We study the thermodynamics and phase structures of the asymptotically flat dilatonic black holes in 4 dimensions, placed in a cavity {\it a la} York, in string theory for an arbitrary dilaton coupling. We consider these charged black systems in canonical ensemble for which the temperature at the wall of and the charge inside the cavity are fixed. We find that the dilaton coupling plays the key role in the underlying phase structures. The connection of these black holes to higher dimensional brane systems via diagonal (double) and/or direct dimensional reductions indicates that the phase structures of the former may exhaust all possible ones of the latter, which are more difficult to study, under conditions of similar settings. Our study also shows that a diagonal (double) dimensional reduction preserves the underlying phase structure while a direct dimensional reduction has the potential to change it.
We provide an efficient method of blowing up to compute leading order contributions of the recently introduced stringy canonical forms. The method is related to the well-known Hironaka's polyhedra game, and the given algorithm is also useful on similar problems, e.g. sector decomposition.
We show that several WZW coset models can be obtained by applying O(d,d) symmetry transformations (referred to as twisting) on WZW models. This leads to a conjecture that WZW models gauged by U(1)^n subgroup can be obtained by twisting (ungauged) WZW models. In addition, a class of solutions that describe charged black holes in four dimensions is derived by twisting SL(2,R)\times SU(2) WZW.
Static spherically symmetric asymptotically flat charged black hole solutions are constructed within the magnetic SU(3) sector of the 4-dimensional heterotic string effective action. They possess non-abelian hair in addition to the Coulomb magnetic field and are qualitatively similar to the Einstein-Yang-Mills colored SU(3) black holes except for the extremal case. In the extremality limit the horizon shrinks and the resulting geometry around the origin coincides with that of an extremal abelian dilatonic black hole with magnetic charge. Non-abelian hair exibits then typical sphaleron structur…
We study the leading $α^\prime$ corrections to the entropy of certain black holes with AdS$_5\times S^5$ asymptotics. We find that, in the supersymmetric limit, the entropy does not receive $α^\prime$ corrections. This result strengthens recent calculations that match the index of $\mathcal{N}=4$ Super-Yang-Mills with the corresponding partition function in the supersymmetric limit. In the small temperature regime, we find that the entropy corrections are concordant with the weak gravity conjecture.
We numerically study the superradiant instability of charged massless scalar field in the background of charged stringy black hole with mirror-like boundary condition. We compare the numerical result with the previous analytical result and show the dependencies of this instability upon various parameters of black hole charge $Q$, scalar field charge $q$, and mirror radius $r_m$. Especially, we have observed that imaginary part of BQN frequencies grows with the scalar field charge $q$ rapidly.
We introduce the notion of stringy E-function for an arbitrary normal irreducible algebraic variety X with at worst log-terminal singularities. We prove some basic properties of stringy E-functions and compute them explicitly for arbitrary Q-Gorenstein toric varieties. Using stringy E-functions, we propose a general method to define stringy Hodge numbers for projective algebraic varieties with at worst Gorenstein canonical singularities. This allows us to formulate the topological mirror duality test for arbitrary Calabi-Yau varieties with canonical singularities. In Appendix we explain non-Ar…
We study the timelike geodesics and geodesic deviation for a two-dimensional stringy blackhole spacetime in Schwarzschild gauge. We have analyzed the properties of effective potential along with the structure of the possible orbits for test particles with different settings of blackhole parameters. The exactly solvable geodesic deviation equation is used to obtain corresponding deviation vector. The nature of deviation and tidal force is also examined in view of the behavior of corresponding deviation vector.The results are also compared with an another two-dimensional stringy blackhole spacet…
We study the stability under perturbations of a charged four dimensional stringy black hole arising from gauging a previously studied WZW model. We find that the black hole is stable only in the extremal case $Q=M$.
