We derive exact, asymptotically flat black hole solutions of Einstein-scalar gravity sourced by a non trivial scalar field with $1/r$ asymptotic behaviour. They are determined using an ansatz for the scalar field profile and working out, together with the metric functions, the corresponding form of the scalar self-interaction potential. Near to the singularity the black hole behaves as the Janis-Newmann-Winicour-Wyman solution. We also work out a consistent thermodynamical description of our black hole solutions. For large mass our hairy black holes have the same thermodynamical behaviour of the Schwarzschild black hole, whereas for small masses they differ substantially from the latter.
We construct asymptotically flat black hole solutions of Einstein-scalar gravity sourced by a nontrivial scalar field with 1/r asymptotic behaviour. Near the singularity the black hole behaves as the Janis-Newmann-Winicour-Wyman solution. The hairy black hole solutions allow for a consistent thermodynamical description. At large mass they have the same thermodynamical behaviour of the Schwarzschild black hole, whereas for small masses they differ substantially from the latter.
In a recent paper, Hod started a study on no scalar hair theorem for asymptotically flat spherically symmetric neutral horizonless reflecting compact stars. In fact, Hod's approach only rules out massive scalar fields. In the present paper, for massless scalar fields outside neutral horizonless reflecting compact stars, we provide a rigorous mathematical proof on no hair theorem. We show that asymptotically flat spherically symmetric neutral horizonless reflecting compact stars cannot support exterior massless scalar field hairs.
We show that a $3d$ sourced conformal Carrollian field theory has the right kinematic properties to holographically describe gravity in $4d$ asymptotically flat spacetime. The external sources encode the leaks of gravitational radiation at null infinity. The Ward identities of this theory are shown to reproduce those of the $2d$ celestial CFT after relating Carrollian to celestial operators. This suggests a new set of interplays between gravity in asymptotically flat spacetime, sourced conformal Carrollian field theory and celestial CFT.
We find a new exact vacuum solution in the framework of the Poincaré Gauge field theory with massive torsion. In this model, torsion operates as an independent field and introduces corrections to the vacuum structure present in General Relativity. The new static and spherically symmetric configuration shows a Reissner-Nordström-like geometry characterized by a spin charge. It extends the known massless torsion solution to the massive case. The corresponding Reissner-Nordström-de Sitter solution is also compatible with a cosmological constant and additional U(1) gauge fields.
We study the propagation of a massless scalar wave in de Sitter spacetime perturbed by an arbitrary central mass. By focusing on the late time limit, this probes the portion of the scalar signal traveling inside the null cone. Unlike in asymptotically flat spacetimes, the amplitude of the scalar field detected by an observer at timelike infinity does not decay back to zero but develops a spacetime constant shift - both at zeroth and first order in the central mass M. This indicates that massless scalar field propagation in asymptotically de Sitter spacetimes exhibits both linear and nonlinear …
In this paper we derive a generic expression, which is valid for scales larger than Hubble radius and contains only the local terms, for the second order curvature perturbations for more than one field, provided the expansion is sourced by the energy density of a single field. As an application, motivated by our previous paper [1], we apply our formalism to two fields during preheating, where the inflaton oscillations are sourced by $λϕ^4$ potential which is governing the expansion of the Universe. A second field $σ$, coupled to the inflaton through $g^2ϕ^2σ^2$, is excited from the vacuum fluc…
We present a simple and complete classification of static solutions in the Einstein-Maxwell system with a massless scalar field in arbitrary $n(\ge 3)$ dimensions. We consider spacetimes which correspond to a warped product $M^2 \times K^{n-2}$, where $K^{n-2}$ is a $(n-2)$-dimensional Einstein space. The scalar field is assumed to depend only on the radial coordinate and the electromagnetic field is purely electric. Suitable Ansätze enable us to integrate the field equations in a general form and express the solutions in terms of elementary functions. The classification with a non-constant re…
We consider here the existence and structure of trapped surfaces, horizons and singularities in spherically symmetric static massless scalar field spacetimes. Earlier studies have shown that there exists no event horizon in such spacetimes if the scalar field is asymptotically flat. We extend this result here to show that this is true in general for spherically symmetric static massless scalar field spacetimes, whether the scalar field is asymptotically flat or not. Other general properties and certain important features of these models are also discussed.
