Results for "Peter K. Friz"

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Continuity of the Ito-Map for Hoelder rough paths with applications to the support theorem in Hoelder normApr 30 2003Aug 08 2003Lyons' Rough Path theory is currently formulated in p-variation topology. We extend his main-result, the Universal Limit Theorem, to a stronger Hoelder topology. Several approximations to Brownian Rough Paths are studied. As application of our approach, ... More
Cubature on Wiener space: pathwise convergenceApr 16 2013Cubature on Wiener space [Lyons, T.; Victoir, N.; Proc. R. Soc. Lond. A 8 January 2004 vol. 460 no. 2041 169-198] provides a powerful alternative to Monte Carlo simulation for the integration of certain functionals on Wiener space. More specifically, ... More
On the existence of SLE trace: finite energy drivers and non-constant $κ$Nov 09 2015Existence of Loewner trace is revisited. We identify finite energy paths (the "skeleton of Wiener measure") as natural class of regular drivers for which we find simple and natural estimates in terms of their (Cameron--Martin) norm. Secondly, now dealing ... More
Canonical RDEs and general semimartingales as rough pathsApr 26 2017Apr 26 2018In the spirit of Marcus canonical stochastic differential equations, we study a similar notion of rough differential equations (RDEs), notably dropping the assumption of continuity prevalent in the rough path literature. A new metric is exhibited in which ... More
On the regularity of SLE traceNov 01 2016We revisit regularity of SLE trace, for all $\kappa \neq 8$, and establish Besov regularity under the usual half-space capacity parametrization. With an embedding theorem of Garsia--Rodemich--Rumsey type, we obtain finite moments (and hence almost surely) ... More
Differential equations driven by rough paths with jumpsSep 15 2017We develop the rough path counterpart of It\^o stochastic integration and - differential equations driven by general semimartingales. This significantly enlarges the classes of (It\^o / forward) stochastic differential equations treatable with pathwise ... More
Stochastic scalar conservation laws driven by rough pathsMar 26 2014We prove the existence and uniqueness of solutions to a class of stochastic scalar conservation laws with joint space-time transport noise and affine-linear noise driven by a geometric p-rough path. In particular, stability of the solutions with respect ... More
Precise asymptotics: robust stochastic volatility modelsNov 01 2018We present a new methodology to analyze large classes of (classical and rough) stochastic volatility models, with special regard to short-time and small noise formulae for option prices. Our main tool is the theory of regularity structures, which we use ... More
Malliavin Calculus for regularity structures: the case of gPAMNov 28 2015Malliavin calculus is implemented in the context of [M. Hairer, A theory of regularity structures, Invent. Math. 2014]. This involves some constructions of independent interest, notably an extension of the structure which accomodates a robust, and purely ... More
Rough path metrics on a Besov--Nikolskii type scaleSep 11 2016Apr 25 2017It is known, since the seminal work [T. Lyons, Differential equations driven by rough signals, Rev. Mat. Iberoamericana, 14 (1998)], that the solution map associated to a controlled differential equation is locally Lipschitz continuous in $q$-variation ... More
Stochastic partial differential equations: a rough path viewDec 19 2014We discuss regular and weak solutions to rough partial differential equations (RPDEs), thereby providing a (rough path-)wise view on important classes of SPDEs. In contrast to many previous works on RPDEs, our definition gives honest meaning to RPDEs ... More
On the Variational Regularity of Cameron-Martin pathsMay 13 2013Oct 31 2013It is a well-known fact that finite rho-variation of the covariance (in 2D sense) of a general Gaussian process implies finite rho-variation of Cameron-Martin paths. In the special case of fractional Brownian motion (think: 2H=1/rho), in the rougher than ... More
Rough path metrics on a Besov-Nikolskii type scaleSep 11 2016It is known, since the seminal work [T. Lyons: Differential equations driven by rough signals, In: Rev. Mat. Iberoam. (1998)], that the It\^{o}-map is locally Lipschitz continuous in $q$-variation resp. $1/q$-H\"{o}lder type (rough path) metrics, for ... More
