Self-gravitating Scalar Field Research Articles

NON-SINGULAR GLOBAL COSMIC STRINGS

Non-singular global cosmic strings are found in a non-linear sigma model with a potential term for a self-gravitating complex scalar field. Stationary solutions with angular momentum and possibly linear momentum are obtained by assuming an oscillatory dependence of the scalar field on t, φ and z. This dependence has an effect similar to gauging the global U(1) symmetry of the model, which is actually a Kaluza-Klein reduction from four to three spacetime dimensions. The method of analysis can be regarded as an extension of the gravito-electromagnetism formalism beyond the weak field limit.

Physics of the interior of a spherical, charged black hole with a scalar field

We analyze the physics of nonlinear gravitational processes inside a spherical charged black hole perturbed by a self-gravitating massless scalar field. For this purpose we created an appropriate numerical code. Throughout the paper, in addition to investigation of the properties of the mathematical singularities where some curvature scalars are equal to infinity, we analyze the properties of the physical singularities where the Kretschmann curvature scalar is equal to the Planckian value. Using a homogeneous approximation we analyze the properties of the spacetime near a spacelike singularity in spacetimes influenced by different matter contents, namely, a scalar field, pressureless dust and matter with ultrarelativistic isotropic pressure. We also carry out full nonlinear analyses of the scalar field and geometry of spacetime inside black holes by means of an appropriate numerical code with adaptive mesh refinement capabilities. We use this code to investigate the nonlinear effects of gravitational focusing, mass inflation, matter squeeze, and these effects dependence on the initial boundary conditions. It is demonstrated that the position of the physical singularity inside a black hole is quite different from the positions of the mathematical singularities. In the case of the existence of a strong outgoing flux of the scalar field inside a black hole it is possible to have the existence of two null singularities and one central $r=0$ singularity simultaneously.

Symmetries of distributional domain wall geometries

Generalizing the Lie derivative of smooth tensor fields to distribution-valued tensors, we examine the Killing symmetries and the collineations of the curvature tensors of some distributional domain wall geometries. The chosen geometries are rigorously the distributional thin wall limit of self-gravitating scalar field configurations representing thick domain walls and the permanence and/or the rising of symmetries in the limit process is studied. We show that, for all the thin wall space–times considered, the symmetries of the distributional curvature tensors turns out to be the Killing symmetries of the pullback of the metric tensor to the surface where the singular part of these tensors is supported. Remarkably enough, for the nonreflection symmetric domain wall studied, these Killing symmetries are not necessarily symmetries of the ambient space–time on both sides of the wall.

Nonsingular stationary global strings

A field-theoretical model for non-singular global cosmic strings is presented. The model is a non-linear sigma model with a potential term for a self-gravitating complex scalar field. Non-singular stationary solutions with angular momentum and possibly linear momentum are obtained by assuming an oscillatory dependence of the scalar field on t, phi and z. This dependence has an effect similar to gauging the global U(1) symmetry of the model, which is actually a Kaluza-Klein reduction from four to three spacetime dimensions. The method of analysis can be regarded as an extension of the gravito-electromagnetism formalism beyond the weak field limit. Some D=3 self-dual solutions are also discussed.

Approximately self-similar critical collapse in 2+1 dimensions

Critical collapse of a self-gravitating scalar field in a (2+1)-dimensional spacetime with negative cosmological constant seems to be dominated by a continuously self-similar solution of the field equations without cosmological constant. However, previous studies of linear perturbations in this background were inconclusive. We extend the continuously self-similar solutions to solutions of the field equations with negative cosmological constant, and analyze their linear perturbations. The extended solutions are characterized by a continuous parameter. A suitable choice of this parameter seems to improve the agreement with the numerical results. We also study the dynamics of the apparent horizon in the extended background.

Classical and quantum decay of oscillations: Oscillating self-gravitating real scalar field solitons

The oscillating gravitational field of an oscillaton of finite mass M causes it to lose energy by emitting classical scalar field waves, but at a rate that is non-perturbatively tiny for small GMm, where m is the scalar field mass: d(GM)/dt ~ -3797437.776333015 e^[-39.433795197160163/(GMm)]/(GMm)^2. Oscillatons also decay by the quantum process of the annihilation of scalarons into gravitons, which is only perturbatively small in GMm, giving by itself d(GM)/dt ~ - 0.008513223934732692 G m^2 (GMm)^5. Thus the quantum decay is faster than the classical one for Gmm < 39.4338/[ln(1/Gm^2)}-7ln(GMm)+19.9160]. The time for an oscillaton to decay away completely into free scalarons and gravitons is ~ 2/(G^5 m^11) ~ 10^324 yr (1 meV/m)^11. Oscillatons of more than one real scalar field of the same mass generically asymptotically approach a static-geometry U(1) boson star configuration with GMm = GM_0 m, at the rate d(GM/c^3)/dt ~ [(C/(GMm)^4)e^{-alpha/(GMm)}+Q(m/m_{Pl})^2(GMm)^3] [(GMm)^2-(GM_0 m)^2], with GM_0 m depending on the magnitudes and relative phases of the oscillating fields, and with the same constants C, alpha, and Q given numerically above for the single-field case that is equivalent to GM_0 m = 0.

