Phase-plane formulation of weak gravitational deflection in static spherical spacetimes | Paper Citation Record

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This paper cites Einstein, The foundation of the general theory of relativity., Annalen Phys.49, 769 (1916).

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Einstein, The foundation of the general theory of relativity., Annalen Phys.49, 769 (1916)

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Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Unresolved cited work

Reference 2

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This paper cites −dy dq q=ϵsin 3 Θ −1 # dΘ.(4.28) The symmetry sin(π−Θ) = sin Θ(4.29) implies that the integrand is symmetric about closest approach. We may therefore write α= 2 Z π/2 0.

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes −dy dq q=ϵsin 3 Θ −1 # dΘ.(4.28) The symmetry sin(π−Θ) = sin Θ(4.29) implies that the integrand is symmetric about closest approach. We may therefore write α= 2 Z π/2 0

Reference 3

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Observation ce7e1d86-cd19-4818-9317-92f5abd3dc8f · outbound

This paper cites (4.12) givesq c = 1/(3 √ 3).

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes (4.12) givesq c = 1/(3 √ 3)

Reference 4

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Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Unresolved cited work

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Observation d5500fcf-e2bd-4a60-8ea7-c7ea8e348b8a · outbound

This paper cites Einstein, Lens-Like Action of a Star by the Deviation of Light in the Gravitational Field, Science84, 506 (1936).

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Einstein, Lens-Like Action of a Star by the Deviation of Light in the Gravitational Field, Science84, 506 (1936)

Reference 6

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Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Unresolved cited work

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Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Unresolved cited work

Reference 8

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Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Unresolved cited work

Reference 9

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Observation 1efe6196-75db-4dc9-addc-6b5a572f6b97 · outbound

This paper cites An Exact Universal Gravitational Lensing Equation.

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes An Exact Universal Gravitational Lensing Equation

Reference 10

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Observation 4b85b87c-454f-454b-90fc-feb773084725 · outbound

This paper cites Spacetime perspective of Schwarzschild lensing.

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Spacetime perspective of Schwarzschild lensing

Reference 11

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Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Unresolved cited work

Reference 12

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Observation 9689cf4c-5549-4d7f-80c5-15185a95dbe9 · outbound

This paper cites On the exact gravitational lens equation in spherically symmetric and static spacetimes.

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes On the exact gravitational lens equation in spherically symmetric and static spacetimes

Reference 13

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Observation a66b4c0e-3866-48c2-81ee-2a484196b5f5 · outbound

This paper cites Perlick, Gravitational lensing from a spacetime perspective, Living Rev.

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Perlick, Gravitational lensing from a spacetime perspective, Living Rev

Reference 14

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Observation 38c07550-6e3c-4232-a003-fca8232a3b76 · outbound

This paper cites Epstein and I.

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Epstein and I

Reference 15

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This paper cites Fischbach and B.

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Fischbach and B

Reference 16

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Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Unresolved cited work

Reference 17

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Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Unresolved cited work

Reference 18

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Observation 888714d9-7daa-4aad-bd22-9d8fb0593abe · outbound

This paper cites Bodenner and C.

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Bodenner and C

Reference 19

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Observation ea0b4c8e-67b0-40b1-8ba6-db10b6a92f1f · outbound

This paper cites Gravitational lensing in metric theories of gravity.

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Gravitational lensing in metric theories of gravity

Reference 20

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Observation d3fcc88f-0b02-4870-898d-127f4f3bdf6d · outbound

This paper cites Formalism for Testing Theories of Gravity Using Lensing by Compact Objects. I: Static, Spherically Symmetric Case.

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Formalism for Testing Theories of Gravity Using Lensing by Compact Objects. I: Static, Spherically Symmetric Case

Reference 21

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This paper cites Formalism for testing theories of gravity using lensing by compact objects. II: Probing Post-Post-Newtonian metrics.

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Formalism for testing theories of gravity using lensing by compact objects. II: Probing Post-Post-Newtonian metrics

Reference 22

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This paper cites Light's Bending Angle due to Black Holes: From the Photon Sphere to Infinity.

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Light's Bending Angle due to Black Holes: From the Photon Sphere to Infinity

Reference 23

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Observation 1c576e21-d1ee-403a-8c1d-f20c3fd957ed · outbound

This paper cites A comparison of approximate gravitational lens equations and a proposal for an improved new one.

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes A comparison of approximate gravitational lens equations and a proposal for an improved new one

Reference 24

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Observation 9dbe35ec-a86c-4525-8e86-e7f15474c183 · outbound

This paper cites A generalized lens equation for light deflection in weak gravitational fields.

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes A generalized lens equation for light deflection in weak gravitational fields

Reference 25

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This paper cites Analytical formulas for gravitational lensing.

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Analytical formulas for gravitational lensing

Reference 26

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Observation 7b384564-09c0-4fe9-95c5-65daabda44ff · outbound

This paper cites Analytical formulas for gravitational lensing: higher order calculation.

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Analytical formulas for gravitational lensing: higher order calculation

Reference 27

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Observation 92b64dc5-f43d-4713-a3e3-e2d97adda015 · outbound

This paper cites Computation of the general relativistic perihelion precession and of light deflection via the Laplace-Adomian Decomposition Method.

