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We show that higher form fields, specifically 2- and 3-forms in four spacetime dimensions, suffer from loss of hyperbolicity when they have self interaction. The equations of motion lose their wave-like characteristic in certain parts of the configuration space, and such problematic regions can also be reached dynamically from healthy initial data. These findings are analogous to recent results for vector fields, which are equivalently 1-forms, however, the details of the pathology can be different for higher forms. We also show that the possibility of more than one self interaction term in higher forms also leads to the amelioration of hyperbolicity problems., Comment: 11 pages, 1 figure

We demonstrate some shortcomings of "fixing the equations," an increasingly popular remedy for time evolution problems of effective field theories (EFTs). We compare the EFTs and their "fixed" versions to the UV theories from which they can be derived in two cases: K-essence and nonlinear Proca theory. We find that when an EFT breaks down due to loss of hyperbolicity, fixing does not approximate the UV theory well if the UV solution does not quickly settle down to vacuum. We argue that this can be related to the EFT approximation itself becoming invalid, which cannot be rectified by fixing., Comment: 5+4 pages. Version published as a PRD letter

Various groups recently demonstrated that the time evolution of simplest self-interacting vector fields, those with self-interaction potentials, can break down after a finite duration in what is called loss of hyperbolicity. We establish that this is not an isolated issue, and other generalizations of the Proca theory suffer from the same problem. Specifically, we show that vector field theories with derivative self-interactions have a similar pathology. For this, we derive the effective metric that governs the dynamics, and show that it can change signature during time evolution. We also show that, generalized Proca theories may suffer from tachyonic instabilities as well, which lead to another form of unphysical behavior., Comment: 10 pages, 4 figures; added a reference

Simultaneous measurements of neutron star masses and radii can be used to constrain deviations from general relativity (GR) as was recently demonstrated for the spontaneous scalarization model of Damour and Esposito-Far\`{e}se (DEF). Here, we investigate the general applicability of the same procedure beyond this single example. We first show that a simple variation of the DEF model renders the same mass-radius measurements ineffective for obtaining constraints. On the other hand, a recently popular and distinct model of scalarization that arises in scalar-Gauss-Bonnet theory can be constrained similarly to the original DEF model, albeit due to a slightly different underlying mechanism. These establish that using the mass-radius data can potentially constrain various theories of gravity, but the method also has limitations., Comment: 18 pages, 11 figures. Published version. A larger dataset was used in the analysis and a chapter explaining the effect of the dataset size is added in this version

Various groups recently argued that self-interacting vector field theories lack a well-defined time evolution when the field grows to large amplitudes, which has drastic consequences for models in gravity and high energy theory. Such field amplitudes can be a result of an external driving mechanism, or occur intrinsically, due to large values of the field and its derivatives in the initial data. This brings a natural question: is small amplitude initial data guaranteed to evolve indefinitely in these theories in the absence of an outside driving term? We answer this question in the negative, demonstrating that arbitrarily low amplitude initial data can still lead to the breakdown of the theory. Namely, ingoing spherically symmetric wave packets in more than one spatial dimensions grow as an inverse power of the radius, and their amplitudes can generically reach high enough values where time evolution ceases to exist. This simple example further establishes the pervasiveness of the pathology of self-interacting vector field theories., Comment: 5 pages, 1 figure. Published version in PRD

Self-interacting vectors are seeing a burst of interest where various groups demonstrated that the field evolution ends in finite time. Two nonequivalent criteria have been offered to identify this breakdown: (i) the vector constraint equation cannot be satisfied beyond a point where the breakdown occurs, (ii) the dynamics is governed by an effective metric that becomes singular at the breakdown. We show that (i) identifies a coordinate singularity, and can be removed by a change of coordinates. Hence, it does not signify a physical problem, and cannot determine the validity of a theory., Comment: 5 pages, 2 figures. Minor changes to bring into line with published version in PRL

