Einstein Maxwell Dilaton Research Articles

Black string solutions in Lifshitz spacetime

In this paper we study black string solutions considering the Lifshitz anisotropic scaling. We have shown that a new class of asymptotically Lifshitz solutions can be generated by an Einstein–Maxwell-Dilaton theory with a cosmological constant. In the limit where we recover conformal scale invariance, we retrieve the usual black string solution. Furthermore, we demonstrated that to incorporate the effects of electric charge in the black string, at least two independent gauge fields coupled to the dilaton field are necessary. The charged black string solution exhibits new horizons that depend on the potential in Lifshitz exponent z. The stability of these new solutions is investigated through the thermodynamic analysis of the charged black string. The temperature, entropy, and heat capacity indicate that these modified black strings are thermodynamically stable.

Extended thermodynamics and critical behavior of generalized dilatonic Lifshitz black holes

We study a particular Einstein–Maxwell–Dilaton black hole configuration with cosmological constant, expressed in terms of the curvature radius, from the point of view of quasi-homogeneous thermodynamics. In particular, we show that the curvature radius and the coupling constant of the matter fields can be treated as thermodynamic variables in the framework of extended thermodynamics, leading in both cases to a van der Waals-like behavior. We also investigate in detail the stability and critical properties of the black holes and obtain results, which are compatible with the mean field approach.

Remarks on the light ring images and the optical appearance of hairy black holes in Einstein–Maxwell-dilaton gravity

The behaviors of null geodesics in the spherical symmetric black holes in Einstein–Maxwell-dilaton (EMD) theory with coupling function f(Φ)=e-2αΦ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(\\Phi )=e^{-2\\alpha \\Phi }$$\\end{document} are meticulously analyzed. We investigate the effects of coupling constant α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} on the effective potential of photon trajectories within three ranges, namely 0<α<1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0<\\alpha <1$$\\end{document}, α=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha =1$$\\end{document} and α>1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha >1$$\\end{document}. We find that the thicknesses of lensing and photon rings are smaller at larger α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} and fixed electric charge in the unit of mass q, whereas they are larger at fixed α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} and larger q. This behavior can be described by using the angular Lyapunov exponent γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma $$\\end{document} in the vicinity of the critical curve. Remarkably, the behaviors of photon trajectories are found to be more interesting when α>1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha >1$$\\end{document}. Namely, the radius of the black hole shadow Rs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R_\ ext {s}$$\\end{document} becomes to be smaller than the photon sphere radius rph\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_\ ext {ph}$$\\end{document} when α>1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha > 1$$\\end{document} and q>q∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$q>q^*$$\\end{document}. Moreover, Rs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R_\ ext {s}$$\\end{document} goes to zero as q saturates the extremal limit, beyond which the photon orbit becomes absent. Furthermore, we construct the optical appearance of black holes surrounded by optically and geometrically thin accretion disk with three cases of Gralla–Lupsasca–Marrone (GLM) emission profile. Our results indicate that the observed flux originating from the lensing and photon rings exhibits suppression as α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} increases, while it undergoes amplification with the increasing parameter q.

Accelerating Kaluza–Klein black hole and Kerr/CFT correspondence

We construct a new solution in the Einstein–Maxwell-dilaton theory describing accelerating, charged, and rotating black hole, i.e. the accelerating Kaluza–Klein black hole. Some properties the spacetime are discussed, such as the electromagnetic fields, the area-temperature product, and the holography according to Kerr/CFT correspondence. As expected, the macroscopic Bekenstein–Hawking entropy for an extremal accelerating Kaluza–Klein black hole can be recovered by using Cardy formula of a two dimensional conformal field theory. An interesting feature is found, namely the area-temperature product is just the one belongs to the vacuum Einstein seed solution.

The exact relativistic scalar quasibound states of the dyonic Kerr–Sen black hole: quantized energy, and Hawking radiation

We consider Klein–Gordon equation in the Dyonic Kerr–Sen black hole background, which is the charged rotating axially symmetric solution of the Einstein–Maxwell–Dilaton–Axion theory of gravity. The black hole incorporates electric, magnetic, dilatonic and axionic charges and is constructed in 3+1 dimensional spacetime. We begin our investigations with the construction of the scalar field’s governing equation, i.e., the covariant Klein–Gordon equation. With the help of the ansatz of separation of variables, we successfully separate the polar part, and find the exact solution in terms of Spheroidal Harmonics, while the radial exact solution is obtained in terms of the Confluent Heun function. The quantization of the quasibound state is done by applying the polynomial condition of the Confluent Heun function that gives rise to discrete complex-valued energy levels for massive scalar fields. The real part is the scalar field relativistic quantized energy, while the imaginary part represents the quasibound states’s decay. We present all of the sixteen possible exact energy solutions for both massive and massless scalars. We also present the investigation the Hawking radiation of the Dyonic Kerr–Sen black hole’s apparent horizon, via the Sigurd–Sannan method by making use of the obtained exact scalar wave functions. The radiation distribution function, and the Hawking temperature are also obtained.