Regularity of the Schramm-Loewner field and refined Garsia-Rodemich-Rumsey estimatesJun 27 2019Schramm-Loewner evolution (SLE$_\kappa$) is classically studied via Loewner evolution with half-plane capacity parametrization, driven by $\sqrt{\kappa}$ times Brownian motion. This yields a (half-plane) valued random field $\gamma = \gamma (t, \kappa; ... More
Parabolic comparison revisited and applicationsFeb 28 2011We consider the Cauchy-Dirichlet problem $\partial_t u - F(t,x,u,Du,D^2 u) = 0 on (0,T)\times \R^n$ in viscosity sense. Comparison is established for bounded semi-continuous (sub-/super-)solutions under structural assumption (3.14) of the User's Guide ... More
How to make Dupire's local volatility work with jumpsFeb 22 2013There are several (mathematical) reasons why Dupire's formula fails in the non-diffusion setting. And yet, in practice, ad-hoc preconditioning of the option data works reasonably well. In this note we attempt to explain why. In particular, we propose ... More
The Jain-Monrad criterion for rough paths and applications to random Fourier series and non-Markovian Hörmander theoryJul 12 2013Feb 10 2016We discuss stochastic calculus for large classes of Gaussian processes, based on rough path analysis. Our key condition is a covariance measure structure combined with a classical criterion due to Jain and Monrad [Ann. Probab. 11 (1983) 46-57]. This condition ... More
A note on higher dimensional $p$-variationFeb 22 2011We discuss $p$-variation regularity of real-valued functions defined on $[0,T]^2$, based on rectangular increments. When $p>1$, there are two slightly different notions of $p$-variation; both of which are useful in the context of Gaussian rough paths. ... More
Large Deviation Principle for Enhanced Gaussian ProcessesDec 10 2005Nov 23 2006We study large deviation principles for Gaussian processes lifted to the free nilpotent group of step N. We apply this to a large class of Gaussian processes lifted to geometric rough paths. A large deviation principle for enhanced (fractional) Brownian ... More
Superdiffusive limits for deterministic fast-slow dynamical systemsJul 10 2019We consider deterministic fast-slow dynamical systems on $\mathbb{R}^m\times Y$ of the form \[ \begin{cases} x_{k+1}^{(n)} = x_k^{(n)} + n^{-1} a(x_k^{(n)}) + n^{-1/\alpha} b(x_k^{(n)}) v(y_k)\;,\quad y_{k+1} = f(y_k)\;, \end{cases} \] where $\alpha\in(1,2)$. ... More
The enhanced Sanov theorem and propagation of chaosFeb 25 2016We establish a Sanov type large deviation principle for an ensemble of interacting Brownian rough paths. We give also an application to propagation of chaos for a class for interacting diffusions with limit of McKean-Vlasov type.
Spatial rough path lifts of stochastic convolutionsOct 31 2012Nov 01 2013We present sufficient conditions for finite controlled rho-variation of the covariance of Gaussian processes with stationary increments, based on concavity or convexity of their variance function. The motivation for this type of conditions comes from ... More
The enhanced Sanov theorem and propagation of chaosFeb 25 2016Nov 28 2016We establish a Sanov type large deviation principle for an ensemble of interacting Brownian rough paths. As application a large deviations for the ($k$-layer, enhanced) empirical measure of weakly interacting diffusions is obtained. This in turn implies ... More
General Rough integration, Levy Rough paths and a Levy--Kintchine type formulaDec 24 2012Nov 27 2014We consider rough paths with jumps. In particular, the analogue of Lyons' extension theorem and rough integration are established in a jump setting, offering a pathwise view on stochastic integration against cadlag processes. A class of Levy rough paths ... More
On Uniformly Subelliptic Operators and Stochastic AreaAug 31 2006Nov 01 2007We consider uniformly subelliptic operators on certain unimodular Lie groups of polynomial growth. It was shown by Saloff-Coste and Stroock that classical results of De Giorgi, Nash, Moser, Aronson extend to this setting. It was then observed by Sturm ... More
On the splitting-up method for rough (partial) differential equationsAug 03 2010This article introduces the splitting method to systems responding to rough paths as external stimuli. The focus is on nonlinear partial differential equations with rough noise but we also cover rough differential equations. Applications to stochastic ... More
Backward stochastic differential equations with rough driversAug 02 2010Backward stochastic differential equations (BSDEs) in the sense of Pardoux-Peng [Backward stochastic differential equations and quasilinear parabolic partial differential equations, Lecture Notes in Control and Inform. Sci., 176, 200--217, 1992] provide ... More
