We study here the evolution of a massless scalar field in a spacetime, developing from a regular initial spacelike surface. The Einstein equations and regularity and boundary conditions governing the same are specified. Both homogeneous and inhomogeneous collapse models are considered and we analyze when the occurrence of singularity will be simultaneous or otherwise. In the inhomogeneous collapse case, we characterize a wide family of black hole solutions arising in scalar field collapse. We also discuss the possibility of existence of classes of non-singular models where collapse could almost freeze if suitable conditions are satisfied.
The interaction of massless minimally coupled scalar field and spinor field $ \left( Ψ+ Φ_m \rightarrow Ψ+ Φ_m \right) $ is investigated and the behavior of interaction and scattering matrix in Minkowski limit is studied. It is seen that the massless minimally coupled scalar field operator, the interaction Lagrangian and the scattering matrix become zero. Also the incoming and outgoing spinor fields, which in de Sitter space-time are different and are interacted with massless minimally coupled scalar field, in null curvature limit are the same and no interaction seen. In other word, the massle…
The massless minimally coupled scalar field in de Sitter ambient space formalism might play a similar role to what the Higgs scalar field accomplishes within the electroweak standard model. With the introduction of a "local transformation" for this field, the interaction Lagrangian between the scalar field and the spinor field can be made similar to a gauge theory. In the null curvature limit, the Yukawa potential can be constructed from that Lagrangian. Finally the one-loop correction of the scalar-spinor interaction is presented, which is free of any infrared divergence.
Casimir effect for massless minimally coupled scalar field is studied. An explicit answer for de Sitter spacetime is obtained and analized. Cosmological implications of the result are discussed.
In this paper we study a massless, minimally coupled scalar field in a FLRW spacetime with periods of different constant deceleration parameter. We assume the Bunch-Davies vacuum during inflation and then use a sudden matching approximation to match it onto radiation era and subsequently onto matter era. We then proceed to calculate the one-loop energy-momentum tensor from the inflationary quantum vacuum fluctuations in different eras. The energy-momentum tensor has the form of an ideal (quantum) fluid, characterized by an equation of state. When compared with the background, far away from the…
We present in this paper a fully covariant quantization of the minimally-coupled massless field on de Sitter space. We thus obtain a formalism free of any infrared (e.g logarithmic) divergence. Our method is based on a rigorous group theoretical approach combined with a suitable adaptation (Krein spaces) of the Wightman-Gärding axiomatic for massless fields (Gupta-Bleuler scheme). We make explicit the correspondence between unitary irreducible representations of the de Sitter group and the field theory on de Sitter space-time. The minimally-coupled massless field is associated with a represent…
The scalar-spinor interaction Lagrangian is presented by the Yukawa potential. In dS ambient space formalism, the interaction Lagrangian of scalar-spinor fields was obtained from a new transformation which is very similar to the guage theory. The interaction of massless minimally coupled scalar and spinor fields was investigated. The Minkowski limit of the massless minimally coupled scalar field and massive spinor field interaction in the ambient space formalism of de Sitter space time is calculated. The interaction Lagrangian and massless minimally coupled scalar field in the null curvature l…
We study {\it analytically} the physical and mathematical properties of spatially regular massless scalar field configurations which are non-minimally coupled to the electromagnetic field of a spherically symmetric charged reflecting shell. In particular, the Klein-Gordon wave equation for the composed charged-reflecting-shell-nonminimally-coupled-linearized-massless-scalar-field system is solved analytically. Interestingly, we explicitly prove that the discrete resonance spectrum $\{R_{\text{s}}(Q,α,l;n)\}^{n=\infty}_{n=1}$ of charged shell radii that can support the non-minimally coupled mas…
We, in the first part, contemplate a massless minimally coupled scalar which is Yukawa-coupled to a massless Dirac fermion in a locally de Sitter background of an inflating spacetime. We compute the scalar's quantum corrected mode function, power spectrum, spectral index and the running of the spectral index at one-loop order. We find that the spectrum is slightly blue-tilted; hence, the amplitudes of fluctuations grow slightly toward the smaller scales. Then, in the second part, we apply the computation method used in the first part to a massless minimally coupled scalar with a quartic self-i…
We study the critical gravitational collapse of a massless scalar field non-minimally coupled to gravity, using a quadratic coupling function with a strength parameter $ξ$. We concentrate on critical phenomena of type II, and determine with an accuracy of at least $10^{-12}$ the value of the critical amplitude for collapse to a black hole, as well as the values of the critical and echoing exponents. Obtaining such high accuracy in the critical amplitude requires us to do a coordinate radial transformation that effectively increases resolution near the central regions by a factor of at least $1…