Stability and phase transition of black holes in Einstein-Maxwell-dilaton gravity

In this research, we study black hole stability and phase transition in Einstein-Maxwell-dilaton (EMD) gravity. A dilaton field is non-minimally related to the Maxwell field in the EMD gravity and is an intriguing alternative for General Relativity. By using the thermodynamic laws of the black holes, temperature, entropy, heat capacity, pressure, critical points and Gibbs free energy of charged static dilaton black holes in EMD gravity were all thoroughly explored and effects of dilaton constant on these quantities are studied and the results are compared with Schwarzschild, Reissner-Nordström, and Gibbons-Maeda-Garfinkle-Horowitz-Strominger (GMGHS) black holes. In other cases, the system has stable and unstable areas. Since the heat capacity is discontinuous, the system experiences a phase transition, and Van der Waals-like phase transitions occur between the small and large black holes. It has been observed that the heat capacity for the GMGHS and Schwarzschild black holes is always negative, making these systems unstable.

Towards a Warm Holographic Equation of State by an Einstein–Maxwell-Dilaton Model

The holographic Einstein–Maxwell-dilaton model is employed to map state-of-the-art lattice QCD thermodynamics data from the temperature (T) axis towards the baryon–chemical potential (μB) axis and aims to gain a warm equation of state (EoS) of deconfined QCD matter which can be supplemented with a cool and confined part suitable for subsequent compact (neutron) star (merger) investigations. The model exhibits a critical end point (CEP) at TCEP=O(100) MeV and μBCEP=500…700 MeV with an emerging first-order phase transition (FOPT) curve which extends to large values of μB without approaching the μB axis. We consider the impact and peculiarities of the related phase structure on the EoS for the employed dilaton potential and dynamical coupling parameterizations. These seem to prevent the design of an overall trustable EoS without recourse to hybrid constructions.

New exact solutions, thermodynamics and phase transition in the Einstein–Maxwell-dilaton theory

New exact solutions, thermodynamics and phase transition in the Einstein–Maxwell-dilaton theory

Holographic supersymmetric Rényi entropies from hyperbolic black holes with scalar hair

We study holographic supersymmetric Rényi entropies from a family of hyperbolic black holes in an Einstein-Maxwell-dilaton (EMD) system under the BPS condition. We calculate the thermodynamic quantities of these hyperbolic black holes. We find a remarkably simple formula of the supersymmetric Rényi entropy that unifies (interpolates) 11 cases embeddable to 10 or 11 dimensional supergravity. It reproduces many known results in the literature, and gives new results with distinctive features. We show that the supersymmetric version of the modular entropy and the capacity of entanglement cannot be mapped to thermal quantities, due to the dependence of the temperature and the chemical potential by the BPS condition. We also calculate the entanglement spectrum. We derive the potential of the EMD system from a V = 0 solution and obtain two neutral solutions with scalar hair as a byproduct.

Gravitational Waves of Holographic QCD Phase Transition with Hyperscaling Violation

In this paper, we study the gravitational waves of holographic QCD phase transition with hyperscaling violation. We consider an Einstein–Maxwell Dilaton background and discuss the confinement–deconfinement phase transition between thermally charged AdS and AdS black holes. We find that hyperscaling violation reduces the phase transition temperature. In a further study, we discuss the effect of hyperscaling violation on the GW spectrum. We found that the hyperscaling violation exponent suppresses the peak frequency of the total GW spectrum. Moreover, the results of the GW spectrum may be detected by IPTA, SKA, BBO, and NANOGrav. We also find that the hyperscaling violation exponent suppresses the peak frequency of the bubble-collision spectrum h2Ωenv. Hyperscaling violation enhances the energy densities of the sound wave spectrum h2Ωsw and the MHD turbulence spectrum h2Ωturb. The total GW spectrum is dominated by the contribution of the bubble collision in runaway bubbles case.

