Bulletin of the American Physical Society
APS April Meeting 2019
Volume 64, Number 3
Saturday–Tuesday, April 13–16, 2019; Denver, Colorado
Session X11: Exact Solutions and Mathematical Relativity 
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Sponsoring Units: DGRAV Chair: Sam Gralla, University of Arizona Room: Sheraton Governor's Square 17 
Tuesday, April 16, 2019 10:45AM  10:57AM 
X11.00001: An analytic metric for the exterior spacetime of neutron stars in scalarGaussBonnet gravity Alexander G Saffer, Hector Okada da Silva, Nicolas Yunes Probing the interior composition of neutron stars is currently an active research area in nuclear physics. Experiments, such as the Neutron star Interior Composition ExploreR (NICER), are aiming to probe the composition of neutron stars based on pulse profiles of Xray hotspots. To understand what these profiles look like, accurate knowledge of the spacetime right outside a neutron star is needed. In this talk, I will present an analytical exterior metric for a neutron star in scalarGaussBonnet gravity. This metric modifies a variety of general relativity properties, such as the innermost stable circular orbit and Kepler's third law for a small body in orbit around a neutron star, as well as the visible fraction of the star, which can be observed with Xray telescopes. In the future, light curves generated with this new metric could be compared to real light curve data from NICER to place constraints on scalarGaussBonnet gravity. 
Tuesday, April 16, 2019 10:57AM  11:09AM 
X11.00002: Exact Black Hole Solutions in Modified Gravity Theories: Spherical Symmetry Case Andrew Sullivan, Thomas Sotiriou, Nicolas Yunes We develop a numerical code that can solve for stationary and spherically symmetric spacetimes that represent black holes in a wide class of modified theories of gravity. The code makes use of a relaxed NewtonRaphson method to solve the discretized field equations with a Newton's polynomial finite difference scheme. We test and validate this code through studies both in General Relativity, as well as in EinsteindilatonGaussBonnet gravity with a linear and an exponential coupling. As a byproduct of the latter, we find that analytic solutions obtained in the small coupling approximation are in excellent agreement with our fully nonlinear solutions when using a linear coupling, although differences arise when using an exponential coupling. We then use these numerical solutions to construct a fitted analytical model which we then use to calculate physical observables such as the innermost stable circular orbit and photon sphere and compare them to the numerical results. This code lays the foundation for more detailed calculations of black hole observables that can be compared with data in the future.

Tuesday, April 16, 2019 11:09AM  11:21AM 
X11.00003: Curvature Invariants for Lorentzian Traversable Wormholes Brandon Mattingly, Abinash Kar, MD Ali, Andrew Baas, Caleb Elmore, Cooper Watson, Bahram Shakerin, Eric Davis, Gerald B. Cleaver A process for using curvature invariants is applied as a new means to evaluate the traversability of Lorentzian wormholes. This approach was formulated by Henry, Overduin and Wilcomb for Black Holes in Reference [1]. Curvature invariants are independent of coordinate basis, so the process is free of coordinate mapping distortions. The fourteen G'eh'eniau and Debever (GD) invariants are calculated and the nonzero, independent curvature invariant functions are plotted. Three example traversable wormhole metrics (i) thinshell flatface, (ii) spherically symmetric Morris and Thorne, and (iii) thinshell Schwarzschild wormholes are investigated and are demonstrated to be traversable. [1] Henry, R. C., Overduin, J. and Wilcomb K. (2016), "A New Way to See Inside Black Holes," arXiv:1512.02762v2 [grqc]. 
Tuesday, April 16, 2019 11:21AM  11:33AM 
X11.00004: Analysis of the Curvature Invariants for the Natario Warp Metric Abinash Kar, Brandon Mattingly, Caleb Elmore, Cooper Watson, William Julius, Matthew Gorban, Bahram Shakerin, Eric Davis, Gerald Cleaver A process for using curvature invariants is applied as a new means to evaluate the Natario Warp Drive Metric [1]. This approach was formulated by Henry et al. for Black Holes [2] and was further generalized to accommodate the case of Lorentzian Traversable Wormholes by Mattingly et al. [3]. Curvature invariants are independent of coordinate basis, so the process is free of coordinate mapping distortions. Thirteen curvature invariants are calculated and the nontrivial ones are plotted. The constant velocity and accelerating Natario metrics [4] are examined. The dynamics of the warp bubble as it evolves in time is analyzed by plotting the invariants. A spaceship may harbour in the interior of the warp bubble, which the invariant plots show to be flat and free of any fluctuations.
