Dilaton Coupling Research Articles

Quasinormal modes of dilatonic Reissner\u2013Nordstr\xf6m black holes

We calculate the quasinormal modes of static spherically symmetric dilatonic Reissner–Nordström black holes for general values of the electric charge and of the dilaton coupling constant. The spectrum of quasinormal modes is composed of five families of modes: polar and axial gravitational-led modes, polar and axial electromagnetic-led modes, and polar scalar-led modes. We make a quantitative analysis of the spectrum, revealing its dependence on the electric charge and on the dilaton coupling constant. For large electric charge and large dilaton coupling, strong deviations from the Reissner–Nordström modes arise. In particular, isospectrality is strongly broken, both for the electromagnetic-led and the gravitational-led modes, for large values of the charge.

Relating non-relativistic string theories

Non-relativistic string theories promise to provide simpler theories of quantum gravity as well as tractable limits of the AdS/CFT correspondence. However, several apparently distinct non-relativistic string theories have been constructed. In particular, one approach is to reduce a relativistic string along a null isometry in target space. Another method is to perform an appropriate large speed of light expansion of a relativistic string. Both of the resulting non-relativistic string theories only have a well-defined spectrum if they have nonzero winding along a longitudinal spatial direction. In the presence of a Kalb-Ramond field, we show that these theories are equivalent provided the latter direction is an isometry. Finally, we consider a further limit of non-relativistic string theory that has proven useful in the context of AdS/CFT (related to Spin Matrix Theory). In that case, the worldsheet theory itself becomes non-relativistic and the dilaton coupling vanishes.

Self-similar solutions and critical behavior in Einstein-Maxwell-dilaton theory sourced by charged null fluids

We investigate continuously self-similar solutions of four-dimensional Einstein-Maxwell-dilaton theory supported by charged null fluids. We work under the assumption of spherical symmetry and the dilaton coupling parameter a is allowed to be arbitrary. First, it is proved that the only such vacuum solutions with a time-independent asymptotic value of the dilaton necessarily have vanishing electric field, and thus reduce to Roberts’ solution of the Einstein-dilaton system. Allowing for additional sources, we then obtain Vaidya-like families of self-similar solutions supported by charged null fluids. By continuously matching these solutions to flat spacetime along a null hypersurface one can study gravitational collapse analytically. Capitalizing on this idea, we compute the critical exponent defining the power-law behavior of the mass contained within the apparent horizon near the threshold of black hole formation. For the heterotic dilaton coupling a = 1 the critical exponent takes the value 1/2 typically observed in similar analytic studies, but more generally it is given by γ = a2(1 + a2)−1. The analysis is complemented by an assessment of the classical energy conditions. Finally, and on a different note, we report on a novel dyonic black hole spacetime, which is a time-dependent vacuum solution of this theory. In this case, the presence of constant electric and magnetic charges naturally breaks self-similarity.

Dyon-Like Black Hole Solutions in the Model with Two Abelian Gauge Fields

Dilatonic black hole dyon-like solutions are overviewed in the gravitational 4D model with a scalar field, two 2-forms, two dilatonic coupling constants λi ≠ 0, i = 1, 2, obeying λ1 ≠ − λ2, and the sign parameter e = ±1 before the scalar field kinetic term. Here e = −1 corresponds to a phantom scalar field. The solutions are defined up to solutions of two master equations for two moduli functions, when $$\lambda_i^2 \neq 1/2$$ for e = −1. Several integrable cases, corresponding to the Lie algebras A1 + A1, A2, B2 = C2 and G2 are considered. Some physical parameters of the solutions are derived: the gravitational mass, scalar charge, Hawking temperature, black hole area entropy and PPN parameters β and γ. Bounds on the gravitational mass and scalar charge, based on a certain conjecture, are presented.

Black holes that repel

The recent observation that black holes in certain Einstein-Maxwell-Dilaton (EMD) theories can violate the entropy super-additivity led to the suggestion that these black holes might repel each other. In this paper, we consider EMD theories with two Maxwell fields $A_i$, with general exponential couplings $\exp(a_i \phi)$ in their kinetic terms. We calculate the gravi-electrostatic force between charged black holes $(m_1,e_1)$ and $(M_2,Q_2)$; the former is sufficiently small and can be treated as a point-like object. We find there is a potential barrier caused by the dilaton coupling at $r_0$ outside the back hole horizon $r_+$, provided that $-a_1 a_2> 2(D-3)/(D-2)$. As the black hole approaches extremality, both $r_+$ and $r_0$ vanish, the barrier becomes infinitesimally thin but infinitely high, and the two black holes repel each other in the whole space. There is no electrostatic force between them; the dilaton is the antigravity agent. Furthermore we find that the exact constraint on $a_1 a_2$ can be derived from the requirements that two-charged extremal black holes have a fusion bomb like mass formula and the violation of entropy super-additivity can occur. The two very different approaches give a consistent picture of the black hole repulsion.