Rough path stability of (semi-)linear SPDEsMay 11 2010Jan 16 2013We give meaning to linear and semi-linear (possibly degenerate) parabolic partial differential equations with (affine) linear rough path noise and establish stability in a rough path metric. In the case of enhanced Brownian motion (Brownian motion with ... More
Don't stay local - extrapolation analytics for Dupire's local volatilityMay 06 2011A robust implementation of a Dupire type local volatility model is an important issue for every option trading floor. Typically, this (inverse) problem is solved in a two step procedure : (i) a smooth parametrization of the implied volatility surface; ... More
From rough path estimates to multilevel Monte CarloMay 24 2013Jun 17 2016New classes of stochastic differential equations can now be studied using rough path theory (e.g. Lyons et al. [LCL07] or Friz--Hairer [FH14]). In this paper we investigate, from a numerical analysis point of view, stochastic differential equations driven ... More
Smile Asymptotics II: Models with Known Moment Generating FunctionAug 24 2006In a recent article the authors obtained a formula which relates explicitly the tail of risk neutral returns with the wing behavior of the Black Scholes implied volatility smile. In situations where precise tail asymptotics are unknown but a moment generating ... More
Regular Variation and Smile AsymptoticsMar 06 2006Mar 07 2006We consider risk-neutral returns and show how their tail asymptotics translate directly to asymptotics of the implied volatility smile, thereby sharpening Roger Lee's celebrated moment formula. The theory of regular variation provides the ideal mathematical ... More
Non-standard approximations of the Ito-mapAug 03 2008The Wong-Zakai theorem asserts that ODEs driven by "reasonable" (e.g. piecewise linear) approximations of Brownian motion converge to the corresponding Stratonovich stochastic differential equation. With the aid of rough path analysis, we study "non-reasonable" ... More
Approximations of the Brownian Rough Path with Applications to Stochastic AnalysisAug 26 2003A geometric p-rough path can be seen to be a genuine path of finite p-variation with values in a Lie group equipped with a natural distance. The group and its distance lift (R^{d},+,0) and its Euclidean distance. This approach allows us to easily get ... More
Densities for Rough Differential Equations under Hoermander's ConditionAug 28 2007We consider stochastic differential equations dY=V(Y)dX driven by a multidimensional Gaussian process X in the rough path sense. Using Malliavin Calculus we show that Y(t) admits a density for t in (0,T] provided (i) the vector fields V=(V_1,...,V_d) ... More
Convergence rates for the full Gaussian rough pathsAug 04 2011May 04 2012Under the key assumption of finite {\rho}-variation, {\rho}\in[1,2), of the covariance of the underlying Gaussian process, sharp a.s. convergence rates for approximations of Gaussian rough paths are established. When applied to Brownian resp. fractional ... More
Partial differential equations driven by rough pathsMar 14 2008Mar 24 2008We study a class of linear first and second order partial differential equations driven by weak geometric $p$-rough paths, and prove the existence of a unique solution for these equations. This solution depends continuously on the driving rough path. ... More
A generalized Fernique theorem and applicationsApr 12 2010Apr 13 2010We prove a generalisation of Fernique's theorem which applies to a class of (measurable) functionals on abstract Wiener spaces by using the isoperimetric inequality. Our motivation comes from rough path theory where one deals with iterated integrals of ... More
Integrability of (non-)linear rough differential equations and integralsApr 04 2011Mar 08 2012Integrability properties of (classical, linear, linear growth) rough differential equations (RDEs) are considered, the Jacobian of the RDE flow driven by Gaussian signals being a motivating example. We revisit and extend some recent ground-breaking work ... More
The Burkholder-Davis-Gundy Inequality for Enhanced MartingalesAug 31 2006Multi-dimensional continuous local martingales, enhanced with their stochastic area process, give rise to geometric rough paths with a.s. finite homogenous p-variation, p>2. Here we go one step further and establish quantitative bounds of the p-variation ... More
