Four-dimensional Solutions Research Articles

How a four-dimensional de Sitter solution remains outside the swampland

We argue that, in the presence of time-dependent fluxes and quantum corrections, four-dimensional de Sitter solutions should appear in the type IIB string landscape and not in the swampland. Our construction considers generic choices of local and non-local quantum terms and satisfies the no-go and the swampland criteria, the latter being recently upgraded using the trans-Planckian cosmic censorship. Interestingly, both time-independent Newton constant and moduli stabilization may be achieved in such backgrounds even in the presence of time-dependent fluxes and internal spaces. However, once the time-dependence is switched off, any four-dimensional solution with de Sitter isometries appears to have no simple effective field theory descriptions and is back in the swampland.

Black holes in 4D Einstein\u2013Maxwell\u2013Gauss\u2013Bonnet gravity coupled with scalar fields

Einstein–Maxwell–Gauss–Bonnet-axion theory in 4-dimensional spacetime is investigated in this paper through a “Kaluza–Klein-like” process. Dual to systems at finite temperature with background magnetic field on three dimensions, the four-dimensional dyonic black hole solution coupled with higher derivative terms is obtained. After the tensor-type perturbation is added, the shear viscosity to entropy density ratio is calculated at high temperature and low temperature separately. The behaviour of shear viscosity to entropy density ratio of uncharged black holes is found to be similar with that in 5-dimensional spacetime, violating the Kovtun–Starinets–Son bound as well when temperature becomes lower. In addition, the main feature of this ratio remains almost unchanged in 4 dimensions, which is characterised by (T/varDelta )^2 at low temperature T, with varDelta proportional to the coefficient beta from scalar fields. The difficulty in causal analysis is also discussed, which is mainly caused by the vanishing momentum term in equations of motion.

Quantum BTZ black hole

We study a holographic construction of quantum rotating BTZ black holes that incorporates the exact backreaction from strongly coupled quantum conformal fields. It is based on an exact four-dimensional solution for a black hole localized on a brane in AdS4, first discussed some years ago but never fully investigated in this manner. Besides quantum CFT effects and their backreaction, we also investigate the role of higher-curvature corrections in the effective three-dimensional theory. We obtain the quantum-corrected geometry and the renormalized stress tensor. We show that the quantum black hole entropy, which includes the entanglement of the fields outside the horizon, satisfies the first law of thermodynamics exactly, even in the presence of backreaction and with higher-curvature corrections, while the Bekenstein-Hawking-Wald entropy does not. This result, which involves a rather non-trivial bulk calculation, shows the consistency of the holographic interpretation of braneworlds. We compare our renormalized stress tensor to results derived for free conformal fields, and for a previous holographic construction without backreaction effects, which is shown to be a limit of the solutions in this article.

Towards an explicit construction of de Sitter solutions in classical supergravity

We revisit the stringy construction of four-dimensional de-Sitter solutions using orientifolds O8±, proposed by Córdova et al. (2019) [1]. While the original analysis of the supergravity equations is largely numerical, we obtain semi-analytic solutions by treating the curvature as a perturbative parameter. At each order we verify that the (permissive) boundary conditions at the orientifolds are satisfied. To illustrate the advantage of our result, we calculate the four-dimensional Newton constant as a function of the cosmological constant. We also discuss how the discontinuities at O8− can be accounted for in terms of corrections to the worldvolume action.

Topological Born\u2013Infeld charged black holes in Einsteinian cubic gravity

In this paper, we study four-dimensional topological black hole solutions of Einsteinian cubic gravity in the presence of nonlinear Born–Infeld electrodynamics and a bare cosmological constant. First, we obtain the field equations which govern our solutions. Employing Abbott–Deser–Tekin and Gauss formulas, we present the expressions of conserved quantities, namely total mass and total charge of our topological black solutions. We disclose the conditions under which the model is unitary and perturbatively free of ghosts with asymptotically (A)dS and flat solutions. We find that, for vanishing bare cosmological constant, the model is unitary just for asymptotically flat solutions, which only allow horizons with spherical topology. We compute the temperature for these solutions and show that it always has a maximum value, which decreases as the values of charge, nonlinear coupling or cubic coupling grows. Next, we calculate the entropy and electric potential. We show that the first law of thermodynamics is satisfied for spherical asymptotically flat solutions. Finally, we peruse the effects of model parameters on thermal stability of these solutions in both canonical and grand canonical ensembles.

