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Theoretical filters for shift-symmetric Horndeski gravities
Oct 10, 2025Athanasios Bakopoulos, Christos Charmousis, Nikos Chatzifotis, and Theodoros Nakas
We investigate the structure of nontrivial maximally symmetric vacua and compact-object solutions in shift-symmetric scalar-tensor theories. Focusing on Horndeski gravity, we derive consistency conditions directly from the field equations to identify the subclasses that admit Minkowski and de Sitter vacua with a nontrivial scalar field. In doing so, we obtain a filtering mechanism that operates independently of observational data. In this context, we introduce the notion of stealth vacua, where the scalar field remains active without altering the vacuum. Following this, we examine the theoretical framework of Horndeski theories that admit homogeneous geometries and we extract the implicit form of the solution pertaining to the entire family of theories. Building upon these frameworks, we construct exact solutions in beyond-Horndeski gravity by applying a linear disformal transformation to the regularized Einstein-Gauss-Bonnet black hole. This procedure yields solitonic spacetimes with scalar hair as well as black holes carrying primary scalar hair, demonstrating how disformal maps can qualitatively modify solution properties. We delineate the parameter space in which the transformation is well-defined and analyze the solutions. Our results provide both a principled criterion for selecting viable Horndeski models and a framework for exploring rich solution spaces in beyond-Horndeski gravity.arXiv-pdf DOI cite
Smarr formula for black holes with primary and secondary scalar hair
May 5, 2025Yun Soo Myung and Theodoros Nakas
In this work, we revisit the thermodynamics of black holes endowed with primary and secondary scalar hair in the shift and symmetric subclass of beyond Horndeski gravity. Under a specific fine-tuning of the scalar parameter in terms of the black hole mass, the singular black-hole solution with primary scalar hair reduces to the regular Bardeen solution featuring secondary scalar hair. We first demonstrate that the traditional thermodynamic approach fails to yield a consistent Smarr formula for both solutions under consideration. To address this issue, we adopt the approach introduced in [Phys Rev Lett. 132 (2024) 19, 191401], and we derive both the first law of black hole thermodynamics and the Smarr formula, offering a consistent thermodynamic description for scalar-hairy black holes. As an additional outcome, our analysis reveals a connection between the solutions with primary and secondary scalar hair.arXiv-pdf DOI cite
The CosmoVerse White Paper: Addressing observational tensions in cosmology with systematics and fundamental physics
April 2, 2025Eleonora Di Valentino, Jackson Levi Said et al.
The standard model of cosmology has provided a good phenomenological description of a wide range of observations both at astrophysical and cosmological scales for several decades. This concordance model is constructed by a universal cosmological constant and supported by a matter sector described by the standard model of particle physics and a cold dark matter contribution, as well as very early-time inflationary physics, and underpinned by gravitation through general relativity. There have always been open questions about the soundness of the foundations of the standard model. However, recent years have shown that there may also be questions from the observational sector with the emergence of differences between certain cosmological probes. In this White Paper, we identify the key objectives that need to be addressed over the coming decade together with the core science projects that aim to meet these challenges. These discordances primarily rest on the divergence in the measurement of core cosmological parameters with varying levels of statistical confidence. These possible statistical tensions may be partially accounted for by systematics in various measurements or cosmological probes but there is also a growing indication of potential new physics beyond the standard model. After reviewing the principal probes used in the measurement of cosmological parameters, as well as potential systematics, we discuss the most promising array of potential new physics that may be observable in upcoming surveys. We also discuss the growing set of novel data analysis approaches that go beyond traditional methods to test physical models. [Abridged]arXiv-pdf DOI cite
On the uplift of 4D wormholes in Braneworld models and their 5D structure
Dec 27, 2024Thomas D. Pappas and Theodoros Nakas