Canonical forms of positive geometries play an important role in revealing hidden structures of scattering amplitudes, from amplituhedra to associahedra. In this paper, we introduce "stringy canonical forms", which provide a natural definition and extension of canonical forms for general polytopes, deformed by a parameter $α'$. They are defined by real or complex integrals regulated with polynomials with exponents, and are meromorphic functions of the exponents, sharing various properties of string amplitudes. As $α' \to 0$, they reduce to the usual canonical form of a polytope given by the Mi…
We study the motion of massive particles with electric and magnetic charges in the background of a magnetically charged Garfinkle-Horowitz-Strominger stringy black hole. We solve analytically the equations of motion of the test particles and we describe the orbital motion in terms of the Weierstrass elliptic functions. We find that there are critical values of the magnetic charge of the black hole and the magnetic charge of the test particle which characterize the bound and unbound orbits and we study two observables, the perihelion shift and the Lense-Thirring effect. The trajectories depend …
The stringy description for the instabilities in the $RR$ charged $D_{p}-\bar{D}_{p}$ pairs is now well understood in terms of the open string tachyon condensation. The quantum interpretation presumably via the stringy description for the instabilities in the $NSNS$-charged $F1-\bar{F1}$ and $NS5-\bar{NS5}$ pairs in IIA/IIB theories, however, has not been established yet. This would be partly because of the absence (for the $F1-\bar{F1}$ case) or our relatively poor understanding (for the $NS5-\bar{NS5}$ case) of their worldvolume (gauge theory) dynamics. In the present work, using the well-kn…
We investigate the stability of charged black holes in two-dimensional heterotic string theories that were recently discussed by McGuidan, Nappi and Yost. In the framework of small time-dependent perturbation, we find that these black holes are linearly stable.
Stringy canonical forms are a class of integrals that provide $α'$-deformations of the canonical form of any polytopes. For generalized associahedra of finite-type cluster algebra, there exist completely rigid stringy integrals, whose configuration spaces are the so-called binary geometries, and for classical types are associated with (generalized) scattering of particles and strings. In this paper we propose a large class of rigid stringy canonical forms for another class of polytopes, generalized permutohedra, which also include associahedra and cyclohedra as special cases (type $A_n$ and $B…
A canonical Lorentz invariant field theory extension of collective field theory of d=1 matrix models is presented. We show that the low density, discrete, sector of collective field theory includes single eigenvalue Euclidean instantons which tunnel between different vacua of the extended theory. These "stringy" instantons induce non-perturbative effective operators of strength $e^{-{1/g}}$. The relationship of the world sheet description of string theory and Liouville theory to the effective space-time theory is explained.
Non-local (alpha prime) corrections to Schwarzschild black holes are shown to invalidate the thermodynamical interpretation of black holes. In particular, the canonical and Bekenstein-Hawking temperatures are not equal. The particle number density of fields quantized in the (alpha prime modified) black hole background is no longer thermal. In the non-perturbative region (alpha prime going to infinity or mass going to zero), an analytic continuation to the number density is shown to vanish exponentially.
Flat electrical charged black holes in 5-dimensional anti-de Sitter space have been applied to the study of the phase diagram of quark matter via AdS/CFT correspondence. In such application it is argued that since the temperature of the quark gluon plasma is bounded away from zero, the dual black hole cannot be arbitrarily cold, but becomes unstable due to stringy instability once it reaches sufficiently low temperature. We study the stringy stability of flat dilaton black holes with dilaton coupling $α=1$ in asymptotically anti-de Sitter space and show that unlike the purely electrically char…
Motivated by the recent interest on models with varying constants and whether black hole physics can constrain such theories, two-dimensional charged stringy black holes are considered. We exploit the role of two-dimensional stringy black holes as toy models for exploring paradoxes which may lead to constrains on a theory. A two-dimensional charged stringy black hole is investigated in two different settings. Firstly, the two-dimensional black hole is treated as an isolated object and secondly, it is contained in a thermal environment. In both cases, it is shown that the temperature and the en…
It is reported that massive scalar fields can form bound states around Kerr black holes [C. Herdeiro, and E. Radu, Phys. Rev. Lett. 112, 221101 (2014)]. These bound states are called scalar clouds, which have a real frequency $ω=mΩ_H$, where $m$ is the azimuthal index and $Ω_H$ is the horizon angular velocity of Kerr black hole. In this paper, we study scalar clouds in a spherically symmetric background, i.e. charged stringy black holes, with the mirror-like boundary condition. These bound states satisfy the superradiant critical frequency condition $ω=qΦ_H$ for the charged scalar field, where…
We examine the two-dimensional spacetimes that emerge from string theory. We find all the solutions with no tachyons, and show that the only non-trivial solution is the black hole spacetime. We examine the role of duality in this picture. We then explore the thermodynamics of these solutions which is complicated by the fact that only in two spacetime dimensions is it impossible to redefine the dilaton field in terms of a canonical scalar field. Finally, we extend our analysis to the heterotic string, and briefly comment on exact, as opposed to perturbative, solutions.