A Variation Embedding Theorem and ApplicationsNov 21 2005Fractional Sobolev spaces, also known as Besov or Slobodetzki spaces, arise in many areas of analysis, stochastic analysis in particular. We prove an embedding into certain q-variation spaces and discuss a few applications. First we show q-variation regularity ... More
Differential Equations Driven by Gaussian Signals IJul 02 2007We consider multi-dimensional Gaussian processes and give a new condition on the covariance, simple and sharp, for the existence of stochastic area(s). Gaussian rough paths are constructed with a variety of weak and strong approximation results. Together ... More
Differential Equations Driven by Gaussian Signals IINov 05 2007Large classes of multi-dimensional Gaussian processes can be enhanced with stochastic Levy area(s). In a previous paper, we gave sufficient and essentially necessary conditions, only involving variational properties of the covariance. Following T. Lyons, ... More
Isoperimetry and Rough Path RegularityNov 01 2007Optimal sample path properties of stochastic processes often involve generalized H\"{o}lder- or variation norms. Following a classical result of Taylor, the exact variation of Brownian motion is measured in terms of $\psi (x) \equiv $ $x^{2}/\log \log ... More
Doob--Meyer for rough pathsMay 11 2012Recently, Hairer--Pillai proposed the notion of $\theta$-roughness of a path which leads to a deterministic Norris lemma. In the Gubinelli framework (Hoelder, level 2) of rough paths, they were then able to prove a Hoermander type result (SDEs driven ... More
A Note on the Notion of Geometric Rough PathsMar 06 2004We use simple sub-Riemannian techniques to prove that an arbitrary geometric p-rough path in the sense of Lyons (98) is the limit in sup-norm of a sequence of canonically lifted smooth paths, which are uniformly bounded in p-variation, clarifying the ... More
Euler Estimates of Rough Differential EquationsFeb 16 2006We consider controlled differential equations and give new estimates for higher order Euler schemes. Our proofs are inspired by recent work of A. M. Davie who considers first and second order schemes. In order to implement the general case we make systematic ... More
Deterministic homogenization for discrete-time fast-slow systems under optimal moment assumptionsMar 25 2019We consider discrete-time fast-slow systems of the form $$ X^{(n)}_{k+1} = X^{(n)}_k + n^{-1}a_n(X_k^{(n)},Y_k^{(n)}) + n^{-1/2}b_n(X_k^{(n)},Y_k^{(n)})\;, \quad Y_{k+1}^{(n)} = T_nY_k^{(n)}\;.$$ We give conditions under which the dynamics of the slow ... More
Varadhan's formula, conditioned diffusions, and local volatilitiesNov 06 2013Jun 14 2016Motivated by marginals-mimicking results for It\^o processes via SDEs and by their applications to volatility modeling in finance, we discuss the weak convergence of the law of a hypoelliptic diffusions conditioned to belong to a target affine subspace ... More
Multiscale systems, homogenization, and rough pathsDec 04 2017Mar 25 2019In recent years, substantial progress was made towards understanding convergence of fast-slow deterministic systems to stochastic differential equations. In contrast to more classical approaches, the assumptions on the fast flow are very mild. We survey ... More
Short-time near-the-money skew in rough fractional volatility modelsMar 15 2017Mar 09 2018We consider rough stochastic volatility models where the driving noise of volatility has fractional scaling, in the "rough" regime of Hurst parameter $H < 1/2$. This regime recently attracted a lot of attention both from the statistical and option pricing ... More
On the probability density function of basketsJun 12 2013Apr 05 2016The state price density of a basket, even under uncorrelated Black-Scholes dynamics, does not allow for a closed from density. (This may be rephrased as statement on the sum of lognormals and is especially annoying for such are used most frequently in ... More
Support theorem for a singular semilinear stochastic partial differential equationSep 15 2014Mar 04 2016We consider the generalized parabolic Anderson equation (gPAM) in 2 dimensions with periodic boundary. This is an example of a singular semilinear stochastic partial differential equations, solutions of which require renormalization and have only be understood ... More