Localization of Energy and Momentum in an Asymptotically Reissner-Nordström Non-Singular Black Hole Space-Time Geometry

The space-time geometry exterior to a new four-dimensional, spherically symmetric and charged black hole solution that, through a coupling of general relativity with a non-linear electrodynamics, is non-singular everywhere, for small r it behaves as a de Sitter metric, and asymptotically it behaves as the Reissner-Nordström metric, is considered in order to study energy-momentum localization. For the calculation of the energy and momentum distributions, the Einstein, Landau-Lifshitz, Weinberg and Møller energy-momentum complexes were applied. The results obtained show that in all prescriptions the energy depends on the mass M of the black hole, the charge q, two parameters a ∈ Z + and γ ∈ R + , and on the radial coordinate r. The calculations performed in each prescription show that all the momenta vanish. Additionally, some limiting and particular cases for r and q are studied, and a possible connection with strong gravitational lensing and microlensing is attempted.

Extended thermodynamics and microstructures of four-dimensional charged Gauss-Bonnet black hole in AdS space

The discovery of new four-dimensional black hole solutions presents a new approach to understand the Gauss-Bonnet gravity in low dimensions. In this paper, we test the Gauss-Bonnet gravity by studying the phase transition and microstructures for the four-dimensional charged AdS black hole. In the extended phase space, where the cosmological constant and the Gauss-Bonnet coupling parameter are treated as thermodynamic variables, we find that the thermodynamic first law and the corresponding Smarr formula are satisfied. Both in the canonical ensemble and grand canonical ensemble, we observe the small-large black hole phase transition, which is similar to the case of the van der Walls fluid. This phase transition can also appear in the neutral black hole system. Furthermore, we construct the Ruppeiner geometry, and find that besides the attractive interaction, the repulsive interaction can also dominate among the microstructures for the small black hole with high temperature in a charged or neutral black hole system. This is quite different from the five-dimensional neutral black hole, for which only dominant attractive interaction can be found. The critical behaviors of the normalized scalar curvature are also examined. These results will shed new light into the characteristic property of four-dimensional Gauss-Bonnet gravity.

Optimal design of hybrid DG systems for microgrid reliability enhancement

While the concept of microgrids and renewable energy systems is not entirely new, these integrated technologies have become a special topic of interest for researchers, utility providers and governments. Many challenges must be overcome to achieve better integration of renewable sources into the energy framework. This study presents some viable possibilities for the utilisation of a hybridised microgrid system. The hybridisation is achieved by an efficient design approach for the enhancement of both load and system reliability indices through the intelligent placement and sizing of hybrid distributed generation (DG) systems. Real-time models of solar photovoltaics, wind turbines, batteries and thermal DGs are presented and implemented. Also, network component failures are stochastically modelled via Monte Carlo simulations, and a general tie-set algorithm using an adapted breadth-first search is proposed. Moreover, mixed-integer multi-objective particle swarm optimisation is employed, giving a four-dimensional Pareto solution that is attained by optimising four reliability-related objectives, namely system average interruption frequency index, System Average Interruption Duration Index (SAIDI), Energy Not Supplied (ENS) and total cost.

Kerr-Newman from minimal coupling

We show that at 1PN all four-dimensional black hole solutions in asymptotically flat spacetimes can be derived from leading singularities involving minimally coupled three-particle amplitudes. Furthermore, we show that the rotating solutions can be derived from their non-rotating counterparts by a spin-factor deformation of the relevant minimally coupled amplitudes. To show this, we compute the tree-level and one-loop leading singularities for a heavy charged source with generic spin s. We compute the metrics both with and without a spin factor and show that we get both the Kerr-Newman and Reissner- Nordström solutions respectively. We then go on to compute the impulse imparted to the probe particle in the infinite spin limit and show that the spin factor induces a complex deformation of the impact parameter, as was recently observed for Kerr black holes in [1]. We interpret these observations as being the on-shell avatar of the Janis-Newman algorithm for charged black holes.

