Multipole representation of a generic gravitational lens. (arXiv:2108.07172v1 [gr-qc])
<a href="http://arxiv.org/find/gr-qc/1/au:+Turyshev_S/0/1/0/all/0/1">Slava G. Turyshev</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Toth_V/0/1/0/all/0/1">Viktor T. Toth</a>
We consider gravitational lensing by a generic extended mass distribution. We
represent the static external gravitational field of the lens as a potential
via an infinite set of symmetric trace free (STF) moments. We discuss the
possibility of determining the physical characteristics of the lens including
its shape, orientation and composition via gravitational lensing. To do that,
we consider STF multipole moments for several well-known solids with uniform
density. We discuss the caustics formed by the point spread function (PSF) of
such lenses, and also the view seen by an imaging telescope placed in the
strong interference region of the lens. We show that at each STF order, all the
bodies produce similar caustics that are different only by their magnitudes and
orientations. Furthermore, there is ambiguity in determining the shape of the
lens and its mass distribution if only a limited number of moments are used in
the model. This result justifies the development of more comprehensive lens
models that contain a greater number of multipole moments. At the same time,
inclusion of higher multipole moments leads to somewhat limited improvements as
their contributions are suppressed by corresponding powers of the small
parameter $(R/b)^ell$, where $R$ characterizes the body’s physical size and
$b$ is the impact parameter, resulting in a weaker signature from those
multipole moments in the PSF. Thus, in realistic observations there will always
be some ambiguity in the optical properties of a generic lens, unless the
properties of the lens can be determined independently, as in the case of the
solar gravitational lens (SGL). Our results are novel and offer new insight
into gravitational lensing by realistic astrophysical systems.
We consider gravitational lensing by a generic extended mass distribution. We
represent the static external gravitational field of the lens as a potential
via an infinite set of symmetric trace free (STF) moments. We discuss the
possibility of determining the physical characteristics of the lens including
its shape, orientation and composition via gravitational lensing. To do that,
we consider STF multipole moments for several well-known solids with uniform
density. We discuss the caustics formed by the point spread function (PSF) of
such lenses, and also the view seen by an imaging telescope placed in the
strong interference region of the lens. We show that at each STF order, all the
bodies produce similar caustics that are different only by their magnitudes and
orientations. Furthermore, there is ambiguity in determining the shape of the
lens and its mass distribution if only a limited number of moments are used in
the model. This result justifies the development of more comprehensive lens
models that contain a greater number of multipole moments. At the same time,
inclusion of higher multipole moments leads to somewhat limited improvements as
their contributions are suppressed by corresponding powers of the small
parameter $(R/b)^ell$, where $R$ characterizes the body’s physical size and
$b$ is the impact parameter, resulting in a weaker signature from those
multipole moments in the PSF. Thus, in realistic observations there will always
be some ambiguity in the optical properties of a generic lens, unless the
properties of the lens can be determined independently, as in the case of the
solar gravitational lens (SGL). Our results are novel and offer new insight
into gravitational lensing by realistic astrophysical systems.
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