M. C. Werner

Duke University, Durham, North Carolina, United States

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Publications (15)122.07 Total impact

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    ABSTRACT: Objects of known brightness, like Type Ia supernovae (SNIa), can be used to measure distances. If a massive object warps spacetime to form multiple images of a background SNIa, a direct test of cosmic expansion is also possible. However, these lensing events must first be distinguished from other rare phenomena. Recently, a supernova was found to shine much brighter than normal for its distance, which resulted in a debate: was it a new type of superluminous supernova or a normal SNIa magnified by a hidden gravitational lens? Here we report that a spectrum obtained after the supernova faded away shows the presence of a foreground galaxy--the first found to strongly magnify a SNIa. We discuss how more lensed SNIa may be found than previously predicted.
    Science 04/2014; 344(6182):396-9. DOI:10.1126/science.1250903 · 31.48 Impact Factor
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    ABSTRACT: Starting from the geometrical concept of a 4-dimensional de-Sitter configuration of spheres in Euclidean 3-space and modelling voids in the Universe as spheres, we show that a uniform distribution over this configuration space implies a power-law for the void number density which is consistent with results from the excursion set formalism and from data, for an intermediate range of void volumes. We also discuss the effect of restricting the survey geometry on the void statistics. This work is a new application of de-Sitter geometry to cosmology and also provides a new geometrical perspective on self-similarity in cosmology.
    Monthly Notices of the Royal Astronomical Society 08/2013; 438(2). DOI:10.1093/mnras/stt2298 · 5.23 Impact Factor
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    ABSTRACT: Recently, Chornock and co-workers announced the Pan-STARRS discovery of a transient source reaching an apparent peak luminosity of ~4x10^44 erg s^-1. We show that the spectra of this transient source are well fit by normal Type Ia supernova (SNIa) templates. The multi-band colors and light-curve shapes are also consistent with normal SNeIa at the spectroscopically determined redshift of z=1.3883; however, the observed flux is a constant factor of ~30 times too bright in each band over time as compared to the templates. At minimum, this shows that the peak luminosities inferred from the light-curve widths of some SNeIa will deviate significantly from the established, empirical relation used by cosmologists. We argue on physical grounds that the observed fluxes do not reflect an intrinsically luminous SNIa, but rather PS1-10afx is a normal SNIa whose flux has been magnified by an external source. The only known astrophysical source capable of such magnification is a gravitational lens. Given the lack of obvious lens candidates, such as galaxy clusters, in the vicinity, we further argue that the lens is a supermassive black hole or a comparatively low-mass dark matter halo. In this case, the lens continues to magnify the underlying host galaxy light. If confirmed, this discovery could impact a broad range of topics including cosmology, gamma-ray bursts, and dark matter halos.
    The Astrophysical Journal Letters 02/2013; 768(1). DOI:10.1088/2041-8205/768/1/L20 · 5.60 Impact Factor
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    Gary W. Gibbons, Marcus C. Werner
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    ABSTRACT: The cumulative size-frequency distributions of impact craters on planetary bodies in the solar system appear to approximate a universal inverse square power-law for small crater radii. In this article, we show how this distribution can be understood easily in terms of geometrical statistics, using a de-Sitter geometry of the configuration space of circles on the Euclidean plane and on the unit sphere. The effect of crater overlap is also considered.
    Monthly Notices of the Royal Astronomical Society 09/2012; 429(2). DOI:10.1093/mnras/sts401 · 5.23 Impact Factor
  • Gary W Gibbons, Marcus C Werner
    Nature 07/2012; 487(7408):432. DOI:10.1038/487432c · 42.35 Impact Factor
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    M. C. Werner
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    ABSTRACT: A new geometric method to determine the deflection of light in the equatorial plane of the Kerr solution is presented, whose optical geometry is a surface with a Finsler metric of Randers type. Applying the Gauss-Bonnet theorem to a suitable osculating Riemannian manifold, adapted from a construction by Naz\i m, it is shown explicitly how the two leading terms of the asymptotic deflection angle of gravitational lensing can be found in this way.
    General Relativity and Gravitation 05/2012; 44(12). DOI:10.1007/s10714-012-1458-9 · 1.73 Impact Factor