We present a new hybrid Cauchy-characteristic evolution method that is particularly suited for the study of gravitational collapse in spherically-symmetric asymptotically (global) Anti-de Sitter (AdS) spacetimes. The Cauchy evolution allows us to track the scalar field through the different bounces off the AdS boundary while the characteristic method can bring us very close to the point of formation of an apparent horizon. Here, we describe all the details of the method, including the transition between the two evolution schemes and the details of the numerical implementation for the case of m…
Emmy, a child prodigy, writes a letter to Santa Claus asking for a Vaidya solution sourced by a massless scalar field with null gradient for Christmas. Santa writes back explaining why such a toy cannot be built and offers an exact plane wave sourced by a scalar field with lightlike gradient as a replacement.
In this paper we obtain exact asymptotically anti-de Sitter black hole solutions and asymptotically Lifshitz black hole solutions with dynamical exponents $z=0$ and $z=4$ of four-dimensional conformal gravity coupled with a self-interacting conformally invariant scalar field. Then, we compute their thermodynamical quantities, such as the mass, the Wald entropy and the Hawking temperature. The mass expression is obtained by using the generalized off-shell Noether potential formulation. It is found that the anti-de Sitter black holes as well as the Lifshitz black holes with $z=0$ have zero mass …
There exist well-known no-hair theorems forbidding the existence of hairy black hole solutions in general relativity coupled to a scalar conformal field theory in asymptotically flat space. Even in the presence of cosmological constant, where no-hair theorems can usually be circumvented and black holes with conformal scalar hair were shown to exist in dimensions three and four, no-go results were reported for D>4. In this paper we prove that these obstructions can be evaded and we answer in the affirmative a question that remained open: Whether hairy black holes do exist in general relativity …
In this talk we review recent calculations of the asymptotic supergravity fields sourced by bound states of D1 and D5-branes carrying travelling waves. We compute disk one-point functions for the massless closed string fields. At large distances from the branes, the effective open string coupling is small, even in the regime of parameters where the classical D1-D5-P black hole may be considered. The fields sourced by the branes differ from the black hole solution by various multipole moments, and have led to the construction of a new 1/8-BPS ansatz in type IIB supergravity.
We present a "holographic" reconstruction of bulk spacetime geometry using correlation functions of a massless field living at the "future boundary" of the spacetime, namely future null infinity $\mathscr{I}^+$. It is holographic in the sense that there exists a one-to-one correspondence between correlation functions of a massless field in four-dimensional spacetime $\mathcal{M}$ and those of another massless field living in three-dimensional null boundary $\mathscr{I}^+$. The idea is to first reconstruct the bulk metric $g_{μν}$ by "inverting" the bulk correlation functions and re-express the…
We discuss whether the minimally coupled massless Klein-Gordon and Dirac fields have well defined quasinormal modes in single horizon, asymptotically flat two-dimensional black holes. To get the result we solve the equations of motion in the massless limit and we also calculate the effective potentials of Schrodinger type equations. Furthermore we calculate exactly the quasinormal frequencies of the Dirac field propagating in the two-dimensional uncharged Witten black hole. We compare our results on its quasinormal frequencies with other already published.