Recent developments in the consistent embedding of general 4D static and spherically-symmetric spacetimes in arbitrary single-brane braneworld models [Phys.Rev.D 109 (2024) 4, L041501] initiated the program of studying the bulk structure of braneworld wormholes. In this article, adopting a completely generic approach, we derive the general conditions that the metric functions of any braneworld spacetime must satisfy to describe a wormhole structure in the bulk. Particular emphasis is placed on clarifying the proper uplift of 4D wormholes, expressed in terms of various radial coordinates on the brane, and we demonstrate the important role of the circumferential radius metric function for the embedding. Additionally, the flare-out conditions for braneworld wormholes are presented for the first time and are found to differ from the case of flat extra dimensions. To illustrate the method, we first perform the uplift into the Randall-Sundrum II braneworld model for three well-known 4D wormhole spacetimes; the effective braneworld wormhole solutions of Casadio-Fabbri-Mazzacurati and Bronnikov-Kim, and the Simpson-Visser spacetime. Subsequently, we study their bulk features by means of curvature invariants, flare-out conditions, energy conditions and embedding diagrams. Our analysis reveals that the assumption of a warped extra dimension has non-trivial implications for the structure of 5D wormholes.arXiv-pdf DOI cite
Exact black holes in string-inspired Euler-Heisenberg theory
Feb 19, 2024Athanasios Bakopoulos, Thanasis Karakasis, Nick E. Mavromatos, Theodoros Nakas, and Eleftherios Papantonopoulos
We consider higher-order derivative gauge field corrections that arise in the fundamental context of dimensional reduction of String Theory and Lovelock-inspired gravities and obtain an exact and asymptotically flat black-hole solution, in the presence of non-trivial dilaton configurations. Specifically, by considering the gravitational theory of Euler-Heisenberg non-linear electrodynamics coupled to a dilaton field with specific coupling functions, we perform an extensive analysis of the characteristics of the black hole, including its geodesics for massive particles, the energy conditions, thermodynamical and stability analysis. The inclusion of a dilaton scalar potential in the action can also give rise to asymptotically (A)dS spacetimes and an effective cosmological constant. Moreover, we find that the black hole can be thermodynamically favored when compared to the Gibbons-Maeda-Garfinkle-Horowitz-Strominger (GMGHS) black hole for those parameters of the model that lead to a larger black-hole horizon for the same mass. Finally, it is observed that the energy conditions of the obtained black hole are indeed satisfied, further validating the robustness of the solution within the theoretical framework, but also implying that this self-gravitating dilaton-non-linear-electrodynamics system constitutes another explicit example of bypassing modern versions of the no-hair theorem without any violation of the energy conditions.arXiv-pdf DOI cite
Compact objects with primary hair in shift and parity symmetric beyond Horndeski gravities
Dec 28, 2023Athanasios Bakopoulos, Nikos Chatzifotis, and Theodoros Nakas
In this work, we delve into the model of the shift symmetric and parity-preserving Beyond Horndeski theory in all its generality. We present an explicit algorithm to extract static and spherically symmetric black holes with primary scalar charge adhering to the conservation of the Noether current emanating from the shift symmetry. We show that when the functionals \(G_2\) and \(G_4\) of the theory are linearly dependent, analytic homogeneous black-hole solutions exist, which can become regular by virtue of the primary charge contribution. Such geometries can easily enjoy the preservation of the Weak Energy Conditions, elevating them into healthier compact objects than most hairy black holes in modified theories of gravity. Finally, we revisit the concept of disformal transformations as a solution-generating mechanism and discuss the case of generic \(G_2\) and \(G_4\) functionals.arXiv-pdf DOI cite
Black holes with primary scalar hair
Oct 18, 2023Athanasios Bakopoulos, Christos Charmousis, Panagiota Kanti, Nicolas Lecoeur, and Theodoros Nakas
We present explicit black holes endowed with primary scalar hair within the shift-symmetric subclass of Beyond Horndeski theories. These solutions depend, in addition to the conventional mass parameter, on a second free parameter encoding primary scalar hair. The properties and characteristics of the solutions at hand are analyzed with varying scalar charge. We observe that when the scalar hair parameter is close to zero or relatively small in comparison to the black hole mass, the solutions closely resemble the Schwarzschild spacetime. As the scalar hair increases, the metric solutions gradually depart from General Relativity. Notably, for a particular relation between mass and scalar hair, the central singularity completely disappears, resulting in the formation of regular black holes or solitons. The scalar field accompanying the solutions is always found to be regular at future or past horizon(s), defining a distinct time direction for each. As a final byproduct of our analysis, we demonstrate the existence of a stealth Schwarschild black hole in Horndeski theory with a non-trivial kinetic term.arXiv-pdf DOI cite