Editorial note to: On the Newtonian limit of Einstein’s theory of gravitation (by Jürgen Ehlers)

We give an overview of literature related to J\"urgen Ehlers' pioneering 1981 paper on Frame theory--a theoretical framework for the unification of General Relativity and the equations of classical Newtonian gravitation. This unification encompasses the convergence of one-parametric families of four-dimensional solutions of Einstein's equations of General Relativity to a solution of equations of a Newtonian theory if the inverse of a causality constant goes to zero. As such the corresponding light cones open up and become space-like hypersurfaces of constant absolute time on which Newtonian solutions are found as a limit of the Einsteinian ones. It is explained what it means to not consider the `standard-textbook' Newtonian theory of gravitation as a complete theory unlike Einstein's theory of gravitation. In fact, Ehlers' Frame theory brings to light a modern viewpoint in which the `standard' equations of a self-gravitating Newtonian fluid are Maxwell-type equations. The consequences of Frame theory are presented for Newtonian cosmological dust matter expressed via the spatially projected electric part of the Weyl tensor, and for the formulation of characteristic quasi-Newtonian initial data on the light cone of a Bondi-Sachs metric.

Traversable asymptotically flat wormholes with short transit times

We construct traverseable wormholes by starting with simple four-dimensional classical solutions respecting the null energy condition and containing a pair of oppositely charged black holes connected by a non-traverseable wormhole. We then consider the perturbative back-reaction of bulk quantum fields in Hartle–Hawking states. Our geometries have zero cosmological constant and are asymptotically flat except for a cosmic string stretching to infinity that is used to hold the black holes apart. Another cosmic string wraps the non-contractible cycle through the wormhole, and its quantum fluctuations provide the negative energy needed for traversability. Our setting is closely related to the non-perturbative construction of Maldacena, Milekhin, and Popov (MMP), but the analysis is complementary. In particular, we consider cases where back-reaction slows, but fails to halt, the collapse of the wormhole interior, so that the wormhole is traverseable only at sufficiently early times. For non-extremal backgrounds, we find the integrated null energy along the horizon of the classical background to be exponentially small, and thus traversability to be exponentially fragile. Nevertheless, if there are no larger perturbations, and for appropriately timed signals, a wormhole with mouths separated by a distance d becomes traverseable with a minimum transit time . Thus is smaller than for the eternally traverseable MMP wormholes by more than a factor of 2, and approaches the value that, at least in higher dimensions, would be the theoretical minimum. For contrast we also briefly consider a ‘cosmological wormhole’ solution where the back-reaction has the opposite sign, so that negative energy from quantum fields makes the wormhole harder to traverse.

Scale-dependent planar anti-de Sitter black hole

In this work, we investigate four-dimensional planar black-hole solutions in anti-de Sitter spacetimes in light of the so-called scale-dependent scenario. To obtain this new family of solutions, the classical couplings of the theory, i.e., the gravitational coupling G0 and the cosmological constant $ \Lambda_{0}$, are not taken to be fixed values anymore. Thus, those classical parameters evolve to functions which change along the “height” coordinate, z . The effective Einstein field equations are solved, and the results are analyzed and compared with the classical counterpart. Finally, some thermodynamic properties of the presented scale-dependent black hole are investigated.

On stationary solutions to the non-vacuum Einstein field equations

We derive a local curvature estimate for four-dimensional stationary solutions to the Einstein equations coupled with electro-magnetic fields or scalar fields. In particular, it implies that any such stationary geodesically complete solution with vanishing Poynting vector and proper coupling constants is flat. We also generalize the results in static case to higher dimensions.

Quantum corrections and the de Sitter swampland conjecture

Recently a swampland criterion has been proposed that rules out de Sitter vacua in string theory. Such a criterion should hold at all points in the field space and especially at points where the system is on-shell. However there has not been any attempt to examine the swampland criterion against explicit equations of motion. In this paper we study four-dimensional de Sitter and quasi-de Sitter solutions using dimensionally reduced M-theory that includes quantum corrections. These quantum corrections are found to allow for de Sitter solutions provided certain constraints are satisfied. A careful study however shows that generically such a constrained system does not allow for an effective field theory description in four-dimensions. Nevertheless, if some hierarchies between the various quantum pieces could be found, certain solutions with an effective field theory description might exist. Such hierarchies appear once some mild time dependence is switched on, in which case certain quasi-de Sitter solutions may be found without a violation of the swampland criterion.