Evolution of the Schrödinger-Newton system for a self-gravitating scalar field

Using numerical techniques, we study the collapse of a scalar field configuration in the Newtonian limit of the spherically symmetric Einstein--Klein--Gordon (EKG) system, which results in the so called Schr\"odinger--Newton (SN) set of equations. We present the numerical code developed to evolve the SN system and topics related, like equilibrium configurations and boundary conditions. Also, we analyze the evolution of different initial configurations and the physical quantities associated to them. In particular, we readdress the issue of the gravitational cooling mechanism for Newtonian systems and find that all systems settle down onto a 0--node equilibrium configuration.

Self-gravitating scalar field in spherically symmetric comoving system: Solutions depending on one variable

The scalar and Einstein field equations are considered in the general symmetric comoving system. The self-gravitational interaction of the scalar field is expressed by identifying the energy momentum tensor with the one canonically associated to the scalar field. It is shown that the scalar field can depend only on the radial and time variables and that the energy momentum tensor is implicitly conserved. Two classes of solutions are then studied. A first class, that contains the static case previously considered and the complete time-dependent case, is determined by a priori assuming the unknown functions to depend on one only variable. This class is meaningful essentially for massless field. A second class of solutions refers to the a priori assumption that the scalar field alone depends on r or on t. In both cases some comments are developed for the massive scalar field and for a large class of massless fields we are able to determine the solutions.

‘No-scalar-hair’ theorems for nonminimally coupled fields with quartic self-interaction

Self-gravitating scalar fields with nonminimal coupling to gravity and a quartic self-interaction are considered in the domain of outer communications of a static black hole. It is shown that there is no value of the nonminimal coupling parameter ζ for which nontrivial static black-hole solutions exist. This result establishes the correctness of Bekenstein ‘no-scalar-hair’ conjecture for quartic self-interactions.

A scalar-tensor cosmological model with dynamical light velocity

The dynamical consequences of a bimetric scalar-tensor theory of gravity with a dynamical light speed are investigated in a cosmological setting. The model consists of a minimally-coupled self-gravitating scalar field coupled to ordinary matter fields in the standard way through the metric: g μν + B∂ μ φ∂ ν φ. We show that in a universe with matter that has a radiation-dominated equation of state, the model allows solutions with a de Sitter phase that provides sufficient inflation to solve the horizon and flatness problems. This behaviour is achieved without the addition of a potential for the scalar field, and is shown to be largely independent of its introduction. We therefore have a model that is fundamentally different than the potential-dominated, slowly-rolling scalar field of the standard models inflationary cosmology. The speed of gravitational wave propagation is predicted to be significantly different from the speed of matter waves and photon propagation in the early universe.

BEYOND THE HORIZON TO UNKNOWN TERRITORIES: THE SINGULARITY INSIDE BLACK HOLES

We study the Cauchy horizon singularity inside a spherical charged black hole, coupled to a self-gravitating scalar field. We show that all the radial causal geodesics terminate at a weak singularity according to the Tipler classification. Our result is valid anywhere along the singularity, in particular in the regime where nonlinear effects are crucial.

All nonspherical perturbations of the Choptuik spacetime decay

We study the nonspherical linear perturbations of the discretely self-similar and spherically symmetric solution for a self-gravitating scalar field discovered by Choptuik in the context of marginal gravitational collapse. We find that all nonspherical perturbations decay. Therefore critical phenomena at the threshold of gravitational collapse, originally found in spherical symmetry, will extend to (at least slightly) nonspherical initial data.

Singularity deep inside the spherical charged black hole core

We study analytically the spacelike singularity inside a spherically symmetric, charged black hole coupled to a self-gravitating spherical massless scalar field. We assume spatial homogeneity, and find a generic solution in terms of a formal series expansion. This solution is tested against fully nonlinear and inhomogeneous numerical simulations. We find full compliance between our analytical solution and the pointwise behavior of the singularity in the numerical simulations. This is a strong scalar-curvature monotonic spacelike singularity, which connects to a weak null singularity at asymptotically late advanced time.

