x}'$$ x → = x → ′ . A possible geometry is modeled locally in polar coordinates $$(r,\varphi )$$ ( r , φ ) by $$\mathrm{d}s^2=\mathrm{d}r^2+r^2\mathrm{d}\varphi ^2,\varphi \cong \varphi +2\pi -\alpha $$ d s 2 = d r 2 + r 2 d φ 2 , φ ≅ φ + 2 π - α . In this letter we show that there exists another family of ”exact” geometries for arbitrary values of the $$\alpha $$ α . A pair of exact solutions are found for the case of $$\alpha =0$$ α = 0 . One represents the static patch of the AdS and the other one is the non-static patch of the AdS metric. These solutions were used to construct the Green function for the inhomogeneous model with $$\alpha \ne 0$$ α ≠ 0 . We address a type of phase transition between different patches of the AdS in theory because of the discontinuity in the first derivative of the metric at $$x=x'$$ x = x ′ . We extended the study to the exact space of metrics satisfying the constraint $$R(x)+2=2\sum _{i=1}^{k}\alpha _i\delta ^{(2)}(x-x'_i)$$ R ( x ) + 2 = 2 ∑ i = 1 k α i δ ( 2 ) ( x - x i ′ ) as a modulus diffeomorphisms for an arbitrary set of deficit parameters $$(\alpha _1,\alpha _2,\ldots ,\alpha _k)$$ ( α 1 , α 2 , … , α k ) . The space is the moduli space of Riemann surfaces of genus g with k conical singularities located at $$x'_k$$ x k ′ , denoted by $$\mathcal {M}_{g,k}$$ M g , k .

BH solutions with toroidal horizon in dilaton gravity inspired by power-law electrodynamics: PV criticality and quasinormal modes

In this work, a new class of black hole solutions in dilaton gravity has been obtained where the dilaton field is coupled with nonlinear Maxwell invariant as a source. The background space–time in this works is considered as the [Formula: see text]-dimensional toroidal metric. In the presence of the dilaton field (for some unique values of [Formula: see text][Formula: see text] a ), the electric field increases as we got farther away from the origin. In the absence of the dilaton field [Formula: see text], the electric field always decreases as one goes farther away from the origin. In the thermodynamical analysis, we obtain the Smarr formula for our solution. We find that the presence of the dilaton field makes the solutions to be locally stable near the origin. Also, this field vanishes the global stability near the origin compared to the no dilaton field case [Formula: see text]. We can say that the dilaton field has a crucial impact on the thermodynamical stability and it is a key factor in stability analysis. We study the quasinormal modes (QNMs) of black hole solutions in dilaton gravity. For this purpose, we use the WKB approximation method upto first order corrections. We have shown the perturbations decay in corresponding diagrams when the dilaton parameter [Formula: see text] and coupling constant [Formula: see text] change. Motivated by the thermodynamical analogy of black holes and Van der Waals liquid/gas systems, in this work, we investigate PV criticality of the obtained solution. We extend the phase space by considering the cosmological constant as thermodynamic pressure. We obtain the equation of state (EOS) and plot the relevant PV [Formula: see text] diagrams. We also present a class of interior solutions corresponding to the exterior solution in dilaton gravity. The solution which is obtained for a linear equation of state is regular and well-behaved at the stellar interior. a Dilaton field representation.

Conditions for Vacuum Instability in Holographic Theories with Dilaton Field

We investigate the vacuum instability in the presence of dilaton field in a holographic setup. Although the dilaton is a bulk field, it leads to the vacuum instability on the boundary. We show that the whole process crucially depends on the probe brane position and as well on the radial coordinate so that the effects of dilaton scale parameter in different regions of the bulk or for different probe brane positions are different. We also observe that in our study, the temperature can strengthen the effect of scale parameter in reducing the potential barrier. Finally, we show that this Schwinger-like effect, although is interesting by itself, does not produce a considerable pair production rate.

A new black hole solution in dilaton gravity inspired by power-law electrodynamics

In this work, a new class of slowly rotating black hole solutions in dilaton gravity has been obtained where dilaton field is coupled with nonlinear Maxwell invariant. The background space–time is a stationary axisymmetric geometry. Here, it has been shown that the dilaton potential can be written in the form of generalized three Liouville-type potentials. In the presence of these three Liouville-type dilaton potentials, the asymptotic behavior of the obtained solutions is neither flat nor (A)dS. One bizarre property of the electric field is that the electric field goes to zero when [Formula: see text] and diverges at [Formula: see text]. We show the validity of the first law of thermodynamics in thermodynamic investigations. The local and global thermodynamical stability are investigated through the use of heat capacity and Gibbs free energy. Also, the bounded, phase transition and the Hawking–Page phase transition points as well as the ranges of black hole stability have been shown in the corresponding diagrams. From these diagrams, we can say that the presence of the dilaton field makes the solutions to be locally stable near origin and vanishes the global stability of our solutions. In final thermodynamics analysis, we obtain the Smarr formula for our solution. We will show that the presence of dilaton field brings a new term in the Smarr formula. Also, we find that the dilaton field makes the black hole (AdS) mass to decrease for every fix values of [Formula: see text] (entropy).