Over the last ten years interest in the physics of de Sitter spacetime has been growing very fast. Besides the supposed existence of a "de sitterian period" in inflation theories, the observational evidence of an acceleration of the universe expansion (interpreted as a positive cosmological constant or a "dark energy" or some form of "quintessence") has triggered a lot of attention in the physics community. A specific de sitterian field called "massless minimally coupled field" (mmc) plays a fundamental role in inflation models and in the construction of the de sitterian gravitational field. A…
We derive a simple form for the propagator of a massless, minimally coupled scalar in a locally de Sitter geometry of arbitrary spacetime dimension. We then employ it to compute the fully renormalized stress tensor at one and two loop orders for a massless, minimally coupled phi^4 theory which is released in Bunch-Davies vacuum at t=0 in co-moving coordinates. In this system the uncertainty principle elevates the scalar above the minimum of its potential, resulting in a phase of super-acceleration. With the non-derivative self-interaction the scalar's breaking of de Sitter invariance becomes o…
The 2+1-dimensional geodesic circularly symmetric solutions of Einstein-massless-scalar field equations with negative cosmological constant are found and their local and global properties are studied. It is found that one of them represents gravitational collapse where black holes are always formed.
We derive an exact solution belonging to Kundt class of spacetimes both with and without a cosmological constant that are minimally coupled to a free massless scalar field. We show the algebraic type of these solutions and give interpretation of the results. Subsequently, we look for solutions additionally containing an electromagnetic field satisfying nonlinear field equations.
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.
We study the spherically symmetric collapse of a cloud of dust in VCDM, a class of gravitational theories with two local physical degrees of freedom. We find that the collapse corresponds to a particular foliation of the Oppenheimer-Snyder solution in general relativity (GR) which is endowed with a constant trace for the extrinsic curvature relative to the time $t$ constant foliation. For this solution, we find that the final state of the collapse leads to a static configuration with the lapse function vanishing at a radius inside the apparent horizon. Such a point is reached in an infinite ti…
Self-similar solutions of a collapsing perfect fluid and a massless scalar field with kinematic self-similarity of the first kind in 2+1 dimensions are obtained. Their local and global properties of the solutions are studied. It is found that some of them represent gravitational collapse, in which black holes are always formed, and some may be interpreted as representing cosmological models.
''Massless'' spin-2 field equation in de Sitter space, which is invariant under the conformal transformation, has been obtained. The frame work utilized is the symmetric rank-2 tensor field of the conformal group. Our method is based on the group theoretical approach and six-cone formalism, initially introduced by Dirac. Dirac's six-cone is used to obtain conformally invariant equations on de Sitter space. The solution of the physical sector of massless spin-2 field (linear gravity) in de Sitter ambient space is written as a product of a generalized polarization tensor and a massless minimally…
We consider the late time one-loop quantum backreaction from inflationary fluctuations of a non-minimally coupled, massless scalar field. The scalar is assumed to be a spectator field in an inflationary model with a constant principal slow roll $ε$ parameter. We regulate the infrared by matching onto a pre-inflationary radiation era. We find a large late time backreaction when the nonminimal coupling $ξ$ is negative (in which case the scalar exhibits a negative mass term during inflation). The one-loop quantum backreaction becomes significant today for moderately small non-minimal couplings, $…
In this paper we have studied the propagation of a massless scalar field minimally coupled to a black hole with the source of cloud of strings in $2+1$ $f(R)$gravity theory. In particular we have found analytical results for the decay rate, reflection coefficient, greybody factors, as well as the black hole temperature. On the other hand, our quasinormal modes analyses reveals stability in the propagation of a massless scalar field in the cloud of strings black hole spacetime. However, under a suitable choose of parameters an instability is found. Furthermore based on the Bekenstein conjecture…
We consider single graviton loop corrections to the effective field equation of a massless, minimally coupled scalar on de Sitter background in the simplest gauge. We find a large temporal logarithm in the approach to freeze-in at late times, but no correction to the feeze-in amplitude. We also find a large spatial logarithm (at large distances) in the scalar potential generated by a point source, which can be explained using the renormalization group with one of the higher derivative counterterms regarded as a curvature-dependent field strength renormalization. We discuss how these results se…
We present results from the first study of critical behavior in 3-d gravitational collapse. The source of the gravitational field is a massless scalar field. This is a well-studied case for spherically symmetric gravitational collapse, allowing us to understand the reliability and accuracy of the simulations. We study both supercritical and subcritical evolutions to see if one provides more accurate results than the other. We find that even for non-spherical initial data with 35 percent of the power in the $\ell=2$ spherical harmonic, the critical solution is the same as in spherical symmetry.