Bridging dimensions: General embedding algorithm and field-theory reconstruction in 5D braneworld models
Sep 2, 2023Theodoros Nakas, Thomas D. Pappas, and Zdeněk Stuchlík
We develop a general algorithm that enables the consistent embedding of any four-dimensional static and spherically symmetric geometry into any five-dimensional single-brane braneworld model, characterized by an injective and nonsingular warp factor. Furthermore, we supplement the algorithm by introducing a method that allows one to, in principle, reconstruct 5D field theories that support the aforementioned geometries. This approach is based on a conformal transformation of the metric with the conformal factor being identified with the warp factor of the bulk geometry. The reconstructed theories depend solely on the induced brane geometry, since the warp factor is model-independently represented by a scalar field in the Lagrangian density. As a first application of our reconstruction method, we present for the first time a complete theory that supports the five-dimensional brane-localized extension of the Schwarzschild black hole, for any warp factor. The same method is subsequently utilized to illustrate the process of coherently embedding a de Sitter brane in braneworld models.arXiv-pdf DOI cite
Novel exact ultra-compact and ultra-sparse hairy black holes emanating from regular and phantom scalar fields
Mar 16, 2023Athanasios Bakopoulos and Theodoros Nakas
In the framework of a simple gravitational theory that contains a scalar field minimally coupled to gravity, we investigate the emergence of analytic black-hole solutions with non-trivial scalar hair of secondary type. Although it is possible for one to obtain asymptotically (A)dS solutions using our setup, in the context of the present work, we are solely interested in asymptotically flat solutions. At first, we study the properties of static and spherically symmetric black-hole solutions emanating from both regular and phantom scalar fields. We find that the regular-scalar-field-induced solutions are solutions describing ultra-compact black holes, while the phantom scalar fields generate ultra-sparse black-hole solutions. The latter are black holes that can be potentially of very low density since, contrary to ultra-compact ones, their horizon radius is always greater than the horizon radius of the corresponding Schwarzschild black hole of the same mass. Then, we generalize the above static solutions to slowly rotating ones and compute their angular velocities explicitly. Finally, the study of the axial perturbations of the derived solutions takes place, in which we show that there is always a region in the parameter space of the free parameters of our theory that allows the existence of both ultra-compact and ultra-sparse black holes.arXiv-pdf DOI cite
Analytic and asymptotically flat hairy (ultra-compact) black-hole solutions and their axial perturbations
Jul 12, 2021Athanasios Bakopoulos and Theodoros Nakas
In this work, we consider a very simple gravitational theory that contains a scalar field with its kinetic and potential terms minimally coupled to gravity, while the scalar field is assumed to have a coulombic form. In the context of this theory, we study an analytic, asymptotically flat, and regular (ultra-compact) black-hole solutions with non-trivial scalar hair of secondary type. At first, we examine the properties of the static and spherically symmetric black-hole solution -- firstly appeared in 1504.08209 [gr-qc] -- and we find that in the causal region of the spacetime the stress-energy tensor, needed to support our solution, satisfies the strong energy conditions. Then, by using the slow-rotating approximation, we generalize the static solution into a slowly rotating one, and we determine explicitly its angular velocity \(\omega(r)\). We also find that the angular velocity of our ultra-compact solution is always larger compared to the angular velocity of the corresponding equally massive slow-rotating Schwarzschild black hole. In addition, we investigate the axial perturbations of the derived solutions by determining the Schrödinger-like equation and the effective potential. We show that there is a region in the parameter space of the free parameters of our theory, which allows for the existence of stable ultra-compact black hole solutions. Specifically, we calculate that the most compact and stable black hole solution is \(0.551\) times smaller than the Schwarzschild one, while it rotates \(2.491\) times faster compared to the slow-rotating Schwarzschild black hole. Finally, we present without going into details the generalization of the derived asymptotically flat solutions to asymptotically (A)dS solutions.arXiv-pdf DOI cite