Eikonal equations and pathwise solutions to fully non-linear SPDEsFeb 15 2016We study the existence and uniqueness of the stochastic viscosity solutions of fully nonlinear, possibly degenerate, second order stochastic pde with quadratic Hamiltonians associated to a Riemannian geometry. The results are new and extend the class ... More
Good rough path sequences and applications to anticipating stochastic calculusJul 31 2007We consider anticipative Stratonovich stochastic differential equations driven by some stochastic process lifted to a rough path. Neither adaptedness of initial point and vector fields nor commuting conditions between vector field is assumed. Under a ... More
Semi-Closed Form Cubature and Applications to Financial Diffusion ModelsSep 24 2010Cubature methods, a powerful alternative to Monte Carlo due to Kusuoka~[Adv.~Math.~Econ.~6, 69--83, 2004] and Lyons--Victoir~[Proc.~R.~Soc.\\Lond.~Ser.~A 460, 169--198, 2004], involve the solution to numerous auxiliary ordinary differential equations. ... More
A regularity structure for rough volatilityOct 20 2017A new paradigm recently emerged in financial modelling: rough (stochastic) volatility, first observed by Gatheral et al. in high-frequency data, subsequently derived within market microstructure models, also turned out to capture parsimoniously key stylized ... More
Stochastic control with rough pathsMar 28 2013May 20 2013We study a class of controlled rough differential equations. It is shown that the value function satisfies a HJB type equation; we also establish a form of the Pontryagin maximum principle. Deterministic problems of this type arise in the duality theory ... More
Physical Brownian motion in magnetic field as rough pathFeb 11 2013The indefinite integral of the homogenized Ornstein-Uhlenbeck process is a well-known model for physical Brownian motion, modelling the behaviour of an object subject to random impulses [L. S. Ornstein, G. E. Uhlenbeck: On the theory of Brownian Motion. ... More
Good Rough Path Sequences and Applications to Anticipating & Fractional Stochastic CalculusJan 13 2005We consider anticipative Stratonovich stochastic differential equations driven by some stochastic process (not necessarily a semi-martingale). No adaptedness of initial point or vector fields is assumed. Under a simple condition on the stochastic process, ... More
Pathwise stability of likelihood estimators for diffusions via rough pathsNov 05 2013Sep 28 2016We consider the classical estimation problem of an unknown drift parameter within classes of nondegenerate diffusion processes. Using rough path theory (in the sense of T. Lyons), we analyze the Maximum Likelihood Estimator (MLE) with regard to its pathwise ... More
A (rough) pathwise approach to a class of non-linear stochastic partial differential equationsFeb 19 2009Nov 08 2010We consider nonlinear parabolic evolution equations of the form $\partial_{t}u=F(t,x,Du,D^{2}u) $, subject to noise of the form $H(x,Du) \circ dB$ where $H$ is linear in $Du$ and $\circ dB$ denotes the Stratonovich differential of a multidimensional Brownian ... More
Is the minimum value of an option on variance generated by local volatility?Jan 22 2010Jan 05 2011We discuss the possibility of obtaining model-free bounds on volatility derivatives, given present market data in the form of a calibrated local volatility model. A counter-example to a wide-spread conjecture is given.
Varieties of Signature TensorsApr 23 2018Jan 15 2019The signature of a parametric curve is a sequence of tensors whose entries are iterated integrals. This construction is central to the theory of rough paths in stochastic analysis. It is here examined through the lens of algebraic geometry. We introduce ... More
Non-degeneracy of Wiener functionals arising from rough differential equationsJul 02 2007Nov 12 2007Malliavin Calculus is about Sobolev-type regularity of functionals on Wiener space, the main example being the Ito map obtained by solving stochastic differential equations. Rough path analysis is about strong regularity of solution to (possibly stochastic) ... More
Option Pricing in the Moderate Deviations RegimeApr 05 2016We consider call option prices in diffusion models close to expiry, in an asymptotic regime ("moderately out of the money") that interpolates between the well-studied cases of at-the-money options and out-of-the-money fixed-strike options. First and higher ... More
From random walks to rough pathsOct 15 2008Donsker's invariance principle is shown to hold for random walks in rough path topology. As application, we obtain Donsker-type weak limit theorems for stochastic integrals and differential equations.