The effect of scalar hair on the charged black hole with the images from accretions disk

In this paper, we investigate the optical properties of a charged black hole with scalar hair (CSH) within the context of four-dimensional Einstein–Maxwell–Dilaton gravity. To achieve this, we consider three distinct toy models of thin accretion disks. The presence of dilaton coupling allows us to express both the solutions of CSH and the Reissner–Nordström (RN) black hole in terms of their mass (M) and charge (Q). Our findings reveal differences in the effective potentials Veff\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V_{eff}$$\\end{document}, photon sphere radii rph\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_{ph}$$\\end{document}, and innermost stable circular orbit risco\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_{isco}$$\\end{document} between the CSH and RN black hole cases, which become increasingly pronounced as the charge parameter Q increases. However, no noticeable distinctions are observed concerning the critical impact parameter bph\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$b_{ph}$$\\end{document}. When the ratio of the photon ring band and the lensed ring band exceeds 0.1, it may suggest the presence of a charged black hole with scalar hair. Furthermore, our results underscore the significant influence of the charge parameter Q on the brightness distributions of the direct, lensed ring, and photon ring for three standard emission functions. These findings emphasize the potential for distinguishing between CSH and RN black holes through an analysis of direct intensity and peak brightness in specific accretion disk models.

QGP probes from a dynamical holographic model of AdS/QCD

In this paper, we employ the gauge/gravity duality to study some features of the quark–gluon plasma. For this purpose, we implement a holographic QCD model constructed from an Einstein–Maxwell-dilaton gravity at finite temperature and finite chemical potential. The model captures both the confinement and deconfinement phases of QCD and we use it to study the effect of temperature and chemical potential on a heavy quark moving through the plasma. We calculate the drag force, Langevin diffusion coefficients and also the jet quenching parameter, and our results align with other holographic QCD models and the experimental data.

Trajectories of photons around a rotating black hole with unusual asymptotics

Most black hole solutions are characterized with asymptotically flat, or asymptotically (anti) de-Sitter behaviors, but some black holes with unusual asymptotics have also been constructed, which is believed to provide remarkable insights into our understanding of the nature of gravity. In this paper, focusing on a rotating black hole with unusual asymptotics in Einstein–Maxwell-dilaton (EMD) theory, we innovatively analyze the photons’ trajectories around this black hole background, showing that the unusual asymptotics has significant influences on the photons’ trajectories. We expect that our analysis could give more insights in the scenario of black holes’ shadow and image.

Exact massive and massless scalar quasibound states solutions of the Einstein–Maxwell-dilaton (EMD) black hole

In this letter, we will focus on the Klein–Gordon equation with static spherically symmetric black hole solution of the Einstein–Maxwell-dilaton (EMD) theory as its 3+1 background space-time. The Klein–Gordon equation represents quasibound states of both massive and massless scalar fields which are localized in the black hole potential well. By using the covariant Klein–Gordon equation, we investigate the behaviour of both massive and massless scalars in the EMD black hole space-time. We successfully exactly solved the relativistic wave equation and are going to present the novel exact results in this letter. The exact solutions, the wave functions and the energy levels, describe the decaying nature of the relativistic scalar field bound in the curved space-time. The massive scalar quasibound state has complex-valued energy levels where the real part is the massive scalar’s energy while the imaginary part represents the decay. For the massless scalar quasibound state, pure imaginary energy levels are discovered. In this letter, by using the obtained exact scalar particle’s wave functions, we also consider the Hawking radiation of the apparent horizon of the EMD black hole that is calculated via Damour–Ruffini method. In principle, the investigation of black hole quasibound states could provide possibility for laboratory testing of effects whose nature are absolutely related with quantum effects in gravity.

Holographic energy loss near critical temperature in an anisotropic background

We study the energy loss of a quark moving in a strongly coupled quark gluon plasma under the influence of anisotropy. The heavy quark drag force, diffusion coefficient, and jet quenching parameter are calculated using the Einstein–Maxwell-dilaton model, where the anisotropic background is characterized by an arbitrary dynamical parameter A. Our findings indicate that as the anisotropic factor A increases, the drag force and jet quenching parameter both increase, while the diffusion coefficient decreases. Additionally, we observe that the energy loss becomes more significant when the quark moves perpendicular to the anisotropy direction in the transverse plane. The enhancement of the rescaled jet quenching parameters near critical temperature T c , as well as drag forces for a fast-moving heavy quark is observed, which presents one of the typical features of quantum chromodynamics phase transition.