We find spherically symmetric and static black holes in shift-symmetric Horndeski and beyond Horndeski theories. They are asymptotically flat and sourced by a non trivial static scalar field. The first class of solutions is constructed in such a way that the Noether current associated with shift symmetry vanishes, while the scalar field cannot be trivial. This in certain cases leads to hairy black hole solutions (for the quartic Horndeski Lagrangian), and in others to singular solutions (for a Gauss-Bonnet term). Additionally, we find the general spherically symmetric and static solutions for …
We propose a formula relating scattering S-matrix amplitudes to correlators of a conformal field theory. The proposal implements a flat limit of the field theory, providing an indirect microscopic description of gravitational theories with asymptotically flat boundary conditions. The formula is valid for both massive and massless external particles, and reduces to existing expressions in the literature when all particles are either simultaneously massless or massive. We test the result in various (2+1)-dimensional examples such as simple BMS3 invariant correlators and blocks. We also study two…
The pure quadratic term of New Massive Gravity in three dimensions admits asymptotically locally flat, rotating black holes. These black holes are characterized by their mass and angular momentum, as well as by a hair of gravitational origin. As in the Myers-Perry solution in dimensions greater than five, there is no upper bound on the angular momentum. We show that, remarkably, the equation for a massless scalar field on this background can be solved in an analytic manner and that the quasinormal frequencies can be found in a closed form. The spectrum is obtained requiring ingoing boundary co…
We study no-hair theorem for horizonless objects, being subject to Neumann boundary conditions. For massive scalar fields, a no hair theorem for Neumann compact stars was proved by us in a previous paper, where the nonzero scalar field mass condition is essential in the proof. In the present work, for massless scalar fields, we prove a no hair theorem, which claims that bound-state massless static scalar fields cannot exist outside asymptotically flat horizonless neutral Neumann compact stars.
We examine a one-parameter family of analytical solutions representing spherically symmetric collapse of a nonlinear massless scalar field with self-interaction in an asymptotically flat spacetime. The time evolution exhibits a type of critical behavior. Depending on the scalar charge parameter $q$ as compared to a critical value $q^*$, the incoming scalar wave collapses either to a globally naked central singularity if $q<q^*$ (weak field) or to a scalar-hairy black hole if $q>q^*$ (strong field), both having finite asymptotic masses. Near the critical evolution, the black hole mass follows a…
As an extension of arXiv:\{2002.02448, 2008.10740\} we present a physical protocol that a set of observers can use to detect a pure state in the bulk when they are spread across a small cut near $\mathcal{I}^+_-$ in flat spacetime. The protocol involves the modification of a bulk state using simple unitary operators and measurements of the energy of the state. The states that we study are constructed by acting with low energy operators on a vacuum state such that a perturbative analysis is valid. We restrict ourselves to $3+1$ dimensional spacetimes and only consider massless excitations. From…
This paper continues the investigation of the formation of naked singularities in the collapse of collisionless matter initiated in [RV]. There the existence of certain classes of non-smooth solutions of the Einstein-Vlasov system was proved. Those solutions are self-similar and hence not asymptotically flat. To obtain solutions which are more physically relevant it makes sense to attempt to cut off these solutions in a suitable way so as to make them asymptotically flat. This task, which turns out to be technically challenging, will be carried out in this paper. [RV] A. D. Rendall and J. J. L…
In a 4-dimensional (4D) weak field geometry governed by the linearized Einstein's equations and sourced primarily by a static, spatially localized, but otherwise arbitrary mass density $T_{00}$, it is known that the leading order tail part of the Green's functions of the minimally coupled massless scalar, Lorenz gauge photon, and de Donder gauge graviton at late times are not only time translation symmetric, but also space-translation and spherically symmetric. Only the monopole moment of the matter source is responsible for the late-time tail of the Green's functions. We provide evidence, in …
We study the evaporation of a four-dimensional spherically symmetric black hole formed in a gravitational collapse. We analyze the back-reaction of a massless quantum scalar field conformally coupled to the scalar curvature by means of the semiclassical Einstein equations. We show that the evaporation is linked to an ingoing negative energy flux at the dynamical horizon and that this flux is induced by the quantum matter trace anomaly outside the black hole horizon whenever a suitable averaged energy condition is satisfied. For illustrative purposes, we evaluate the negative ingoing flux and t…