The issue of de Sitter invariance for a massless minimally coupled scalar field is revisited. Formally, it is possible to construct a de Sitter invariant state for this case provided that the zero mode of the field is quantized properly. Here we take the point of view that this state is physically acceptable, in the sense that physical observables can be computed and have a reasonable interpretation. In particular, we use this vacuum to derive a new result: that the squared difference between the field at two points along a geodesic observer's space-time path grows linearly with the observer's…
The phenomena of collapse and dispersal for a massless scalar field has drawn considerable interest in recent years, mainly from a numerical perspective. We give here a sufficient condition for the dispersal to take place for a scalar field that initially begins with a collapse. It is shown that the change of the gradient of the scalar field from a timelike to a spacelike vector must be necessarily accompanied by the dispersal of the scalar field. This result holds independently of any symmetries of the spacetime. We demonstrate the result explicitly by means of an example, which is the scalar…
We report on a numerical study of the spherically symmetric collapse of a self-gravitating massless scalar field. Earlier results of Choptuik(1992, 1994) are confirmed. The field either disperses to infinity or collapses to a black hole, depending on the strength of the initial data. For evolutions where the strength is close to but below the strength required to form a black hole, we argue that there will be a region close to the axis where the scalar curvature and field energy density can reach arbitrarily large levels, and which is visible to distant observers
Several classes of conformally-flat and spherically symmetric exact solutions to the Einstein field equations coupled with either a massless scalar field or a radiation fluid are given, and their main properties are studied. It is found that some represent the formation of black holes due to the gravitational collapse of the matter fields. When the spacetimes have continuous self-similarity (CSS), the masses of black holes take a scaling form $M_{BH} \propto (P - P^{*})^γ$, where $γ= 0.5$ for massless scalar field and $γ= 1$ for radiation fluid. The reasons for the difference between the value…
We study the propagation of massless scalar fields non-minimally coupled to gravity in the background of five-dimensional Einstein-power-Maxwell black holes, and using the WKB and the pseudospectral Chebyshev methods we obtain the quasinormal frequencies (QNFs), which allow us to show the existence of stable and unstable QNFs depending on the power $k$ of the nonlinear electrodynamics, the $ξ$ parameter, which controls the strength of the non-minimal coupling, and on the size of the black hole.
In de Sitter ambient space formalism, the massless minimally coupled scalar field can be constructed from a massless conformally coupled scalar field and a constant five-vector $A^α$. Also, a constant five-vector $B^α$ appears in the interaction Lagrangian of massless minimally coupled scalar and spinor fields in this formalism. These constant five-vector fields can be fixed in the interaction case in the null curvature limit. Here we will calculate the $\cal S$ matrix elements of scalar-spinor fields interaction in the tree level approximation. Then the constant five-vectors $A^α$ and $B^α$, …
We present results from a numerical study of critical gravitational collapse of axisymmetric distributions of massless scalar field energy. We find threshold behavior that can be described by the spherically symmetric critical solution with axisymmetric perturbations. However, we see indications of a growing, non-spherical mode about the spherically symmetric critical solution. The effect of this instability is that the small asymmetry present in what would otherwise be a spherically symmetric self-similar solution grows. This growth continues until a bifurcation occurs and two distinct region…
We consider the massless scalar field on the four-dimensional sphere $S^4$. Its classical action $S={1\over 2}\int_{S^4} dV (\nabla ϕ)^2$ is degenerate under the global invariance $ϕ\to ϕ+ \hbox{constant}$. We then quantize the massless scalar field as a gauge theory by constructing a BRST-invariant quantum action. The corresponding gauge-breaking term is a non-local one of the form $S^{\rm GB}={1\over {2αV}}\bigl(\int_{S^4} dV ϕ\bigr)^2$ where $α$ is a gauge parameter and $V$ is the volume of $S^4$. It allows us to correctly treat the zero mode problem. The quantum theory is invariant under S…
Gravitational collapse of a massless scalar field with the periodic boundary condition in a cubic box is reported. This system can be regarded as a lattice universe model. We construct the initial data for a Gaussian like profile of the scalar field taking the integrability condition associated with the periodic boundary condition into account. For a large initial amplitude, a black hole is formed after a certain period of time. While the scalar field spreads out in the whole region for a small initial amplitude. It is shown that the expansion law in a late time approaches to that of the radia…
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…