The Bismut-Elworthy-Li formula for jump-diffusions and applications to Monte Carlo pricing in financeApr 13 2006May 08 2007We extend the Bismut-Elworthy-Li formula to non-degenerate jump diffusions and "payoff" functions depending on the process at multiple future times. In the spirit of Fournie et al [13] and Davis and Johansson [9] this can improve Monte Carlo numerics ... More
Pathwise McKean-Vlasov TheoryDec 31 2018We take a pathwise approach to classical McKean-Vlasov stochastic differential equations with additive noise, as e.g. exposed in Sznitmann [33]. Our study was prompted by some concrete problems in battery modelling [17], and also by recent progrss on ... More
Robust filtering: Correlated noise and multidimensional observationJan 09 2012Sep 13 2013In the late seventies, Clark [In Communication Systems and Random Process Theory (Proc. 2nd NATO Advanced Study Inst., Darlington, 1977) (1978) 721-734, Sijthoff & Noordhoff] pointed out that it would be natural for $\pi_t$, the solution of the stochastic ... More
Marginal density expansions for diffusions and stochastic volatility, part II: Applications [to the Stein--Stein model]May 29 2013In the compagnion paper [Marginal density expansions for diffusions and stochastic volatility, part I] we discussed density expansions for multidimensional diffusions $(X^1,...,X^d)$, at fixed time $T$ and projected to their first $l$ coordinates, in ... More
Marginal density expansions for diffusions and stochastic volatility, part I: Theoretical FoundationsNov 10 2011May 29 2013Density expansions for hypoelliptic diffusions $(X^1,...,X^d)$ are revisited. In particular, we are interested in density expansions of the projection $(X_T^1,...,X_T^l)$, at time $T>0$, with $l \leq d$. Global conditions are found which replace the well-known ... More
Gravitational lensing of wormholes in the galactic halo regionNov 10 2013Apr 22 2016A recent study by Rahaman et al. has shown that the galactic halo possesses the necessary properties for supporting traversable wormholes, based on two observational results, the density profile due to Navarro et al. and the observed flat rotation curves ... More
Neutron star interiors and topology changeJul 27 2012Sep 05 2013Quark matter is believed to exist in the center of neutron stars. A combined model consisting of quark matter and ordinary matter is used to show that the extreme conditions existing in the center could result in a topology change, that is, in the formation ... More
The compatibility of thin-shell wormholes with quantum field theoryFeb 03 2012Jul 04 2014It is shown in this paper that thin-shell wormholes, mathematically constructed by the standard cut-and-paste technique, can, under fairly general conditions, be compatible with quantum field theory.
A simple argument for dark matter as an effect of slightly modified gravityMar 21 2014Sep 12 2014This note presents a simple argument showing that dark matter is an effect of $f(R)$ gravity based on the definition of slightly modified gravitational theories previously proposed by the author.
Theoretical construction of Morris-Thorne wormholes compatible with quantum field theoryAug 28 2009Nov 08 2010This paper completes and extends some earlier studies by the author to show that Morris-Thorne wormholes are compatible with quantum field theory. The strategy is to strike a balance between reducing the size of the unavoidable exotic region and the degree ... More
Axially symmetric rotating traversable wormholesJan 08 2004This paper generalizes the static and spherically symmetric traversable wormhole geometry to a rotating axially symmetric one with a time-dependent angular velocity by means of an exact solution. It was found that the violation of the weak energy condition, ... More
Connecting noncommutative geometry to f(R) modified gravityNov 17 2018Feb 07 2019It is shown in this note that a noncommutative-geometry background determines the modified-gravity function $f(R)$ for modeling dark matter.
Spherically symmetric wormholes of embedding class oneNov 04 2018This paper generalizes an earlier result by the author based on well-established embedding theorems that connect the classical theory of relativity to higher-dimensional spacetimes. In particular, an $n$-dimensional Riemannian space is said to be of embedding ... More
Wormholes in f(R) gravity with a noncommutative-geometry backgroundJan 31 2018Aug 07 2018This paper discusses the possible existence of traversable wormholes in f(R) modified gravity while assuming a noncommutative-geometry background, as well as zero tidal forces. The first part of the paper aims for an overview via several shape functions ... More
More on traversable wormholes sustained by an extra spatial dimensionMay 22 2019This paper extends an earlier study by the author [Phys. Rev. D, vol. 98, 064041 (2018), arXiv:1809.01993] in several significant ways. To begin with, the extra spatial dimension is assumed to be time dependent, while the redshift and shape functions, ... More
On the stability of thin-shell wormholesSep 30 2014Mar 04 2016A thin-shell wormhole is theoretically constructible by surgically grafting together two Schwarzschild spacetimes using the so-called cut-and-paste technique. By describing such a wormhole as the limiting case of a spherical shell, it is shown that the ... More
Exactly solvable wormhole and cosmological models with a barotropic equation of stateAug 20 2014Jun 20 2016An exact solution of the Einstein field equations given the barotropic equation of state $p=\omega\rho$ yields two possible models: (1) if $\omega <-1$, we obtain the most general possible anisotropic model for wormholes supported by phantom energy and ... More