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Computation of the general relativistic perihelion precession and of light deflection via the Laplace-Adomian Decomposition Method

Reference 28

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Observation 1b6e902d-23e1-440b-a814-e147dc4d9e11 · outbound

This paper cites Higher-order corrections for the deflection of light around a massive object.

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Higher-order corrections for the deflection of light around a massive object

Reference 29

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Observation 1a8fc997-4eb1-4644-a304-cc94e00194c5 · outbound

This paper cites The perturbative approach for the weak deflection angle.

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes The perturbative approach for the weak deflection angle

Reference 30

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This paper cites Bending of Light and Inhomogeneous Picard-Fuchs Equation.

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Bending of Light and Inhomogeneous Picard-Fuchs Equation

Reference 31

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Observation 36b49131-da05-4471-8e66-a4f2191a5509 · outbound

This paper cites Applications of the Gauss-Bonnet theorem to gravitational lensing.

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Applications of the Gauss-Bonnet theorem to gravitational lensing

Reference 32

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This paper cites Universal properties of the near-horizon optical geometry.

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Universal properties of the near-horizon optical geometry

Reference 33

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Observation d97da2d2-81d2-423e-9cf5-e925506dde5e · outbound

This paper cites Finite-distance corrections to the gravitational bending angle of light in the strong deflection limit.

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Finite-distance corrections to the gravitational bending angle of light in the strong deflection limit

Reference 34

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Observation 9256a10c-9f4d-4b5f-a574-78f4ee5659cd · outbound

This paper cites Gravitational bending angle of light for finite distance and the Gauss-Bonnet theorem.

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Gravitational bending angle of light for finite distance and the Gauss-Bonnet theorem

Reference 35

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This paper cites Weak lensing in a plasma medium and gravitational deflection of massive particles using the Gauss-Bonnet theorem. A unified treatment.

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Weak lensing in a plasma medium and gravitational deflection of massive particles using the Gauss-Bonnet theorem. A unified treatment

Reference 36

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This paper cites Gravitational lensing in dispersive media and deflection angle of charged massive particles in terms of curvature scalars and energy-momentum tensor.

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Gravitational lensing in dispersive media and deflection angle of charged massive particles in terms of curvature scalars and energy-momentum tensor

Reference 37

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This paper cites The effects of finite distance on the gravitational deflection angle of light.

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes The effects of finite distance on the gravitational deflection angle of light

Reference 38

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This paper cites Equivalence of Gibbons-Werner method to geodesics method in the study of gravitational lensing.

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Equivalence of Gibbons-Werner method to geodesics method in the study of gravitational lensing

Reference 39

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This paper cites Reference-renormalized curvature-primitive Gauss-Bonnet formalism for finite-distance weak gravitational lensing in static spherical spacetimes.

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Reference-renormalized curvature-primitive Gauss-Bonnet formalism for finite-distance weak gravitational lensing in static spherical spacetimes

Reference 40

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This paper cites The geometry of photon surfaces.

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes The geometry of photon surfaces

Reference 41

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This paper cites Strong field limit of black hole gravitational lensing.

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Strong field limit of black hole gravitational lensing

Reference 42

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Observation 17c2878c-23a0-42c2-bd32-de42a5b0b5c0 · outbound

This paper cites Gravitational lensing in the strong field limit.

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Gravitational lensing in the strong field limit

Reference 43

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Observation d060df74-6fa7-4514-92c7-c086771e3ac8 · outbound

This paper cites Reissner-Nordstrom black hole lensing.

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Reissner-Nordstrom black hole lensing

Reference 44

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Observation 854974c6-3dd7-44f4-9e61-3465d97a42b9 · outbound

This paper cites Strong deflection limit of black hole gravitational lensing with arbitrary source distances.

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Strong deflection limit of black hole gravitational lensing with arbitrary source distances

Reference 45

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This paper cites Gravitational Lensing by Black Holes.

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Gravitational Lensing by Black Holes

Reference 46

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Observation 66111674-d9b8-472e-86cd-52cfbe887a98 · outbound

This paper cites Deflection angle in the strong deflection limit in a general asymptotically flat, static, spherically symmetric spacetime.

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Deflection angle in the strong deflection limit in a general asymptotically flat, static, spherically symmetric spacetime

Reference 47

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This paper cites Perturbative deflection angle, gravitational lensing in the strong field limit and the black hole shadow.

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Perturbative deflection angle, gravitational lensing in the strong field limit and the black hole shadow

Reference 48

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Observation 6565b845-8336-4799-8f1f-d7aa8f203ec9 · outbound

This paper cites Gravitational lensing inside and outside of a marginally unstable photon sphere in a general, static, spherically symmetric, and asymptotically-flat spacetime in strong deflection limits.

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Gravitational lensing inside and outside of a marginally unstable photon sphere in a general, static, spherically symmetric, and asymptotically-flat spacetime in strong deflection limits

Reference 49

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This paper cites Universal time delay in static spherically symmetric spacetimes for null and timelike signals.

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Universal time delay in static spherically symmetric spacetimes for null and timelike signals

Reference 50

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Observation 501f5aad-1e58-4598-b3aa-01f3098e6e46 · outbound

This paper cites Mayol, R.

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Mayol, R

Reference 51

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Phase-plane formulation of weak gravitational deflection in static spherical spacetimes Unresolved cited work

Reference 52

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