In a recent paper [1], it has been shown that negative norm states are indispensable for a fully covariant quantization of the minimally coupled scalar field in de Sitter space. Their presence, while leaving unchanged the physical content of the theory, offers an automatic and covariant renormalization of the vacuum energy divergence. This paper is a completion of our previous work. An explicit construction of the covariant two-point function of the ``massless'' minimally coupled scalar field in de Sitter space is given, which is free of any infrared divergence. The associated Schwinger commut…
In this work we study the dynamics of gravitational collapse of a homogeneous dust sphere in a model exhibiting a linear non-minimal coupling between matter and curvature. The evolution of the scale factor and the matter density is obtained for different choices of Lagrangean density of matter, highlighting the direct physical relevance of the latter in this theory. Following a discussion of the junction conditions and boundary terms in the action functional, the matching with the outer metric and event horizon is analyzed. We find that a distinct phenomenology arises when compared with standa…
We study the collapse of a massless scalar field coupled to gravity. A class of blackhole solutions are identified. We also report on a class of solutions where collapse starts from a regular spacelike surface but then the collapsing scalar field freezes. As a result, in these solutions, a black hole does not form, neither is there any singularity in the future.
In a recent paper we showed that the collapse to a black hole in one-parameter families of initial data for massless, minimally coupled scalar fields in spherically symmetric semi-classical loop quantum gravity exhibited a universal mass scaling similar to the one in classical general relativity. In particular, no evidence of a mass gap appeared as had been suggested by previous studies. The lack of a mass gap indicated the possible existence of a self-similar critical solution as in general relativity. Here we provide further evidence for its existence. Using an adaptive mesh refinement code,…
We discuss the two-dimensional dilaton gravity with a scalar field as the source matter. The coupling between the gravity and the scalar, massless, field is presented in an unusual form. We work out two examples of these couplings, and solutions with black-hole behaviour are discussed and compared with those found in the literature.
This paper studies the perturbations of the continuously self-similar critical solution of the gravitational collapse of a massless scalar field (Roberts solution). The perturbation equations are derived and solved exactly. The perturbation spectrum is found to be not discrete, but occupying continuous region of the complex plane. The renormalization group calculation gives the value of the mass-scaling exponent equal to 1.
We investigate the dynamics of homogeneous gravitational collapse of a massless vector field in the presence of a positive cosmological constant $Λ$. The corresponding density function $ρ(a)$ obtained for the massless vector field is inversely proportional to the fourth power of the scale factor $a (t)$. The variation of the scale factor shows that for $0\, \leΛ< 1$, we obtain the gravitational collapse of the vector fields leading singularity formation in a {\it finite} comoving time resulting in a {\it Blackhole} such that with increasing $Λ$, the singularity formation time, $t_s$ increases.…
In the gravitational collapse of matter beyond spherical symmetry, gravitational waves are necessarily present. On the other hand, gravitational waves can collapse to a black hole even without matter. One might therefore wonder whether the interaction and competition between the matter fields and gravitational waves affects critical phenomena at the threshold of black hole formation. As a toy model for this, we study type II critical collapse with two matter fields in spherical symmetry, namely a scalar field and a Yang-Mills field. On their own, both display discrete self-similarity (DSS) in …
A detailed study of quantum and semiclassical Euclidean wormholes for Einstein's theory with a minimally coupled scalar field has been performed for a class of potentials. Massless, constant, massive (quadratic in the scalar field) and inverse (linear) potentials admit Hawking and Page wormhole boundary condition both in the classically forbidden and allowed regions. Inverse quartic potential has been found to exhibit semiclassical wormhole configuration. Classical wormholes under suitable back-reaction leading to a finite radius of the throat, where strong energy condition is satisfied, have …
In the de Sitter ambient space formalism the massless fields, which include the linear gravity and massless minimally coupled scalar field, can be written in terms of two separate parts: a massless conformally coupled scalar field and a polarization tensor(-spinor) part. Therefore due to the massless conformally coupled scalar field, there exist an unique Bunch-Davies vacuum state for quantum field theory in the de Sitter space time. In the de Sitter ambient space formalism one can show that the massless fields with spin $s\geq 1$ are gauge invariant. By coupling the massless gauge spin-$2$ an…
In the present work the collapse scenario of some exact non-spherical models with a minimally coupled scalar field is studied. Scalar field collapse with planar as well as toroidal, cylindrical and pseudoplanar symmetries have been investigated. It is shown that the scalar field may have collapsing modes even if it has the equation of state corresponding to that of a dark energy.