Scalarization is a mechanism that endows strongly self-gravitating bodies, such as neutron stars and black holes, with a scalar-field configuration. It resembles a phase transition in that the scalar configuration appears only when a certain quantity that characterizes the compact object, for example, its compactness or spin, is beyond a threshold. A critical and comprehensive review of scalarization, including the mechanism itself, theories that exhibit it, its manifestation in neutron stars, black holes and their binaries, potential extension to other fields, and a thorough discussion of future perspectives, is provided., Comment: 51 pages, 24 figures. Review commissioned by Reviews of Modern Physics, submitted version, comments welcome. v2: more references, improved text, and typos corrected. Updated to match the published version

We show that self-interacting vector field theories exhibit unphysical behaviour even when they are not coupled to any external field. This means any theory featuring such vectors is in danger of being unphysical, an alarming prospect for many proposals in cosmology, gravity, high energy physics and beyond. The problem arises when vector fields with healthy configurations naturally reach a point where time evolution is mathematically ill-defined. We develop tools to easily identify this issue, and provide a simple and unifying framework to investigate it., Comment: 5+4 pages, 3+2 figures. Minor changes to bring into line with published version

We use neutron star mass and radius measurements to constrain the spontaneous scalarization phenomenon in scalar-tensor theories using Bayesian analysis. Neutron star structures in this scenario can be significantly different from the case of general relativity, which can be used to constrain the theory parameters. We utilize this idea to obtain lower bounds on the coupling parameter $\beta$ for the case of massless scalars. These constraints are currently weaker than the ones coming from binary observations, and they have relatively low precision due to the approximations in our method. Nevertheless, our results clearly demonstrate the power of the mass-radius data in testing gravity, and can be further improved with future observations. The picture is different for massive scalars, for which the same data is considerably less effective in constraining the theory parameters in an unexpected manner. We identify the main reason for this to be a large high-likelihood region in the parameter space where deviations from general relativity are relatively small. We hope this initial study to be an invitation to use neutron star structure measurements more commonly to test alternative theories in general., Comment: 18 pages, 14 figures. Published version

In recent papers it has been shown that a large class of vectorization mechanisms in gravity, which involve the vector fields becoming apparently tachyonic in some regime, are actually dominated by ghosts and non-perturbative behavior. Despite this, vectorized compact object solutions have previously been found, which raises the question of how, and if, the newly discovered ghosts are quenched in these cases. Here we develop the tools to study the perturbations of vectorized compact objects, and demonstrate that they suffer from ghosts and gradient instabilities as well. Thus, these vectorized objects do not represent the stable end point of a quenched instability unlike their scalarized counterparts in the spontaneous scalarization literature., Comment: 11 pages, 6 figures. Minor typos are corrected in this version

Spontaneous scalarization is a mechanism that allows a scalar field to go undetected in weak gravity environments and yet develop a nontrivial configuration in strongly gravitating systems. At the perturbative level it manifests as a tachyonic instability around spacetimes that solve Einstein's equations. The endpoint of this instability is a nontrivial scalar field configuration that can significantly modify a compact object's structure and can produce observational signatures of the scalar field's presence. Does such a mechanism exists for vector fields? Here we revisit the model that constitutes the most straightforward generalization of the original scalarization model to a vector field and perform a perturbative analysis. We show that a ghost appears as soon as the square of the naive effective mass squared becomes negative anywhere. This result poses a serious obstacle in generalizing spontaneous scalarization to vector fields., Comment: 12 pages. v2: corrections to Eqs. (23)-(24), new references. v3: matches published version

We show that gravity theories involving disformally transformed metrics in their matter coupling lead to spontaneous growth of various fields in a similar fashion to the spontaneous scalarization scenario in scalar-tensor theories. Scalar-dependent disformal transformations have been investigated in this context, and our focus is understanding the transformations that depend on more general fields. We show that vector-dependent disformal couplings can be obtained in various different ways, each leading to spontaneous vectorization as indicated by the instabilities in linearized equations of motion. However, we also show that spontaneous growth is not evident beyond vectors. For example, we could not identify a spontaneous growth mechanism for a spinor field through disformal transformations, even though there is a known example for conformal transformations. This invites further work on the fundamental differences between the two types of metric transformations. We argue that our results are relevant for observations in strong gravity such as gravitational wave detections due to their promise of large deviations from general relativity in this regime., Comment: 9 pages, to appear in Phys. Rev. D