Sine-Gordon solitonic scalar stars and black holes

We study exact, analytic, static, spherically symmetric, four-dimensional solutions of minimally coupled Einstein-scalar gravity, sourced by a scalar field whose profile has the form of the sine-Gordon soliton. We present a horizonless, everywhere regular and positive-mass solution (a solitonic star) and a black hole. The scalar potential behaves as a constant near the origin and vanishes at infinity. In particular, the solitonic scalar star interpolates between an anti-de Sitter and an asympototically flat spacetime. The black-hole spacetime is unstable against linear perturbations, while due to numerical issues, we were not able to determine with confidence whether or not the star-like background solution is stable.

Propiedades psicométricas del Centro de Estudios Epidemiológicos, Escala de depresión para adolescentes en Bulgaria

En el presente estudio se evaluaron las propiedades psicométricas de la versión búlgara de la “Centre for Epidemiological Studies Depression Scale” (CES-DC), una escala auto-informada de 20 ítems diseñada para medir síntomas depresivos en niños y adolescentes. Un total de 700 adolescentes (323 niñas y 377 niños), de 13 a 17 años, participaron en el estudio. Además de la escala CES-DC, los adolescentes también contestaron el “Strength and Difficulties Questionnaire” (SDQ) y el “Spence Child Anxiety Scale” (SCAS). Los resultados del análisis factorial confirmatorio mostraron índices de ajuste adecuados, demostrando la validez de las cuatro dimensiones de la escala original. La CES-DC correlacionó de manera significativa con las puntuaciones totales de la SDQ y sus subescalas, mostrando que niveles elevados de síntomas depresivos se asocian con niveles altos de problemas emocionales y conductuales. En general, los resultados evidencian la validez factorial y fiabilidad de la versión búlgara de la escala CES-DC en muestras adolescentes de Bulgaria.

De Sitter space from dilatino condensates in massive IIA supergravity

We use the superspace formulation of (massive) IIA supergravity to obtain the explicit form of the dilatino terms, and we find that the quartic-dilatino term is positive. The theory admits a ten-dimensional de Sitter solution, obtained by assuming a nonvanishing quartic-dilatino condensate which generates a positive cosmological constant. Moreover, in the presence of dilatino condensates, the theory admits formal four-dimensional de Sitter solutions of the form $d{S}_{4}\ifmmode\times\else\texttimes\fi{}{M}_{6}$, where ${M}_{6}$ is a six-dimensional K\"ahler-Einstein manifold of positive scalar curvature.

Axionic black branes in the k -essence sector of the Horndeski model

We construct new black brane solutions in the context of Horndeski gravity, in particular in its K-essence sector. These models are supported by axion scalar fields that depend only on the horizon coordinates. The dynamics of these fields is determined by a K-essence term that includes the standard kinetic term $X$ and a correction of the form $X^{k}$. We find both neutral and charged exact and analytic solutions in $D$-dimensions, which are asymptotically anti de Sitter. Then, we describe in detail the thermodynamical properties of the four-dimensional solutions and we compute the dual holographic DC conductivity.

Bounded orbits for photons as a consequence of extra dimensions

In this paper, we study the geodesic structure for a geometry described by a spherically symmetric four-dimensional (4D) solution embedded in a five-dimensional (5D) space known as a brane-based spherically symmetric solution. Mainly, we have found that the extra dimension contributes to the existence of bounded orbits for the photons, such as planetary and circular stable orbits that have not been observed for other geometries.

Thermal stability analysis of nonlinearly charged asymptotic AdS black hole solutions

In this paper, the four-dimensional nonlinearly charged black hole solutions have been considered in the presence of the power Maxwell invariant electrodynamics. Two new classes of anti--de Sitter (AdS) black hole solutions have been introduced according to different amounts of the parameters in the nonlinear theory of electrodynamics. The conserved and thermodynamical quantities of either of the black hole classes have been calculated from geometrical and thermodynamical approaches, separately. It has been shown that the first law of black hole thermodynamics is satisfied for either of the AdS black hole solutions we just obtained. Through the canonical and grand canonical ensemble methods, the black hole thermal stability or phase transitions have been analyzed by considering the heat capacities with the fixed black hole charge and fixed electric potential, respectively. It has been found that the new AdS black holes are stable if some simple conditions are satisfied.