Analytical approximations for $< ϕ^2 >$ of a quantized scalar field in ultrastatic asymptotically flat spacetimes are obtained. The field is assumed to be both massive and massless, with an arbitrary coupling $ξ$ to the scalar curvature, and in a zero or nonzero temperature vacuum state. The expression for $< ϕ^2 >$ is divided into low- and high-frequency parts. The expansion for the high-frequency contribution to this quantity is obtained. This expansion is analogous to the DeWitt-Schwinger one. As an example, the low-frequency contribution to $< ϕ^2 >$ is calculated on the background of the …
Motivated by the desire to understand the causal structure of physical signals produced in curved spacetimes -- particularly around black holes -- we show how, for certain classes of geometries, one might obtain its retarded or advanced minimally coupled massless scalar Green's function by using the corresponding Green's functions in the higher dimensional Minkowski spacetime where it is embedded. Analogous statements hold for certain classes of curved Riemannian spaces, with positive definite metrics, which may be embedded in higher dimensional Euclidean spaces. The general formula is applied…
We outline a proof of the stability of a massless neutral scalar field $ψ$ in the background of a wide class of four dimensional asymptotically flat rotating and ``electrically charged'' solutions of supergravity, and the low energy limit of string theory, known as STU metrics. Despite their complexity, we find it possible to circumvent the difficulties presented by the existence of ergo-regions and the related phenomenon of super-radiance in the original metrics by following a strategy due to Whiting, and passing to an auxiliary metric admitting an everywhere lightlike Killing field and const…
We study an analytical solution to the Einstein's equations in 2+1-dimensions, representing the self-similar collapse of a circularly symmetric, minimally coupled, massless, scalar field. Depending on the value of certain parameters, this solution represents the formation of black holes. Since our solution is asymptotically flat, our black holes do not have the BTZ space-time as their long time limit. They represent a new family of black holes in 2+1-dimensions.
4D Einstein gravity coupled to scalars and abelian gauge fields in its 2-Killing vector reduction is shown to be quasi-renormalizable to all loop orders at the expense of introducing infinitely many essential couplings. The latter can be combined into one or two functions of the `area radius' associated with the two Killing vectors. The renormalization flow of these couplings is governed by beta functionals expressible in closed form in terms of the (one coupling) beta function of a symmetric space sigma-model. Generically the matter coupled systems are asymptotically safe, that is the flow po…
We compute exactly the semi-classical radiation spectrum for a class of non-asymptotically flat charged dilaton black holes, the so-called linear dilaton black holes. In the high frequency regime, the temperature for these black holes generically agrees with the surface gravity result. In the special case where the black hole is massless, we show that, although the surface gravity remains finite, there is no radiation, in agreement with the fact that massless objects cannot radiate.
This paper studies the whole process of gravitational collapse and accretion of a massless scalar field in asymptotically flat spacetime. Two kinds of initial configurations are considered. One is the initial data without black hole, the other contains a black hole. Under suitable initial conditions, we find that multi-horizon will appear, which means that the initial black hole formed by gravitational collapse or existing at the beginning will instantly expand and suddenly grow, rather than grows gradually in the accretion process. A new type of critical behavior is found around the instant e…
We prove the stability of a spacetime with a naked singularity under scalar field perturbations, where the perturbations are regular at the singularity. This spacetime, found by Janis, Newman and Winicour, and independently by Wyman, is sourced by a massless scalar field and also arises as a certain limit of a class of charged dilatonic solutions in string theory. This stability result opens up specific questions for investigation related to the cosmic censorship conjecture and the mechanism by which it is implemented in nature.
A scalar field generalization of Xanthopoulos's cylindrically symmetric solutions of the vacuum Einstein equation is obtained. The obtained solution preserves the properties of the Xanthopoulos solution, which are regular on the axis, asymptotically flat and free from the curvature singularities. The solution describes stable, infinite length of rotating cosmic string interacting with gravitational and scalar waves.