Chaotic motion of scalar particle coupling to Chern–Simons invariant in the stationary axisymmetric Einstein–Maxwell dilaton black hole spacetime

We investigate the motion of a test scalar particle coupling to the Chern–Simons (CS) invariant in the background of a stationary axisymmetric black hole in the Einstein–Maxwell–Dilaton–Axion (EMDA) gravity. Comparing with the case of a Kerr black hole, we observe that the presence of the dilation parameter makes the CS invariant more complex, and changes the range of the coupling parameter and the spin parameter where the chaotic motion appears for the scalar particle. Moreover, we find that the coupling parameter together with the spin parameter also affects the range of the dilation parameter where the chaos occurs. We also probe the effects of the dilation parameter on the chaotic strength of the chaotic orbits for the coupled particle. Our results indicate that the coupling between the CS invariant and the scalar particle yields the richer dynamical behavior of the particle in the rotating EMDA black hole spacetime.

Dilaton photoproduction in a magnetic dipole field of pulsars and magnetars

According to Einstein–Maxwell-dilaton theory, the dilaton field varvec{psi } can be produced by electromagnetic fields with non-zero Maxwell invariant. So electromagnetic wave propagating in an external electromagnetic field is a typical source of dilaton radiation. For study dilaton photoproduction in astrophysical conditions it’s interesting to consider plane elliptically polarized electromagnetic wave propagating in the electromagnetic field of magnetic dipole textbf{m} of pulsars and magnetars. The dilation field equation is solved in case |varvec{psi }| {mathbf {ll 1}}. The angular distribution dilaton radiation is studied in every point of space. It’s shown that spectral composition of dilatons is similar to spectral composition of plane electromagnetic wave. Amount of dilaton energy radiated in time and all directions is greatest in condition ({{varvec{B}}}_{textbf{1}}^{textbf{2}}-{{varvec{B}}}_{textbf{2}}^{textbf{2}})({{varvec{m}}}_{{varvec{x}}}^{textbf{2}}-{{varvec{m}}}_{{varvec{y}}}^{textbf{2}})ge 0, where {{varvec{B}}}_{textbf{1}} and {{varvec{B}}}_{textbf{2}} are electromagnetic wave amplitudes along the axes of polarization ellipse. This condition is valid for many neutron star systems.

Logarithmic correction to black hole entropy in universal low-energy string theory models

We calculate the logarithmic correction to the entropy of asymptotically flat and AdS black holes (rotating, non-rotating, charged, and uncharged) embedded in Einstein-Maxwell-dilaton (EMD) theories with U(1)-charged. The leading quantum gravitational corrections are achieved in both extremal and non-extremal limits of black hole temperature by designing a common Euclidean gravity setup that evaluates the “logarithmic term” from one-loop effective actions via heat kernel method-based calculations. EMD theories are universal building blocks of compactified string theory or supergravity models in 4D. For a concrete example, we generalize the entire setup and calculate logarithmic corrections for black holes in U(1)2-charged EMD models intersecting with mathcal{N} = 4 ungauged and gauged bosonic supergravity. In contrast to flat backgrounds, all the AdS4 results are found to be non-topological, providing a wider “infrared window” into the microscopic degrees of freedom of black holes in string theory.

Hairy extension of the Bertotti–Robinson spacetime in the Einstein–Maxwell-scalar theory is a black hole in closed spatial geometries

In analogy with the Einstein–Maxwell–Dilaton black hole which is a hairy extension of the Reissner–Nordström black hole, we introduce a hairy extension for the Bertotti–Robinson spacetime in the context of the Einstein–Maxwell-scalar theory. The new spacetime is a closed S 3 black hole powered by a pure magnetic field. The energy–momentum tensor is an anisotropic fluid-like form such that p r/ρ and p ⊥/ρ are u (the radial coordinate)-dependent and at the horizon becomes and , respectively. We use the concept of quasilocal mass and find the well-known Misner–Sharp mass to show that the new black hole satisfies the unified first law of the black hole.

Running coupling constant at finite chemical potential and magnetic field from holography * *X.C. is supported by the Research Foundation of Education Bureau of Hunan Province, China (21B0402). L.Z. is supported in part by the Fundamental Research Funds for the Central Universities. D.H. is in part supported by the National Natural Science Foundation of China (11735007, 11890711)

According to gauge/gravity duality, we use an Einstein-Maxwell-dilaton (EMD) model to study the running coupling constant at finite chemical potential and magnetic field. First, we calculate the effect of temperature on the running coupling constant and find the results are qualitatively consistent with lattice guage theory. Subsequently, we calculate the effect of chemical potential and magnetic field on running coupling. It is found that the chemical potential and magnetic field both suppress the running coupling constant. However, the effect of the magnetic field is slightly larger than that of chemical potential for a fixed temperature. Compared with the confinement phase, the magnetic field has a large influence on the running coupling in the deconfinement phase.