Holographic entanglement entropy and Van der Waals transitions in Einstein-Maxwell-dilaton theory

According to the gauge/gravity duality, the Van der Waals transition of charged AdS black holes in extended phase space is conjectured to be dual to a renormalization group flow on the space of field theories. So exploring the Van der Waals transition is potentially valuable for studying holographic properties of charged black hole thermodynamics. There are different transition behaviors for charged dilatonic AdS black holes in Einstein-Maxwell-dilaton (EMD) theory with string-inspired potential with different dilaton coupling constants in diverse dimensions. In this work, we find a special class of charged dilatonic AdS black holes which have the standard Van der Waals transition. We study the extended thermodynamics of the special class of black holes, which, in the extremal limit, have near-horizon geometry conformal to AdS$_2 \times S^{D-2}$. We find that, for these black holes, both the pressure-volume transition in fixed charge ensemble and the inverse temperature-entropy transition in fixed pressure ensemble have the standard Van der Waals behaviors. We also find the holographic entanglement entropy undergoes the same transition behaviors for the same critical temperature in fixing the thermodynamic pressure ensemble.

Anomalous Dimensions for Boundary Conserved Currents in Holography via the Caffarelli–Silvestre Mechanism for p-forms

Although it is well known that the Ward identities prohibit anomalous dimensions for conserved currents in local field theories, a claim from certain holographic models involving bulk dilaton couplings is that the gauge field associated with the boundary current can acquire an anomalous dimension. We resolve this conundrum by showing that all the bulk actions that produce anomalous dimensions for the conserved current generate non-local actions at the boundary. In particular, the Maxwell equations are fractional. To prove this, we generalize to p-forms the Caffarelli/Silvestre (CS) extension theorem. In the context of scalar fields, this theorem demonstrates that second-order elliptic differential equations in the upper half-plane in $${\mathbb{R}_{+}^{n+1}}$$ reduce to one with the fractional Laplacian, $${\Delta^{\gamma}}$$ , with $${\gamma \in {\mathbb{R}}}$$ , when one of the dimensions is eliminated. From the p-form generalization of the CS extension theorem, we show that at the boundary of the relevant holographic models, a fractional gauge theory emerges with equations of motion of the form, $${\Delta^{\gamma} A^{t} = 0}$$ with $${\gamma \in R}$$ and At the boundary components of the gauge field. The corresponding field strength $${F = d_{\gamma} A^{t} = d \Delta ^\frac{\gamma-1}{2} A^t}$$ is invariant under $${A^{t} \rightarrow A^{t} + d_{\gamma} \Lambda}$$ with the fractional differential given by $${d_{\gamma} \equiv (\Delta)^\frac{\gamma-1}{2}{d}}$$ , implying that $${[A^{t}] = \gamma}$$ which is in general not unity.

Topological dyonic dilaton black holes in AdS spaces

We construct a new class of dyonic dilaton black hole solutions in the background of Anti-de Sitter (AdS) spacetime. In order to find an analytical solution which satisfy all the field equations, we should consider the string case where the dilaton coupling is $\alpha=1$. The asymptotic behaviour of the solution ($r\rightarrow\infty$) is exactly AdS, where the dilaton field becomes zero and the metric function reduces to $f(r)\rightarrow -\Lambda r^2/3$. In this spacetime, black hole horizons and cosmological horizons, can be a two-dimensional positive, zero or negative constant curvature surface. We study the physical properties of the solution and show that depending on the metric parameters, these solutions can describe black holes with one or two horizons or a naked singularity. We investigate thermodynamics of the solutions by calculating the charge, mass, temperature, entropy and the electric potential of these solutions and disclose that these conserved and thermodynamic quantities satisfy the first law of black hole thermodynamics. We also analyze thermal stability of the solutions and find the conditions for which we have a stable dyonic dilaton black hole.

Self-similarity in Einstein-Maxwell-dilaton theories and critical collapse

We study continuously self-similar solutions of four-dimensional Einstein-Maxwell-dilaton theory, with an arbitrary dilaton coupling. Self-similarity is an emergent symmetry of gravitational collapse near the threshold of black hole formation. The resulting `critical collapse' picture has been intensively studied in the past for self-gravitating scalar fields or perfect fluids, but little is known concerning other systems. Here we assess the impact of gauge fields on critical collapse, in the context of low-energy string theories. Matter fields need not inherit the symmetries of a spacetime. We determine the homothetic conditions that scale-invariance of the metric imposes on the dilaton and electromagnetic fields, and we obtain their general solution. The inclusion of a potential for the dilaton is compatible with the homothetic conditions if and only if it is of the Liouville type. By imposing also spherical symmetry, a detailed analysis of critical collapse in these systems is possible by casting the field equations as an autonomous system. We find analytically that Choptuik's critical exponent depends on the dilaton coupling. Despite this and the presence of two novel fixed points, the electromagnetic field necessarily vanishes for the critical solution.