We briefly discuss some of the known and new properties of rotating geometries that are relevant to this work. We generalize the analytical method of superposition of fields, known for generating nonrotating solutions, and apply it to construct massless and massive rotating physical wormholes sourced by a source-free electromagnetic field and an exotic fluid both anisotropic. Their stress-energy tensors are presented in compact and general forms. For the massive rotating wormholes there exists a mass-charge constraint yielding almost no more dragging effects than ordinary stars. There are coni…
We discuss various novel features of $n(\ge 4)$-dimensional spacetimes sourced by a massless (non-)phantom scalar field in general relativity. Assuming that the metric is a warped product of static two-dimensional Lorentzian spacetime and an $(n-2)$-dimensional Einstein space $K^{n-2}$ with curvature $k=0, \pm 1$, and that the scalar field depends only on the radial variable, we present a complete classification of static solutions for both signs of kinetic term. Contrary to the case with a non-phantom scalar field, the Fisher solution is not unique, and there exist two additional metrics corr…
We show that the previously obtained subtracted geometry of four-dimensional asymptotically flat multi-charged rotating black holes, whose massless wave equation exhibit $SL(2,\R) \times SL(2,\R) \times SO(3)$ symmetry may be obtained by a suitable scaling limit of certain asymptotically flat multi-charged rotating black holes, which is reminiscent of near-extreme black holes in the dilute gas approximation. The co-homogeneity-two geometry is supported by a dilation field and two (electric) gauge-field strengths. We also point out that these subtracted geometries can be obtained as a particula…
We discuss several aspects of quantum field theory of a scalar field in a Friedmann universe, clarifying and highlighting several conceptual and technical issues. (A) We show that one can map the dynamics of (1) a massless scalar field in a universe with power law expansion to (2) a massive scalar field in the de Sitter spacetime, which allows us to understand several features of either system and clarifies several issues related to the massless limit. (B) We obtain a useful integral representation for the Euclidean Green's function for the de Sitter spacetime, by relating it to the solution o…
We consider $d$-dimensional static spacetimes in Einstein gravity with a cosmological constant in the presence of a minimally coupled massless scalar field. The spacetimes have a $(d-2)$-dimensional base manifold given by an Einstein space and the massless scalar field depends only on the radial coordinate. The field equations are decoupled in the general case, and can be solved exactly for the cases when either the cosmological constant vanishes or the base manifold is Ricci flat. We focus on the case of a negative cosmological constant and a Ricci-flat base manifold. The solution has a curva…
Effects of quantized free scalar fields in cosmological spacetimes with Big Rip singularities are investigated. The energy densities for these fields are computed at late times when the expansion is very rapid. For the massless minimally coupled field it is shown that an attractor state exists in the sense that, for a large class of states, the energy density of the field asymptotically approaches the energy density it would have if it was in the attractor state. Results of numerical computations of the energy density for the massless minimally coupled field and for massive fields with minimal…
We study black hole solutions in the Einstein-Gauss-Bonnet gravity with the dilaton and a negative ``cosmological constant''. We derive the field equations for the static spherically symmetric ($k=1$) and hyperbolically symmetric ($k=-1$) spacetime in general $D$ dimensions. The system has some scaling symmetries which are used in our analysis of the solutions. We find exact solutions, i.e., regular AdS solution for $k=1$ and a massless black hole solution for $k=-1$. Nontrivial asymptotically AdS solutions are obtained numerically in D=4 -- 6 and 10 dimensional spacetimes. For spherically sym…
Motivated by black hole solutions with matter fields outside their horizon, we study the effect of these matter fields in the motion of massless and massive particles. We consider as background a four-dimensional asymptotically AdS black hole with scalar hair. The geodesics are studied numerically and we discuss about the differences in the motion of particles between the four-dimensional asymptotically AdS black holes with scalar hair and their no-hair limit, that is, Schwarzschild AdS black holes. Mainly, we found that there are bounded orbits like planetary orbits in this background. Howeve…
We calculate exactly the quasinormal frequencies of Klein-Gordon and Dirac test fields propagating in two-dimensional uncharged Achucarro-Ortiz black hole. For both test fields we study whether the quasinormal frequencies are well defined in the massless limit. We use their values to discuss the classical stability of the quasinormal modes in uncharged Achucarro-Ortiz black hole and to check the recently proposed Time Times Temperature bound. Furthermore we extend some of these results to the charged Achucarro-Ortiz black hole.