This paper constructs continuously self-similar solution of a spherically symmetric gravitational collapse of a scalar field in n dimensions. The qualitative behavior of these solutions is explained, and closed-form answers are provided where possible. Equivalence of scalar field couplings is used to show a way to generalize minimally coupled scalar field solutions to the model with general coupling.
We obtain a new self-similar solution to the Einstein's equations in four-dimensions, representing the collapse of a spherically symmetric, minimally coupled, massless, scalar field. Depending on the value of certain parameters, this solution represents the formation of naked singularities and black holes. Since the black holes are identified as the Schwarzschild ones, one may naturally see how these black holes are produced as remnants of the scalar field collapse.
We study a theory of minimally modified gravity called cuscuton/VCDM that propagates only two gravitational degrees of freedom. Despite being apparently different from general relativity (GR), it is in principle possible that this theory might be obtained via a field redefinition starting from the GR action. This would make the vacuum theory equivalent to GR and the theory would differ from GR only in the presence of matter. In this paper, studying the dispersion relation of gravitational waves and the dynamics of the Bianchi-I universe, we prove that such a field redefinition does not exist a…
We give the Lagrangian formulation of a generic non-minimally extended Einstein-Maxwell theory with an action that is linear in the curvature and quadratic in the electromagnetic field. We derive the coupled field equations by a first order variational principle using the method of Lagrange multipliers. We look for solutions describing plane-fronted Einstein-Maxwell waves with parallel rays. We give a family of exact solutions associated with a partially massless spin-2 photon and a partially massive spin-2 graviton.
An analytic method is given for deriving the part of the retarded Green's function v(x,x') that contributes to the tail term in the radiation reaction force felt by a particle coupled to a massless minimally coupled scalar field. The method gives an expansion of v(x,x') for small separations of the points x, x' valid for an arbitrary static spherically symmetric spacetime. It is obtained by using a WKB approximation for the Euclidean Green's function for the massless minimally coupled scalar field and is equivalent to the DeWitt-Schwinger expansion for v(x,x'). The first few terms in this expa…
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…
We study the spherically symmetric gravitational collapse of massless scalar matter field in asymptotic flat spacetime in $f(R)$ gravity. In the Einstein frame of $f(R)$ gravity, an additional scalar field arises due to the conformal transformation. We find that besides the usual competition between gravitational energy and kinetic energy in the process of gravitational collapse, the new scalar field brought by the conformal transformation adds one more competing force in the dynamical system. The dynamical competition can be controlled by tuning the amplitudes of the initial perturbations of …
In this letter we study the behavior of non-minimally coupled Einstein-Gauss-Bonnet gravity theories with the constant-roll condition. Recalling the results of the striking GW170817 event, we demand that the velocity of the gravitational waves is equated to unity in natural units, meaning that $c_T^2=1$. This is a powerful restriction since it leads to a decrease in the degrees of freedom and subsequently reveals a connection between the scalar functions of the theory which presumably have different origins. In this framework, we shall assume that a scalar potential is present and can be extra…
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 present a solvable model of two-dimensional dilaton-gravity coupled to a massless scalar field. We locally integrate the field equations and briefly discuss the properties of the solutions. For a particular choice of the coupling between the dilaton and the scalar field the model can be interpreted as the two-dimensional effective theory of 2+1 cylindrical gravity minimally coupled to a massless scalar field.
We revisit the issue of continuous signature transition from Euclidean to Lorentzian metrics in a cosmological model described by FRW metric minimally coupled with a self interacting massive scalar field. Then, using a noncommutative phase space of dynamical variables deformed by Generalized Uncertainty Principle (GUP) we show that the signature transition occurs even for a model described by FRW metric minimally coupled with a free massless scalar field accompanied by a cosmological constant. This indicates that the continuous signature transition might have been easily occurred at early univ…
An analytical model that represents the collapse of a massless scalar wave packet with continuous self-similarity is constructed, and critical phenomena are found. In the supercritical case, the mass of black holes is finite and has the form $M \propto (p - p^{*})^γ$, with $γ= 1/2$.