Quasinormal modes of weakly charged Einstein-Maxwell-dilaton black holes

Einstein-Maxwell-dilaton theory is an interesting and well-motivated theoretical laboratory to explore the impact of new fundamental degrees of freedom in the context of testing the no-hair conjecture, due to the existence of hairy black hole solutions together with the propagation of scalar, vector and tensor modes. In this paper we compute the quasinormal mode spectrum of static and slowly rotating black holes for generic values of the dilaton coupling, within a weak electric charge approximation. Our results suggest that these spacetimes are stable for generic values of the dilaton coupling and the black hole charge. We also show that while gravitational modes are only weakly affected by the coupling with the dilaton, the spectrum of electromagnetic modes exhibits a more pronounced dilaton-dependent breaking of isospectrality between the axial and polar sectors. We further show that the gravitational quasinormal modes are well approximated by the properties of unstable null circular geodesics in those spacetimes, while the treatment of electromagnetic and scalar modes can be simplified by a suitably modified Dudley-Finley scheme for the perturbed equations.

Schwinger effect in inflaton-driven electric field

In a four dimensional inflation theory, a persistent electric field can be established by making the inflaton coupled to the gauge field like a dilaton. We investigate the pair production of scalar particles in the inflaton-driven electric field. In particular, we evaluate the induced current due to the pair production. The presence of the dilatonic coupling ensures the validity of the WKB approximation at the past and the future infinities, without tuning constant parameters. Thus, the semiclassical description is applicable in evaluating the induced current. Solving the field equations with the induced current, we evaluate the first-order backreaction to the electric field. It turns out that the electric field decreases with the cosmic expansion. The result indicates that the no-anisotropic hair theorem for inflation holds true regardless of whether the dilatonic coupling is present or not.

Discreteness of Dyonic Dilaton Black Holes

We show that there are two classes of solutions that describe static spherically symmetric dyonic dilaton black holes with two nonsingular horizons. The first class includes only the already known solutions that exist for a few special values of the dilaton coupling constant. Solutions belonging to the second class have essentially different properties. They exist for continuously varying values of the dilaton coupling constant, but arise only for discrete values of the dilaton field at the horizon. For each given value of the dilaton coupling constant, there may exist several such solutions differing by the number of zeros of the shifted dilaton function in the subhorizon region and separating the domains of singular solutions.

Implications of Dilaton Couplings on the Axion Potential

In particle physics and cosmology, the dilaton is an hypothetical scalar field which can explain many physical phenomena. In this framework, we investigate an extended lagrangian of QCD which involves dilatonic degrees of freedom. Our approach is based on the relationship between the massive dilaton and the nonperturbative effects of QCD. We derive a general axion potential involving the dilaton properties and vacuum condensates.

Gravitational waves from gauge preheating

We study gravitational wave production during Abelian gauge-field preheating following inflation. We consider both scalar and pseudoscalar inflaton models coupled directly to Abelian gauge fields via either a dilatonic coupling to the gauge-field kinetic term or an axial coupling to a Chern-Simons term. In both cases gravitational waves are produced efficiently during the preheating phase, with a signature louder than most cosmological signals. These gravitational waves can contribute to the radiation energy budget of Universe at a level which will be probed by upcoming cosmic microwave background experiments through $N_{\rm eff}$. For axially coupled fields the resulting gravitational wave spectrum is helically polarized---a unique feature that can be used to differentiate it from other stochastic gravitational wave backgrounds. We compute the gravitational topological charge and demonstrate that gauge preheating following axion inflation may be responsible for the matter-antimatter asymmetry of the Universe via gravitational leptogenesis.

Dilatonic imprints on exact gravitational wave signatures

By employing the moduli space approximation, we analytically calculate the gravitational wave signatures emitted upon the merger of two extremally charged dilatonic black holes. We probe several values of the dilatonic coupling constant $a$, and find significant departures from the Einstein--Maxwell ($a=0$) counterpart studied in arXiv:1704.08520. For (low energy) string theory black holes $(a=1)$ there are no coalescence orbits and only a memory effect is observed, whereas for an intermediate value of the coupling $(a=1/\sqrt{3})$ the late-time merger signature becomes exponentially suppressed, compared to the polynomial decay in the $a=0$ case without a dilaton. Such an imprint is in principle observable and could reveal the presence of a scalar field (as for example predicted by string theory) in black hole mergers.