Dynamical evolution of boson stars. II. Excited states and self-interacting fields

The dynamical evolution of self-gravitating scalar field configurations in numerical relativity is studied. The previous analysis on ground state boson stars of non-interacting fields is extended to excited states and to fields with self-couplings. Self-couplings can significantly change the physical dimensions of boson stars, making them much more astrophysically interesting (e.g., having mass of the order of 0.1 solar mass). The stable $(S)$ and unstable $(U)$ branches of equilibrium configurations of boson stars of self-interacting fields are studied; their behavior under perturbations and their quasi-normal oscillation frequencies are determined and compared to the non-interacting case. Excited states of boson stars with and without self-couplings are studied and compared. Excited states also have equilibrium configurations with $S$ and $U$ branch structures; both branches are intrinsically unstable under a generic perturbation but have very different instability time scales. We carry out a detailed study of the instability time scales of these configurations. It is found that highly excited states spontaneously decay through a cascade of intermediate states similar to atomic transitions.

Mass Inflation in Dynamical Gravitational Collapse of a Charged Scalar Field

During the last ten years evidence has been mounting that generically the Cauchy horizon inside a charged or a spinning black hole becomes a null, weak singularity which is a precursor of a strong, spacelike singularity along the $r\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ hypersurface. We present here the missing link in this picture: A complete calculation from a regular initial data to the formation of a black hole and its inner singularities. We follow the gravitational collapse of a self-gravitating charged massless scalar field and observe the formation of an apparent horizon, a null, weak, mass-inflation singularity along the Cauchy horizon, and a final, spacelike, central singularity.

Dynamical evolution of boson stars in Brans-Dicke theory

We study the dynamics of a self-gravitating scalar field solitonic object (boson star) in the Jordan-Brans-Dicke (BD) theory of gravity. We show dynamical processes of this system such as (i) black hole formation of a perturbed equilibrium configuration on an unstable branch, (ii) migration of a perturbed equilibrium configuration from an unstable branch to a stable branch, and (iii) the transition from an excited state to a ground state. We find that the dynamical behavior of boson stars in BD theory is quite similar to that in general relativity (GR), with comparable scalar wave emission. We also demonstrate the formation of a stable boson star from a Gaussian scalar field packet with flat gravitational scalar field initial data. This suggests that boson stars can be formed in the BD theory in much the same way as in GR.

Analytic study of the null singularity inside spherical charged black holes

We study analytically the features of the Cauchy horizon (CH) singularity inside a spherically symmetric charged black hole, nonlinearly perturbed by a self-gravitating massless scalar field. We derive exact expressions for the divergence rate of the blue-shift factors, namely the derivatives in the outgoing direction of the scalar field \ensuremath{\Phi} and the area coordinate $r.$ Both derivatives are found to grow along the contracting CH exactly like $1/r.$ Our results are valid everywhere along the CH singularity, down to the point of full focusing. These exact analytic expressions are verified numerically.

HOMOTHETIC WYMAN SPACETIMES

The time-dependent, spherically symmetric, Wyman sector of the Unified Field Theories is shown to be equivalent to a self-gravitating scalar field with a positive-definite, repulsive interaction potential. A homothetic symmetry is imposed on the fundamental tensor, and the resulting autonomous system is numerically integrated. Near the critical point (between the collapsing and noncollapsing spacetimes) the system displays an approximately periodic alternation between collapsing and dispersive epochs.

Structure of the Black Hole's Cauchy-Horizon Singularity

We study the Cauchy-horizon (CH) singularity of a spherical charged black hole perturbed nonlinearly by a self-gravitating massless scalar field. We show numerically that the singularity is weak both at the early and at the late sections of the CH, where the focusing of the area coordinate $r$ is strong. In the early section the metric is almost Reissner-Nordstr\"om, and the fields behave according to perturbation analysis. We find exact analytical expressions for the gradients of $r$ and of the scalar field, which are valid at both sections. We then verify these analytical results numerically.

Late-time evolution of nonlinear gravitational collapse

We study numerically the fully nonlinear gravitational collapse of a self-gravitating, minimally coupled, massless scalar field in spherical symmetry. Our numerical code is based on double-null coordinates and on free evolution of the metric functions: The evolution equations are integrated numerically, whereas the constraint equations are only monitored. The numerical code is stable (unlike recent claims) and second-order accurate. We use this code to study the late-time asymptotic behavior at fixed $r$ (outside the black hole), along the event horizon, and along future null infinity. In all three asymptotic regions we find that, after the decay of the quasinormal modes, the perturbations are dominated by inverse power-law tails. The corresponding power indices agree with the integer values predicted by linearized theory. We also study the case of a charged black hole nonlinearly perturbed by a (neutral) self-gravitating scalar field, and find the same type of behavior---i.e., quasinormal modes followed by inverse power-law tails, with the same indices as in the uncharged case.