Analytic and exponentially localized brane-world Reissner-Nordström-AdS solution: a top-down approach
May 14, 2021Theodoros Nakas and Panagiota Kanti
In this work, we construct a five-dimensional spherically-symmetric, charged and asymptotically Anti-de Sitter black hole with its singularity being point-like and strictly localised on our brane. In addition, the induced brane geometry is described by a Reissner-Nordström-(A)dS line-element. We perform a careful classification of the horizons, and demonstrate that all of them are exponentially localised close to the brane thus exhibiting a pancake shape. The bulk gravitational background is everywhere regular, and reduces to an AdS5 spacetime right outside the black-hole event horizon. This geometry is supported by an anisotropic fluid with only two independent components, the energy density \(\rho_E\) and tangential pressure \(p_2\). All energy conditions are respected close to and on our brane, but a local violation takes place within the event horizon regime in the bulk. A tensor-vector-scalar field-theory model is built in an attempt to realise the necessary bulk matter, however, in order to do so, both gauge and scalar degrees of freedom need to turn phantom-like at the bulk boundary. The study of the junction conditions reveals that no additional matter needs to be introduced on the brane for its consistent embedding in the bulk geometry apart from its constant, positive tension. We finally compute the effective gravitational equations on the brane, and demonstrate that the Reissner-Nordström-(A)dS geometry on our brane is caused by the combined effect of the five-dimensional geometry and bulk matter with its charge being in fact a tidal charge.arXiv-pdf DOI cite
Localized brane-world black hole analytically connected to an AdS\(_5\) boundary
Dec 16, 2020Theodoros Nakas and Panagiota Kanti
We construct from first principles the geometry of an analytic, exponentially localized five-dimensional brane-world black hole. The black-hole singularity lies entirely on the 3-brane, while the event horizon is shown to have a pancake shape. The induced line-element on the brane assumes the form of the Schwarzschild solution while the bulk geometry is effectively AdS\(_5\) outside the horizon. The derived geometry is supported by an anisotropic fluid in the bulk described only by two independent components, the energy density and tangential pressure, whereas no matter needs to be introduced on the brane for its consistent embedding in the bulk.arXiv-pdf DOI cite
Fermions and baryons as open-string states from brane junctions
Sep 30, 2020Theodoros Nakas and Konstantinos Rigatos
There has been recent progress towards understanding the dynamics of world-volume fermions that arise as open-string modes from brane intersections in the probe limit (\(N_f/N_c\rightarrow 0\)). In this work we consider all possible BPS brane junctions in Type IIA/B supergravity theories. We study in detail the dynamics of these states by deriving their equations of motion. We show the expected degeneracy of the bosonic and fermionic fluctuations as is expected due to the preserved supersymmetry. We also give some supporting evidence and refine the notion that these states can effectively describe baryon operators in a certain regime of the field theory's parameter space. Our piece of evidence is the demonstration of the expected scaling of the mass in the large-\(N_c\) limit of the theory for these fermionic states; \(M^2\sim N^2_c\). Finally, we explain analytically the avoided level crossing that was observed in a previous work after the inclusion of higher dimension operators in the field theory.arXiv-pdf DOI cite
Incorporating Physical Constraints in Braneworld Black-String Solutions for a Minkowski Brane in Scalar-Tensor Gravity
Jan 20, 2020Theodoros Nakas, Panagiota Kanti, and Nikolaos Pappas