R4 terms in supergravities via T -duality constraint

It has been speculated in the literature that the effective actions of string theories at any order of $\alpha'$ should be invariant under the Buscher rules plus their higher covariant derivative corrections. This may be used as a constraint to find effective actions at any order of $\alpha'$, in particular, the metric, the B-field and the dilaton couplings in supergravities at order $\alpha'^3$ up to an overall factor. For the simple case of zero B-field and diagonal metric in which we have done the calculations explicitly, we have found that the constraint fixes almost all the seven independent Riemann curvature couplings. There is only one term which is not fixed, because when metric is diagonal, the reduction of two $R^4$ terms become identical. The Riemann curvature couplings that the T-duality constraint produces for both type II and Heterotic theories are fully consistent with the existing couplings in the literature which have been found by the S-matrix and by the sigma-model approaches.

Asymptotically (A)dS dilaton black holes with nonlinear electrodynamics

It is well known that with an appropriate combination of three Liouville-type dilaton potentials, one can construct charged dilaton black holes in an (anti)-de Sitter [(A)dS] spaces in the presence of linear Maxwell field. However, asymptotically (A)dS dilaton black holes coupled to nonlinear gauge field have not been found. In this paper, we construct, for the first time, three new classes of dilaton black hole solutions in the presence of three types of nonlinear electrodynamics, namely Born–Infeld (BI), Logarithmic (LN) and Exponential nonlinear (EN) electrodynamics. All these solutions are asymptotically (A)dS and in the linear regime reduce to the Einstein–Maxwell-dilaton (EMd) black holes in (A)dS spaces. We investigate physical properties and the causal structure, as well as asymptotic behavior of the obtained solutions, and show that depending on the values of the metric parameters, the singularity can be covered by various horizons. We also calculate conserved and thermodynamic quantities of the obtained solutions. Interestingly enough, we find that the coupling of dilaton field and nonlinear gauge field in the background of (A)dS spaces leads to a strange behavior for the electric field. We observe that the electric field is zero at singularity and increases smoothly until reaches a maximum value, then it decreases smoothly until goes to zero as [Formula: see text]. The maximum value of the electric field increases with increasing the nonlinear parameter [Formula: see text] or decreasing the dilaton coupling [Formula: see text] and is shifted to the singularity in the absence of either dilaton field ([Formula: see text]) or nonlinear gauge field ([Formula: see text]).

Iron line spectroscopy with Einstein–dilaton–Gauss–Bonnet black holes

Einstein–dilaton–Gauss–Bonnet gravity is a well-motivated alternative theory of gravity that emerges naturally from string theory. While black hole solutions have been known in this theory in numerical form for a while, an approximate analytical metric was obtained recently by some of us, which allows for faster and more detailed analysis. Here we test the accuracy of the analytical metric in the context of X-ray reflection spectroscopy. We analyze innermost stable circular orbits (ISCO) and relativistically broadened iron lines and find that both the ISCO and iron lines are determined sufficiently accurately up to the limit of the approximation. We also find that, though the ISCO increases by about 7% as dilaton coupling increases from zero to extremal values, the redshift at ISCO changes by less than 1%. Consequently, the shape of the iron line is much less sensitive to the dilaton charge than expected.

MICROSCOPE Mission: First Constraints on the Violation of the Weak Equivalence Principle by a Light Scalar Dilaton

The existence of a light or massive scalar field with a coupling to matter weaker than gravitational strength is a possible source of violation of the weak equivalence principle. We use the first results on the Eötvös parameter by the MICROSCOPE experiment to set new constraints on such scalar fields. For a massive scalar field of mass smaller than 10^{-12} eV (i.e., range larger than a few 10^{5} m), we improve existing constraints by one order of magnitude to |α|<10^{-11} if the scalar field couples to the baryon number and to |α|<10^{-12} if the scalar field couples to the difference between the baryon and the lepton numbers. We also consider a model describing the coupling of a generic dilaton to the standard matter fields with five parameters, for a light field: We find that, for masses smaller than 10^{-12} eV, the constraints on the dilaton coupling parameters are improved by one order of magnitude compared to previous equivalence principle tests.

The exceptional sigma model

We detail the construction of the exceptional sigma model, which describes a string propagating in the “extended spacetime” of exceptional field theory. This is to U-duality as the doubled sigma model is to T-duality. Symmetry specifies the Weylinvariant Lagrangian uniquely and we show how it reduces to the correct 10-dimensional string Lagrangians. We also consider the inclusion of a Fradkin-Tseytlin (or generalised dilaton) coupling as well as a reformulation with dynamical tension.