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    A. O. Petters, M. C. Werner
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    ABSTRACT: The mathematical theory of gravitational lensing has revealed many generic and global properties. Beginning with multiple imaging, we review Morse-theoretic image counting formulas and lower bound results, and complex-algebraic upper bounds in the case of single and multiple lens planes. We discuss recent advances in the mathematics of stochastic lensing, discussing a general formula for the global expected number of minimum lensed images as well as asymptotic formulas for the probability densities of the microlensing random time delay functions, random lensing maps, and random shear, and an asymptotic expression for the global expected number of micro-minima. Multiple imaging in optical geometry and a spacetime setting are treated. We review global magnification relation results for model-dependent scenarios and cover recent developments on universal local magnification relations for higher order caustics. Comment: 25 pages, 4 figures. Invited review submitted for special issue of General Relativity and Gravitation
    General Relativity and Gravitation 12/2009; 42(9). DOI:10.1007/s10714-010-0968-6 · 1.73 Impact Factor
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    M. C. Werner
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    ABSTRACT: Recent work in gravitational lensing and catastrophe theory has shown that the sum of the signed magnifications of images near folds, cusps and also higher catastrophes is zero. Here, it is discussed how Lefschetz fixed point theory can be used to interpret this result geometrically. It is shown for the generic case as well as for elliptic and hyperbolic umbilics in gravitational lensing.
    Journal of Mathematical Physics 05/2009; 50(8). DOI:10.1063/1.3204970 · 1.18 Impact Factor
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    ABSTRACT: We consider a triality between the Zermelo navigation problem, the geodesic flow on a Finslerian geometry of Randers type, and spacetimes in one dimension higher admitting a timelike conformal Killing vector field. From the latter viewpoint, the data of the Zermelo problem are encoded in a (conformally) Painleve-Gullstrand form of the spacetime metric, whereas the data of the Randers problem are encoded in a stationary generalisation of the usual optical metric. We discuss how the spacetime viewpoint gives a simple and physical perspective on various issues, including how Finsler geometries with constant flag curvature always map to conformally flat spacetimes and that the Finsler condition maps to either a causality condition or it breaks down at an ergo-surface in the spacetime picture. The gauge equivalence in this network of relations is considered as well as the connection to analogue models and the viewpoint of magnetic flows. We provide a variety of examples. Comment: 37 pages, 6 figures
    Physical Review D 11/2008; 79(4):044022. DOI:10.1103/PhysRevD.79.044022 · 4.86 Impact Factor
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    G. W. Gibbons, C. M. Warnick, M. C. Werner
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    ABSTRACT: We interpret the well known fact that the equations for light rays in the Kottler or Schwarzschild-de Sitter metric are independent of the cosmological constant in terms of the projective equivalence of the optical metric for any value of \Lambda. We explain why this does not imply that lensing phenomena are independent of \Lambda. Motivated by this example, we find a large collection of one-parameter families of projectively equivalent metrics including both the Kottler optical geometry and the constant curvature metrics as special cases. Using standard constructions for geodesically equivalent metrics we find classical and quantum conserved quantities and relate these to known quantities.
    Classical and Quantum Gravity 09/2008; DOI:10.1088/0264-9381/25/24/245009 · 3.10 Impact Factor
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    G. W. Gibbons, M. C. Werner
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    ABSTRACT: In this geometrical approach to gravitational lensing theory, we apply the Gauss-Bonnet theorem to the optical metric of a lens, modelled as a static, spherically symmetric, perfect non-relativistic fluid, in the weak deflection limit. We find that the focusing of the light rays emerges here as a topological effect, and we introduce a new method to calculate the deflection angle from the Gaussian curvature of the optical metric. As examples, the Schwarzschild lens, the Plummer sphere and the singular isothermal sphere are discussed within this framework.
    Classical and Quantum Gravity 08/2008; DOI:10.1088/0264-9381/25/23/235009 · 3.10 Impact Factor
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    M. C. Werner, J. An, N. W. Evans