Using the toroidal compactification of string theory on n-dimensional tori, Tn, we investigate dyonic objects in arbitrary dimensions. First, we present a class of dyonic black solutions formed by two different D-branes using a correspondence between toroidal cycles and objects possessing both magnetic and electric charges, belonging to %%%% dyonic gauge symmetry. This symmetry could be associated with electrically charged magnetic monopole solutions in stringy model buildings of the standard model extensions. Then, we consider in some details such black hole classes obtained from even dimensi…
Electrically charged black holes with flat event horizon in anti-de Sitter space have received much attention due to various applications in Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence, from modeling the behavior of quark-gluon plasma to superconductor. Crucial to the physics on the dual field theory is the fact that when embedded in string theory, black holes in the bulk may become vulnerable to instability caused by brane pair-production. Since dilaton arises naturally in the context of string theory, we study the effect of coupling dilaton to Maxwell field on the stabilit…
We consider hairy black hole solutions of Einstein-Yang-Mills-Dilaton theory, coupled to a Gauss-Bonnet curvature term, and we study their stability under small, spacetime-dependent perturbations. We demonstrate that the stringy corrections do not remove the sphaleronic instabilities of the coloured black holes with the number of unstable modes being equal to the number of nodes of the background gauge function. In the gravitational sector, and in the limit of an infinitely large horizon, the coloured black holes are also found to be unstable. Similar behaviour is exhibited by the magnetically…
We consider the two-dimensional "Schwarzschild" and "Reissner-Nordstrom" stringy black holes as systems of Casimir type. We explicitly calculate the energy-momentum tensor of a massless scalar field satisfying Dirichlet boundary conditions on two one-dimensional "walls". These results are obtained using the Wald's axioms. Thermodynamical quantities such as pressure, specific heat, isothermal compressibility and entropy of the two-dimensional stringy black holes are calculated. A comparison is made between the obtained results and the laws of thermodynamics. The results obtained for the extrema…
We continue the study of positive geometries underlying the {\it Grassmannian string integrals}, which are a class of "stringy canonical forms", or stringy integrals, over the positive Grassmannian mod torus action, $G_+(k,n)/T$. The leading order of any such stringy integral is given by the canonical function of a polytope, which can be obtained using the Minkowski sum of the Newton polytopes for the regulators of the integral, or equivalently given by the so-called scattering-equation map. The canonical function of the polytopes for Grassmannian string integrals, or the volume of their dual …
We present a generalization of the $U(1)^{2}$ charged dilaton black holes family whose main feature is that both $U(1)$ fields have electric and magnetic charges, the axion field still being trivial. We show the supersymmetry of these solutions in the extreme case, in which the corresponding generalization of the Bogomolnyi bound is saturated and a naked singularity is on the verge of being visible to external observers. Then we study the action of a subset of the $SL(2,R)$ group of electric-magnetic duality rotations that generates a non-trivial axion field on those solutions. This group of t…
Extreme magnetic dilaton black holes are promoted to exact solutions of heterotic string theory with unbroken supersymmetry. With account taken of alpha' corrections this is accomplished by supplementing the known solutions with SU(2) Yang-Mills vectors and scalars in addition to the already existing Abelian U(1) vector field. The solution has a simple analytic form and includes multi-black-holes. The issue of exactness of other black-hole-type solutions, including extreme dilaton electrically charged black holes and Taub-NUT solutions is discussed.