We generalize the recently introduced extended scalar-tensor-Gauss-Bonnet (ESTGB) theories and their close relatives to include spontaneous growth of nonscalar fields such as vectors. This is analogous to the program that developed spontaneous tensorization from the original spontaneous scalarization theory of Damour and Esposito-Far\`ese (DEF). The new larger family of theories conserves the appeal of the DEF theory in terms of conforming to weak-field tests and also providing large signals in strong gravity. Moreover, they provide a much richer phenomenology including spontaneous tensorization of black holes as in ESTGB. These theories, together with other possible future extensions that we discuss, testify to the ubiquity of spontaneous growth in gravity. We also note that theories with derivative coupling require special attention since they can lead to potentially problematic higher derivatives in the equations of motion., Comment: 6 pages. Published version in PRD. Main conclusions have not changed, but there are substantial updates to the discussion of theories with derivative coupling

We study the Jordan frame formulation of generalizations of scalar-tensor theories conceived by replacing the scalar with other fields such as vectors. The generic theory in this family contains higher order time derivative terms in the Jordan frame action which is indicative of ill-posedness. However, we show that equations of motion can always be reduced to a second-order-in-time form as long as the original Einstein frame formulation is well posed. The inverse transformation from the Jordan frame back to the Einstein frame is not possible for all field values in all theories, but we obtain a fully invertible transformation for vector-tensor theories by a redefinition of the vector field. Our main motivation is a better understanding of spontaneous scalarization and its generalizations, however our conclusions are applicable to a wide class of theories. Jordan frame has been traditionally used for certain calculations in scalar-tensor theories of gravitation, and our results will help researchers generalize these results, enabling comparison to observational data.

We introduce gravity theories featuring spontaneously growing gauge fields where the growth is due to the Higgs mechanism. The underlying physics is inspired by the spontaneous scalarization phenomena in scalar-tensor theories. The tachyonic instability that causes the growth in spontaneous scalarization and its analog for vector fields is introduced not as an explicit potential term, but through a scalar coupling using a Higgs field. The resulting theories are distinct from previous examples of spontaneous tensorization in that they respect the gauge symmetry at the level of the action. Our results are valid for both Abelian and non-Abelian gauge theories, and this is the first study of the spontaneous growth of the latter. We discuss astrophysical implications of these theories and argue their relevance especially in the strong gravity regime., Comment: This version corrects some equations which were also updated in the online version at PRD. Conclusions are unchanged

We show that spinor fields nonminimally coupled to gravity can grow spontaneously in the presence of matter. We name this phenomenon spontaneous spinorization after the spontaneous scalarization scenario in scalar-tensor theories. Underlying reason for the growth of the spinor is an instability similar to the tachyon of spontaneous scalarization. We first present the structure of a tachyonic Dirac equation, and incorporate it into the matter coupling in gravity. This causes the zero-spinor solution to be unstable and leads to spontaneous growth. We investigate the behavior of the resulting theory for a spherically symmetric neutron star that has grown a spinor cloud. Spontaneous spinorization has the potential to lead to order-of-unity deviations from general relativity in strong fields in a similar manner to its close relative spontaneous scalarization. This makes the theory especially relevant to gravitational wave science and neutron star astrophysics., Comment: This version incorporates the corrections due to some missing terms in the equations which were published in the erratum at 10.1103/PhysRevD.100.029903. Conclusions are unchanged