We study black hole formation during the gravitational collapse of a massless scalar field in asymptotically $AdS_D$ spacetimes for $D=4,5$. We conclude that spherically symmetric gravitational collapse in asymptotically $AdS$ spaces is turbulent and characterized by a Kolmogorov-Zakharov spectrum. Namely, we find that after an initial period of weakly nonlinear evolution, there is a regime where the power spectrum of the Ricci scalar evolves as $ω^{-s}$ with the frequency, $ω$, and $s\approx 1.7\pm 0.1$.
We study the quantum effects induced by bulk scalar fields in a model with a de Sitter (dS) brane in a flat bulk (the Vilenkin-Ipser-Sikivie model) in more than four dimensions. In ordinary dS space, it is well known that the stress tensor in the dS invariant vacuum for an effectively massless scalar ($m_\eff^2=m^2+ξ{\cal R}=0$ with ${\cal R}$ the Ricci scalar) is infrared divergent except for the minimally coupled case. The usual procedure to tame this divergence is to replace the dS invariant vacuum by the Allen Follaci (AF) vacuum. The resulting stress tensor breaks dS symmetry but is regul…
The quasinormal modes of a massless Dirac field in the de Rham-Gabadadze-Tolley (dRGT) massive gravity theory with asymptotically de Sitter spacetime are investigated using the Wentzel- Kramers-Brillouin (WKB) approximation. The effective potential for the massless Dirac field due to the dRGT black hole is derived. It is found that the shape of the potential depends crucially on the structure of the graviton mass and the behavior of the quasinormal modes is controlled by the graviton mass parameters. Higher potentials give stronger damping of the quasinormal modes. We compare our results to th…
We employ a late-time expansion to study the interior of rotating black holes coupled to a massless scalar field in asymptotically flat spacetime. We find that decaying fluxes of scalar radiation into the black hole necessitate the existence of a null singularity at the Cauchy horizon and a central spacelike singularity at radius $r = 0$. In particular, the decaying influxes source a localized cloud of scalar radiation near $r=0$ whose amplitude grows unboundedly large as advanced time $v \to \infty$. The scalar cloud inevitably results in a central spacelike singularity at late times $v$, wit…
We write down the relevant field equations for a stationary axially symmetric rigidly rotating dust source in such a way that the general solution depends upon the solution of an elliptic equation and upon harmonic functions. Starting with the dipole Bonnor solution, we built an asymptotically flat solution with two curvature singularities on the rotational axis with diverging mass. Apart from the two point singularities on the axis, the metric is regular everywhere. Finally, we study a non-asymptotically flat solution with NUT charge and a massless ring singularity, but with a well-defined ma…
We extend the work in our earlier article [4] to show that time-periodic, asymptotically-flat solutions of the Einstein equations analytic at scri, whose source is one of a range of scalar-field models, are necessarily stationary. We also show that, for some of these scalar-field sources, in stationary, asymptotically-flat solutions analytic at scri, the scalar field necessarily inherits the symmetry. To prove these results we investigate miscellaneous properties of massless and conformal scalar fields coupled to gravity, in particular Bondi mass and its loss.
In this paper, we probe in 4D Einstein-Gauss-Bonnet black hole and its thermodynamics. We illustrate the three asymptotically 4D EGB spacetime as an asymptotically flat, de Sitter, and Anti-de Sitter. Also, we apply the tunneling of the massless particles from the horizon of 4D EGB gravity and we investigate the correlation between the emission modes and temperature of the horizon. In asymptotically flat spacetime, the existence of the coupling constant alone constructs the regular spacetime, the radiation deviates from the pure thermal, and the temperature of the black hole horizon would be z…
We study the massless scalar field on asymptotically flat spacetimes with closed timelike curves (CTC's), in which all future-directed CTC's traverse one end of a handle (wormhole) and emerge from the other end at an earlier time. For a class of static geometries of this type, and for smooth initial data with all derivatives in $L_2$ on ${\cI}^{-}$, we prove existence of smooth solutions which are regular at null and spatial infinity (have finite energy and finite $L_2$-norm) and have the given initial data on $\cI^-$. A restricted uniqueness theorem is obtained, applying to solutions that fal…