We investigate the thermodynamics of the RR charged two-dimensional type-0A black hole background at finite temperature, and compare with known 0A matrix model results. It has been claimed that there is a disagreement for the free energy between the spacetime and the dual matrix model. Here we find that this discrepancy is sensitive to how the cutoff is implemented on the spacetime side. In particular, the disagreement is resolved once we put the cutoff at a fixed distance away from the horizon, as opposed to a fixed position in space. Furthermore, the mass and the entropy of the black hole it…
With the new physical interpretation of quasinormal modes proposed by Maggiore, the quantum area spectra of black holes have been investigated recently. Adopting the modified Hod's treatment, results show that the area spectra for black holes are equally spaced and the spacings are in a unified form, $\triangle A=8π\hbar$, in Einstein gravity. On the other hand, following Kunstatter's method, the studies show that the area spectrum for a nonrotating black hole with no charge is equidistant. And for a rotating (or charged) black hole, it is also equidistant and independent of the angular moment…
In order to address the issues raised by the recent discovery of non-uniqueness of black holes in five dimensions, we construct a solution of string theory at low energies describing a five-dimensional spinning black ring with three charges that can be interpreted as D1-brane, D5-brane, and momentum charges. The solution possesses closed timelike curves (CTCs) and other pathologies, whose origin we clarify. These pathologies can be avoided by setting any one of the charges, e.g. the momentum, to zero. We argue that the D1-D5-charged black ring, lifted to six dimensions, describes the thermal e…
We present a new class of ${\cal N}=4$ supersymmetric quiver matrix models and argue that it describes the stringy low-energy dynamics of internally wrapped D-branes in four-dimensional anti-de Sitter (AdS) flux compactifications. The Lagrangians of these models differ from previously studied quiver matrix models by the presence of mass terms, associated with the AdS gravitational potential, as well as additional terms dictated by supersymmetry. These give rise to dynamical phenomena typically associated with the presence of fluxes, such as fuzzy membranes, internal cyclotron motion and the ap…
We study the BPS black hole solutions of the (truncated) action for heterotic string theory compactified on a six-torus. The O(3,Z) duality symmetry of the theory, together with the bound state interpretation of extreme black holes, is used to generate the whole spectrum of the solutions. The corresponding spacetime structures, written in terms of the string metric, are analyzed in detail. In particular, we show that only the elementary solutions present naked singularities. The bound states have either null singularities (electric solutions) or are regular (magnetic or dyonic solutions) with …
In a seminal paper by Brown et al. [Phys. Rev. Lett. 116, no. 19, 191301 (2016)] a new conjecture was proposed, namely it was argued that the quantum complexity of a holographic state is equal to action of a Wheeler-DeWitt patch in the late time limit suggesting that the fastest computer in nature are the black holes. Motivated by this conjecture, in the present paper, we study the action growth rate for different types of black holes such as dyonic, nonlinear charge, stringy hair, black hole with a global monopole and a cosmic string. In general we find that action growth rates of the Wheeler…
We use the anti-de Sitter (AdS) conformal field theory correspondence to calculate the conserved charges and the Euclidean actions of the charged rotating black string in four dimensions both in the canonical and the grand-canonical ensemble. The four-dimensional solution of the Einstein-Maxwell equations with a positive cosmological constant is introduced, and its conserved quantities and actions for fixed charge and fixed electric potential are calculated. We also study the thermodynamics of the asymptotically AdS black strings and perform a stability analysis both in the canonical and the g…
In dipole-dipole scattering at large rapidity χ={\rm ln}(s/s_0), the induced instanton on the string worldsheet carries entropy S_k=2(α_{Pk}-1)χwith α_{Pk}-1 the pomeron intercept for a dipole source of N-ality k. This stringy entropy is neither coherent nor thermal. We argue that it is released promptly over a time t_R\approx (b / χ)^3 / (4 α') with α'/2 the pomeron slope and b the impact parameter. This stringy entropy may explain the 3/2 jump in the total charged multiplicities at about 10 participants reported over a wide range of collider energies by PHOBOS. We predict the charged multipl…
Recently striking multiple relations have been found between pure state 2 and 3-qubit entanglement and extremal black holes in string theory. Here we add further mathematical similarities which can be both useful in string and quantum information theory. In particular we show that finding the frozen values of the moduli in the calculation of the macroscopic entropy in the STU model, is related to finding the canonical form for a pure three-qubit entangled state defined by the dyonic charges. In this picture the extremization of the BPS mass with respect to moduli is connected to the problem of…