In the framework of a general scalar-tensor theory, where the scalar field is non-minimally coupled to the five-dimensional Ricci scalar curvature, we investigate the emergence of complete brane-world solutions. By assuming a variety of forms for the coupling function, we solve the field equations in the bulk, and determine in an analytic way the form of the gravitational background and scalar field in each case. The solutions are always characterized by a regular scalar field, a finite energy-momentum tensor, and an exponentially decaying warp factor even in the absence of a negative bulk cosmological constant. The space-time on the brane is described by the Schwarzschild solution leading to either a non-homogeneous black-string solution in the bulk, when the mass parameter \(M\) is non-zero, or a regular anti-de Sitter space-time, when \(M=0\). We construct physically-acceptable solutions by demanding in addition a positive effective gravitational constant on our brane, a positive total energy-density for our brane and the validity of the weak energy condition in the bulk. We find that, although the theory does not allow for all three conditions to be simultaneously satisfied, a plethora of solutions emerge which satisfy the first two, and most fundamental, conditions.arXiv-pdf DOI cite
New Black-String Solutions for an Anti-de Sitter Brane in Scalar-Tensor Gravity
Mar 30, 2019Theodoros Nakas, Nikolaos Pappas, and Panagiota Kanti
We consider a five-dimensional theory with a scalar field non-minimally-coupled to gravity, and we look for novel black-string solutions in the bulk. By appropriately choosing the non-minimal coupling function of the scalar field, we analytically solve the gravitational and scalar-field equations in the bulk to produce black-string solutions that describe a Schwarzschild-Anti-de Sitter space-time on the brane. We produce two complete such solutions that are both characterised by a regular scalar field, a localised-close-to-our brane energy-momentum tensor and a negative-definite, non-trivial bulk potential that may support by itself the warping of the space-time even in the absence of the traditional, negative, bulk cosmological constant. Despite the infinitely-long string singularity in the bulk, the four-dimensional effective theory on the brane is robust with the effective gravity scale being related to the fundamental one and the warping scale. It is worth noting that if we set the mass of the black hole on the brane equal to zero, the black string disappears leaving behind a regular brane-world model with only a true singularity at the boundary of the fifth dimension.arXiv-pdf DOI cite
Anti-Gravitating Brane-World Solutions for a de Sitter Brane in Scalar-Tensor Gravity
Jul 18, 2018Theodoros Nakas and Panagiota Kanti
In the context of a five-dimensional theory with a scalar field non-minimally-coupled to gravity, we look for solutions that describe novel black-string or maximally-symmetric solutions in the bulk. The brane line-element is found to describe a Schwarzschild-(Anti)-de Sitter spacetime, and, here, we choose to study solutions with a positive four-dimensional cosmological constant. We consider two different forms of the coupling function of the scalar field to the bulk scalar curvature, a linear and a quadratic one. In the linear case, we find solutions where the theory, close to our brane, mimics an ordinary gravitational theory with a minimally-coupled scalar field giving rise to an exponentially decreasing warp factor in the absence of a negative bulk cosmological constant. The solution is characterised by the presence of a normal gravity regime around our brane and an anti-gravitating regime away from it. In the quadratic case, there is no normal-gravity regime at all, however, scalar field and energy-momentum tensor components are well-defined and an exponentially decreasing warp factor emerges again. We demonstrate that, in the context of this theory, the emergence of a positive cosmological constant on our brane is always accompanied by an anti-gravitating regime in the five-dimensional bulk.arXiv-pdf DOI cite
Conference Papers
Normal and Phantom Black Holes in Scalar-Tensor Theories
June 06, 2025Athanasios Bakopoulos and Theodoros Nakas
In this work, we explore spherically symmetric black-hole solutions in a specific subclass of the Horndeski theories. By adopting a potential engineering approach, we derive exact analytic black-hole solutions endowed with scalar hair. We analyze the properties of these novel solutions and discover a spectrum that encompasses normal, ultra-compact, and ultra-sparse black holes. Each type of black hole emerges from a distinct range of scalar charge values. Rotating versions of these black holes are also obtained through a perturbation method, and their relative angular velocities are calculated. These rotation signatures may offer potential observational probes to test gravity. Our solutions showcase the richness of black hole geometries permitted in scalar-tensor theories beyond General Relativity. Further efforts to establish stability and astrophysical viability will be important in future directions.DOI cite