Some examples of Hayward wormholesNov 14 2013Apr 02 2014The first part of this paper discusses a model for the theoretical construction of a simple traversable wormhole with zero density that depends on a preexisting black hole. By assuming the interconvertibilty of black holes and wormholes proposed by S.A. ... More
A note on wormholes in slightly modified gravitational theoriesNov 13 2013Dec 26 2013Wormholes that meet the flare-out condition violate the weak energy condition in classical general relativity. The purpose of this note is to show that even a slight modification of the gravitational theory could, under certain conditions, avoid this ... More
Macroscopic wormholes in noncommutative geometryJan 01 2013Dec 24 2013The purpose of this paper is to show that wormholes in noncommutative geometry can be macroscopic, based in part on an earlier study. The necessary violation of the weak energy condition is attributable to the noncommutative-geometry background rather ... More
Wormholes supported by a combination of normal and quintessential matter in Einstein and Einstein-Maxwell gravityDec 01 2012Feb 02 2014It is shown in the first part of this paper that a combined model comprising ordinary and quintessential matter can support a traversable wormhole in Einstein-Maxwell gravity. Since the solution allows zero tidal forces, the wormhole is suitable for a ... More
On the feasibility of charged wormholesApr 24 2011Dec 20 2011While wormhole spacetimes are predictions of the general theory of relativity, specific solutions may not be compatible with quantum field theory. This paper modifies the charged wormhole model of Kim and Lee with the aim of satisfying an extended version ... More
Some remarks on exact wormhole solutionsJan 03 2010Jun 21 2011Exact wormhole solutions, while eagerly sought after, often have the appearance of being overly specialized or highly artificial. A case for the possible existence of traversable wormholes would be more compelling if an abundance of solutions could be ... More
An unexpected topological censorApr 19 2009Dec 20 2011Morris-Thorne wormholes with a cosmological constant \Lambda have been studied extensively, even allowing \Lambda to be replaced by a space variable scalar. These wormholes cannot exist, however, if \Lambda is both space and time dependent. Such a \Lambda ... More
On the stability of thin-shell wormholes in noncommutative geometryMay 22 2012Aug 20 2012This paper reexamines a special class of thin-shell wormholes that are unstable in general relativity in the framework of noncommutative geometry. It is shown that as a consequence of the intrinsic uncertainty these wormholes are stable to small linearized ... More
Theoretical construction of stable traversable wormholesMar 19 2009Jan 28 2013It is shown in this paper that it is possible, at least in principle, to construct a traversable wormhole that is stable to linearized radial perturbations by specifying relatively simple conditions on the shape and redshift functions.
Wormholes with a space- and time-dependent equation of stateJul 31 2007Mar 14 2011The discovery that the Universe is undergoing an accelerated expansion has suggested the existence of an evolving equation of state. This paper discusses various wormhole solutions in a spherically symmetric spacetime with an equation of state that is ... More
Cylindrically symmetric wormholesJul 02 2005Sep 19 2005This paper discusses traversable wormholes that differ slightly but significantly from those of the Morris-Thorne type under the assumption of cylindrical symmetry. The throat is a piecewise smooth cylindrical surface resulting in a shape function that ... More
The effect of conformal symmetry on charged wormholesSep 03 2016This paper discusses the effect that conformal symmetry can have on a charged wormhole. The analysis yields a physical interpretation of the conformal factor in terms of the electric charge. The rate of change of the conformal factor determines much of ... More
The stability of thin-shell wormholes with a phantom-like equation of stateAug 18 2010Jun 09 2016This paper discusses the stability to linearized radial perturbations of spherically symmetric thin-shell wormholes with a "phantom-like" equation of state for the exotic matter at the throat: $P=\omega\sigma$, $\omega<0$, where $\sigma$ is the energy-density ... More
A single model of traversable wormholes supported by generalized phantom energy or Chaplygin gasApr 22 2009Jul 04 2009This paper discusses a new variable equation of state parameter leading to exact solutions of the Einstein field equations describing traversable wormholes. In addition to generalizing the notion of phantom energy, the equation of state generates a mathematical ... More
Could some black holes have evolved from wormholes?Dec 29 2008Apr 30 2011One way to explain the present acceleration of the Universe is Einstein's cosmological constant. It is quite likely, in view of some recent studies, that a time-dependent equation of state had caused the Universe to evolve from an earlier phantom-energy ... More
Viable models of traversable wormholes supported by small amounts of exotic matterJun 06 2008Wormholes allowed by the general theory of relativity that are simultaneously traversable by humanoid travelers are subject to severe constraints from quantum field theory, particularly the so-called quantum inequalities, here slightly extended. Moreover, ... More