We investigate instabilities and their regularization in theories of gravitation. Instabilities can be beneficial since their growth often leads to prominent observable signatures which makes them especially relevant to relatively low signal-to-noise ratio measurements such as gravitational wave detections. An indefinitely growing instability usually renders a theory unphysical, hence a desirable instability should also come with underlying physical machinery that stops the growth at finite values, i.e. regularization mechanisms. The prototypical gravity theory that presents such an instability is the spontaneous scalarization phenomena of scalar-tensor theories, which feature a tachyonic instability. We identify the regularization mechanisms in this theory, and show that they can be utilized to regularize other instabilities as well. Namely, we present theories where spontaneous growth is triggered by a ghost rather than a tachyon, and numerically calculate stationary solutions of scalarized neutron stars in these theories. We speculate on the possibility of regularizing known divergent instabilities in certain gravity theories using our findings, and discuss alternative theories of gravitation where regularized instabilities may be present. Even though we study many specific examples, our main point is the recognition of regularized instabilities as a common theme and unifying mechanism in a vast array of gravity theories., Comment: Updated version that reflects the changes in the published erratum. Conclusions are the same, but some of the missing terms in the equations are added. 6 pages

We show that the spontaneous scalarization scenario in scalar-tensor theories is a specific case of a more general phenomenon. The key fact is that the instability causing the spontaneous growth in scalars is due to the nonminimal coupling in the theory, and not related to the nature of the scalar. Another field with the same form of coupling undergoes spontaneous growth as well. We explicitly demonstrate this idea for vectors, naming it "spontaneous vectorization", and study spherically symmetric neutron stars in such a theory. We also comment on other tensor fields the idea can be applied, naming the general mechanism "spontaneous tensorization"., Comment: 5 pages, 2 figures

We study the effect of a mass term in the spontaneous scalarization of neutron stars, for a wide range of scalar field parameters and neutron star equations of state. Even though massless scalars have been the focus of interest in spontaneous scalarization so far, recent observations of binary systems rule out most of their interesting parameter space. We point out that adding a mass term to the scalar field potential is a natural extension to the model that avoids these observational bounds if the Compton wavelength of the scalar is small compared to the binary separation. Our model is formally similar to the asymmetron scenario recently introduced in application to cosmology, though here we are interested in consequences for neutron stars and thus consider a mass term that does not modify the geometry on cosmological scales. We review the allowed values for the mass and scalarization parameters in the theory given current binary system observations and black hole spin measurements. We show that within the allowed ranges, spontaneous scalarization can have nonperturbative, strong effects that may lead to observable signatures in binary neutron star or black hole-neutron star mergers, or even in isolated neutron stars.

We study the superradiant scattering of gravitational waves by a nearly extremal black hole (dimensionless spin $a=0.99$) by numerically solving the full Einstein field equations, thus including backreaction effects. This allows us to study the dynamics of the black hole as it loses energy and angular momentum during the scattering process. To explore the nonlinear phase of the interaction, we consider gravitational wave packets with initial energies up to $10%$ of the mass of the black hole. We find that as the incident wave energy increases, the amplification of the scattered waves, as well as the energy extraction efficiency from the black hole, is reduced. During the interaction the apparent horizon geometry undergoes sizable nonaxisymmetric oscillations. The largest amplitude excitations occur when the peak frequency of the incident wave packet is above where superradiance occurs, but close to the dominant quasinormal mode frequency of the black hole., Comment: 5 pages, 4 figures; revised to match PRD version

We derive the equations governing static, spherically symmetric vacuum solutions to the Einstein equations, as modified by the frame-dependent effective action arising from trace dynamics. We give analytic and numerical results for the solutions of these equations, first in polar coordinates, and then in isotropic coordinates. General features of the static case are that (i) there is no horizon, since $g_{00}$ is non-vanishing for finite values of the polar radius, and only vanishes (in isotropic coordinates) at the internal singularity, (ii) the Ricci scalar $R$ vanishes identically, and (iii) there is a physical singularity at cosmological distances. The large distance singularity may be an artifact of the static restriction, since we find that the behavior at large distances is altered in a time-dependent solution using the Mc Vittie Ansatz., Comment: 34 pages. This is an expansion of the previous submission to include results obtained in collaboration with Fethi M. Ramazanoglu