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    ABSTRACT: A number of recent surveys for gravitational lenses have found examples of double Einstein rings. Here, we investigate analytically the occurrence of multiple Einstein rings. We prove, under very general assumptions, that at most one Einstein ring can arise from a mass distribution in a single plane lensing a single background source. Two or more Einstein rings can therefore only occur in multi-plane lensing. Surprisingly, we show that it is possible for a single source to produce more than one Einstein ring. If two point masses (or two isothermal spheres) in different planes are aligned with observer and source on the optical axis, we show that there are up to three Einstein rings. We also discuss the image morphologies for these two models if axisymmetry is broken, and give the first instances of magnification invariants in the case of two lens planes. Comment: MNRAS, in press (extra figure included)
    Monthly Notices of the Royal Astronomical Society 04/2008; DOI:10.1111/j.1365-2966.2008.13829.x · 5.23 Impact Factor
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    M. C. Werner, A. O. Petters
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    ABSTRACT: A Kerr black hole with mass parameter m and angular momentum parameter a acting as a gravitational lens gives rise to two images in the weak field limit. We study the corresponding magnification relations, namely the signed and absolute magnification sums and the centroid up to post-Newtonian order. We show that there are post-Newtonian corrections to the total absolute magnification and centroid proportional to a/m, which is in contrast to the spherically symmetric case where such corrections vanish. Hence we also propose a new set of lensing observables for the two images involving these corrections, which should allow measuring a/m with gravitational lensing. In fact, the resolution capabilities needed to observe this for the Galactic black hole should in principle be accessible to current and near-future instrumentation. Since a/m >1 indicates a naked singularity, a most interesting application would be a test of the Cosmic Censorship conjecture. The technique used to derive the image properties is based on the degeneracy of the Kerr lens and a suitably displaced Schwarzschild lens at post-Newtonian order. A simple physical explanation for this degeneracy is also given.
    Physical review D: Particles and fields 07/2007; 76(6). DOI:10.1103/PHYSREVD.76.064024 · 4.86 Impact Factor
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    Marcus C. Werner
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    ABSTRACT: Topological invariants play an important r\^{o}le in the theory of gravitational lensing by constraining the image number. Furthermore, it is known that, for certain lens models, the image magnifications $\mu_i$ obey invariants of the form $\sum_i \mu_i=1$. In this paper, we show that this magnification invariant is the holomorphic Lefschetz number of a suitably defined complexified lensing map, and hence a topological invariant. We also provide a heat kernel proof of the holomorphic Lefschetz fixed point formula which is central to this argument, based on Kotake's proof of the more general Atiyah-Bott theorem. Finally, we present a new astronomically motivated lens model for which this invariant holds.
    Journal of Mathematical Physics 04/2007; 48(5). DOI:10.1063/1.2735443 · 1.18 Impact Factor
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    M. C. Werner, N. W. Evans
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    ABSTRACT: The lensing properties of the Plummer model with a central point mass and external shear are derived, including the image multiplicities, critical curves and caustics. This provides a simple model for a flattened galaxy with a central supermassive black hole. For the Plummer model with black hole, the maximum number of images is 4, provided the black hole mass is less than an upper bound which is calculated analytically. This introduces a method to constrain black hole masses by counting images, thus applicable at cosmological distance. With shear, the maximum number of images is 6 and we illustrate the occurrence of an astroid caustic and two metamorphoses. Comment: 7 pages, 4 figures, MNRAS, in press, small changes made
    Monthly Notices of the Royal Astronomical Society 02/2006; DOI:10.1111/j.1365-2966.2006.10230.x · 5.23 Impact Factor

Publication Stats

143 Citations
122.07 Total Impact Points

Institutions

  • 2009–2014
    • Duke University
      • Department of Mathematics
      Durham, North Carolina, United States
  • 2012–2013
    • The University of Tokyo
      • Institute for the Physics and Mathematics of the Universe (IPMU)
      Edo, Tōkyō, Japan
  • 2006–2009
    • University of Cambridge
      • Institute of Astronomy
      Cambridge, England, United Kingdom