The scattering of R-R gauge bosons off of Dirichlet p-branes is computed to leading order in the string coupling. The results are qualitatively similar to those found in the scattering of massless NS-NS bosons: all p-branes with p >= 0 exhibit stringy properties, in particular the Regge behavior. Both the R-R and NS-NS scattering amplitudes agree in the limit of small momentum transfer with scattering off the extremal R-R charged p-brane solutions found in the low-energy supergravities. We interpret this as evidence that Dirichlet-branes are an exact world-sheet description of the extremal p-b…
We study the thermodynamic stability of charged black holes in gauged supergravity theories in D=5, D=4 and D=7. We find explicitly the location of the Hawking-Page phase transition between charged black holes and the pure anti-de Sitter space-time, both in the grand-canonical ensemble, where electric potentials are held fixed, and in the canonical ensemble, where total charges are held fixed. We also find the explicit local thermodynamic stability constraints for black holes with one non-zero charge. In the grand-canonical ensemble, there is in general a region of phase space where neither th…
The energy condition inequalities for the matter stress energy comprised out of the dilaton and Maxwell fields in the dilaton-Maxwell gravity theories emerging out of string theory are examined in detail. In the simplistic 1+1 dimensional models, $R\le 0$ (where $R$ is the Ricci scalar), turns out to be the requirement for ensuring focusing of timelike geodesics. In 3+1 dimensions, we outline the requirements on matter for pure dilaton theories-these in turn constrain the functional forms of the dilaton. Furthermore, in charged dilaton gravity a curious opposite behaviour of the matter stress …
This is a continuation of our earlier work where we constructed a phenomenologically motivated effective action of the boundary gauge theory at finite temperature and finite gauge coupling on $S^3 \times S^1$. In this paper, we argue that this effective action qualitatively reproduces the gauge theory representing various bulk phases of R-charged black hole with Gauss-Bonnet correction. We analyze the system both in canonical and grand canonical ensemble.
We compute the Euclidean actions of a $d$-dimensional charged rotating black brane both in the canonical and the grand-canonical ensemble through the use of the counterterms renormalization method, and show that the logarithmic divergencies associated with the Weyl anomalies and matter field vanish. We obtain a Smarr-type formula for the mass as a function of the entropy, the angular momenta, and the electric charge, and show that these quantities satisfy the first law of thermodynamics. Using the conserved quantities and the Euclidean actions, we calculate the thermodynamics potentials of the…
As in the grand canonical treatment of Reissner - Nordström black holes in anti-de Sitter spacetime, the canonical ensemble formulation also shows that non-extremal black holes tend to have lower action than extremal ones. However, some small non-extremal black holes have higher action, leading to the possibility of transitions between non-extremal and extremal black holes.
There exists a dramatic difference in phase structure between charged black Dp-branes with $p < 5$ and charged black D5 or D6 branes. In [1], we found that the phase structure of charged black D5 system can be changed qualitatively to that of charged black Dp with $p < 5$ by adding the delocalized D1 branes but the similar change does not happen for the charged black D6 system through adding the delocalized D2 branes (Note that both D1/D5 and D2/D6 belong to the same type of D(p - 4)/Dp system). Adding the delocalized D4 branes to the black D6 branes doesn't work, either. In this paper, we con…
In this work, we investigate the thermodynamical behavior of charged AdS black holes from $f(R)$ gravity corrections with a constant Ricci scalar curvature in the grand-canonical ensemble. Using the holographic entanglement entropy, we show that the physical observables behave as in the case of the thermal entropy. By performing numerical computations associated with the thermodynamical quantities versus the entanglement entropy, we confirm that the same phase portrait persists in the holographic framework. In the grand-canonical ensemble, the present result supports the former finding which r…
We discuss the canonical quantization of Quantum Electrodynamics in $2+1$ dimensions, with a Chern-Simons topological mass term and gauge-covariant coupling to a Dirac spinor field. A gauge-fixing term is used which generates a canonical momentum for $A_0$, so that there are no primary constraints on operator-valued fields. Gauss's Law and the gauge condition, $A_0=0$, are implemented by embedding the formulation in an appropriate physical subspace, in which state vectors remain naturally, in the course of time evolution. The photon propagator is derived from the canonical theory. The electric…
In this paper, we explore means which can be used to change qualitatively the phase structure of charged black systems. For this, we consider a system of black D1/D5 (or its S-dual F/NS5). We find that the delocalized charged black D-strings (F-strings) alone share the same phase structure as the charged black D5 branes (NS5-branes), having no van der Waals-Maxwell liquid-gas type. However, when the two are combined to form D1/D5 (F/NS5), the resulting phase diagram has been changed dramatically to a richer one, containing now the above liquid-gas type. The effect of adding the charged D-strin…