We present a new scheme for constructing initial data for the Einstein field equations using the conformal thin-sandwich formulation that does not assume conformal flatness or approximate Killing vectors. This includes a method for determining free data based on superposition, as well as a way to handle black hole singularities without excision. We numerically solve the constraint equations using a multigrid algorithm with mesh refinement. We demonstrate the efficacy of the method with initial data solutions for several applications: a quasicircular binary black hole merger, a dynamical capture black hole-neutron star merger, and an ultrarelativistic collision., Comment: 12 pages, 8 figures, PRD in production

We present a detailed analysis of results from a new study of the quantum evaporation of Callan-Giddings-Harvey-Strominger (CGHS) black holes within the mean-field approximation. This semi-classical theory incorporates back reaction. Our analytical and numerical calculations show that, while some of the assumptions underlying the standard evaporation paradigm are borne out, several are not. One of the anticipated properties we confirm is that the semi-classical space-time is asymptotically flat at right future null infinity, $\spr$, yet incomplete in the sense that null observers reach a future Cauchy horizon in finite affine time. Unexpected behavior includes that the Bondi mass traditionally used in the literature can become negative even when the area of the horizon is macroscopic; an improved Bondi mass remains positive until the end of semi-classical evaporation, yet the final value can be arbitrarily large relative to the Planck mass; and the flux of the quantum radiation at $\spr$ is non-thermal even when the horizon area is large compared to the Planck scale. Furthermore, if the black hole is initially macroscopic, the evaporation process exhibits remarkable universal properties. Although the literature on CGHS black holes is quite rich, these features had escaped previous analyses, in part because of lack of required numerical precision, and in part due to misinterpretation of certain properties and symmetries of the model. Finally, our results provide support for the full quantum scenario recently developed by Ashtekar, Taveras and Varadarajan, and also offer a number of interesting problems to the mathematical relativity and geometric analysis communities., Comment: Two citations added

Quantum evaporation of Callan-Giddings-Harvey-Strominger (CGHS) black holes is analyzed in the mean field approximation. This semi-classical theory incorporates back reaction. Detailed analytical and numerical calculations show that, while some of the assumptions underlying the standard evaporation paradigm are borne out, several are not. Furthermore, if the black hole is initially macroscopic, the evaporation process exhibits remarkable universal properties (which are distinct from the features observed in the simplified, exactly soluble models). Although the literature on CGHS black holes is quite rich, these features had escaped previous analyses, in part because of lack of required numerical precision, and in part because certain properties and symmetries of the model were not fully recognized. Finally, our results provide support for the full quantum gravity scenario recently developed by Ashtekar, Taveras and Varadarajan., Comment: 4 pages, 3 figures

We present details of a new numerical code designed to study the formation and evaporation of 2-dimensional black holes within the CGHS model. We explain several elements of the scheme that are crucial to resolve the late-time behavior of the spacetime, including regularization of the field variables, compactification of the coordinates, the algebraic form of the discretized equations of motion, and the use of a modified Richardson extrapolation scheme to achieve high-order convergence. Physical interpretation of our results will be discussed in detail elsewhere.

We provide an explicit analytical calculation that shows the asymptotic approach of the one dimensional Caldeira-Leggett model to thermal equilibrium in the high temperature and weak coupling limit. We investigate a free particle and a harmonic oscillator system, using both the Lindblad and the non-Lindblad type master equations for each case, and show that thermal equilibrium is reached exactly for the free particle and aproximately for the harmonic oscillator, irrespective of the initial preparation of the system. We also generalize our calculation to higher dimensions., Comment: 26 pages, no figures

We calculate the photon emission rate from a general atomic system in the mass- proportional CSL model. For an isolated charged particle emitting kilovolt gamma rays, our results agree with those obtained by Fu. For a neutral atomic system, photon emission is strongly suppressed for photon wavelengths much larger than the atomic radius. However, for kilovolt gamma rays, Fu's result is modified by a structure factor that is of order unity, giving no rate suppression. Our calculation is readily generalized to the case of non-white noise, noise couplings that are not mass-proportional, and general (non-Gaussian) spatial correlation functions, and corresponding results are given. We briefly discuss the implications of our calculation for upper bounds on the CSL model parameters., Comment: LaTex 16pages; minor revisions in published version v3, Added Note in v4