[1] Natario, J. "Warp Drive with Zero Expansion", Classical and Quantum Gravity 19 (2002) 11571166 [2] Henry, R. et al. (2016), "A New Way to See Inside Black Holes", arXiv:1512.02762v2 [grqc] [3] Mattingly, B. et al. (2018), "Curvature Invariants for Lorentzian Traversable Wormholes", arXiv:1806.10985v1 [grqc] [4] Loup, F. [Research Report hal01655423] Residencia de Estudantes Universitas (2017) 
Tuesday, April 16, 2019 11:33AM  11:45AM 
X11.00005: Properties of Wormhole Solutions of Einstein’s field equations for the LeviCivita metric Cooper K Watson, Brandon Mattingly, Abinash Kar, William Julius, Matthew Gorban, Caleb Elmore, Bahram Shakerin, Eric W Davis, Gerald Cleaver Previous investigations of the LeviCivita (LC) Effect [1] in the polarizable vacuum have shown that the spacetime geometry of the spatial part of the LC metric [2] describes a threemetric of a hypercylinder S^{2} x Ɍ that can be interpreted as a special class of wormhole [3]. This hypercylinder metric has a position dependent gravitational potential possessing no asymptotically flat region, no flaredout wormhole mouth and no wormhole throat. From the Einstein field equations, we derive the nontrivial curvature invariants of a LC metric. We examine these curvature invariants to determine the similarities and differences of the LC metric to the better known metrics of Lorentzian Traversable Wormholes [4]. References: [1] H.E. Puthoff, Claudio Maccone, E.W. Davis, “LeviCivita Effect in the polarizable vacuum (PV) representation of general relativity,” arXiv:0403064 [physics.genph]. [2] M. Morris and K. Thorn, Am. J. Phys. 56 (1988) 395. [3] C. Maccone, “SETI Via Wormholes,” Proc. 47th Intern’l Astronautical Fed. (IAF) Congress, Beijing, 1996. [4] B. Mattingly, A. Kar, M.D. Ali, A. Baas, C. Elmore, C. Watson, B. Shakerin, E. Davis, G. Cleaver, “Curvature Invariants for Lorentzian Traversable Wormholes,” arXiv:1806.10985[grgc]. 
Tuesday, April 16, 2019 11:45AM  11:57AM 
X11.00006: The symmetry of the energy momentum tensor does not necessarily reflect the spacetime symmetry: a viscous axially symmetric cosmological solution Fatemeh Bagheri, Reza Mansouri Applying the method of conformal metric to a given static axially symmetric vacuum solution of the Einstein equations, we have shown that there is no solution representing a cosmic ideal fluid which is asymtotically FLRW. Letting the cosmic fluid to be imperfect there are axially symmetric solutions tending to FLRW at space infinity. The solution we have found represents an axially symmetric spacetime leading to a spherically symmetric Einstein tensor. Therefore, we have found a solution of Einstein equations representing a spherically symmetric matter distribution corresponding to a spacetime which does not reflect the same symmetry. We have also found another solution of Einstein equation corresponding to the same energy tensor with spherical symmetry. 
Tuesday, April 16, 2019 11:57AM  12:09PM 
X11.00007: Spacetime Groups Charles Torre, Ian Anderson We give a classification of spacetime groups: simply connected fourdimensional spacetimes which admit a simply transitive fourdimensional isometry group. Our classification scheme, which is based upon the NewmanPenrose formalism and standard Lie algebraic invariants, yields 29 distinct classes of spacetime groups. We give a general solution to the equivalence problem for spacetime groups, that is, given a spacetime group we show how to uniquely determine where it belongs in our classification. We have made an extensive study of the Einstein equations with various matter sources for each spacetime group and we have closed a number of open problems in the exact solution literature. 
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