We consider constrained multi-Hamiltonian formulation for the extended Chern-Simons theory with higher derivatives of arbitrary finite order. The order $n$ extension of the theory admits $(n-1)$-parametric series of conserved tensors. The $00$-component of any representative of the series can be chosen as Hamiltonian. The theory admits a series of Hamiltonian formulations, including the canonical Ostrogradski formulation. The Hamiltonian formulations with different Hamiltonians are not connected by canonical transformations. Also, we demonstrate the inclusion of stable interactions with charge…
We study the thermodynamics in the grand canonical ensemble of D-dimensional charged Gauss-Bonnet-AdS black holes in the extended phase space. We find that the usual small-large black hole phase transition, which exhibits analogy with the Van de Waals liquid-gas system holds in five-dimensional spherical charged Gauss-Bonnet-AdS black holes when its potential is fixed within the range $0<Φ<\frac{\sqrt{3}π}{4}$. For the other higher dimensional and topological charged Gauss-Bonnet-AdS black holes, there is no such phase transition. In the limiting case, Reissner-Nordstrom-AdS black holes, with …
In this thesis, two different aspects of asymptotically charged rotating black branes in various dimensions are studied. In the first part, the thermodynamics of these spacetimes is investigated, while in the second part the no hair theorem for these spacetimes in four dimensions is considered. In part I, first, the Euclidean actions of a d-dimensional charged rotating black brane are computed through the use of the counterterms renormalization method both in the canonical and the grand-canonical ensemble, and it is shown that the logarithmic divergencies associated to the Weyl anomalies and m…
The general relativity vacuum black holes (BHs) can be scalarised in models where a scalar field non-minimally couples to the Gauss-Bonnet (GB) invariant. Such GB scalarisation comes in two flavours, depending on the GB sign that triggers the phenomenon. Hereafter these two cases are termed GB$^\pm$ scalarisation. For vacuum BHs, only GB$^+$ scalarisation is possible in the static case, while GB$^-$ scalarisation is $spin$ induced. But for electrovacuum BHs, GB$^-$ is also $charged$ induced. We discuss the GB$^-$ scalarisation of Reissner-Nordström and Kerr-Newman BHs, discussing zero modes an…
We investigate phase transitions and critical phenomena of four dimensional dyonic charged AdS black holes in the framework of thermodynamic geometry. In a mixed canonical grand canonical ensemble with a fixed electric charge and varying magnetic charge these black holes exhibit liquid gas like first order phase transition culminating in a second order critical point similar to the Van der Waals gas. We show that the thermodynamic scalar curvature R for these black holes follow our proposed geometrical characterization of the R-crossing Method for the first order liquid gas like phase transiti…
In this paper, by analyzing the thermodynamic properties of charged AdS black hole and asymptotically flat space-time charged black hole in the vicinity of the critical point, we establish the correspondence between the thermodynamic parameters of asymptotically flat space-time and nonasymptotically flat space-time, based on the equality of black hole horizon area in the two different space-time. The relationship between the cavity radius (which is introduced in the study of asymptotically flat space-time charged black holes) and the cosmological constant (which is introduced in the study of n…
In this talk some essential features of stringy black holes are described. We consider charged four-dimensional axion-dilaton black holes. The Hawking temperature and the entropy of all solutions are shown to be simple functions of the squares of supercharges, defining the positivity bounds. Spherically symmetric and multi black hole solutions are presented. The extreme solutions have some unbroken supersymmetries. Axion-dilaton black holes with zero entropy and zero area of the horizon form a family of stable particle-like objects, which we call holons. We discuss the possibility of splitting…
The physical properties of Reissner-Nordstrom black holes in (n+1)-dimensional anti-de Sitter spacetime are related, by a holographic map, to the physics of a class of n-dimensional field theories coupled to a background global current. Motivated by that fact, and the recent observations of the striking similarity between the thermodynamic phase structure of these black holes (in the canonical ensemble) and that of the van der Waals-Maxwell liquid-gas system, we explore the physics in more detail. We study fluctuations and stability within the equilibrium thermodynamics, examining the specific…
We use the canonical energy method of Hollands and Wald to study the stability properties of asymptotically flat, stationary solutions to a very general class of theories, consisting of a set of coupled scalar fields and p-form gauge fields, minimally coupled to gravity. We find that, provided certain very weak assumptions are made on the coupling coefficients, the canonical energy method can be extended to this class of theories. In particular, we construct a quadratic form E on initial data perturbations, with the properties that E > 0 on all perturbations indicates stability, while E < 0 on…
