An upper bound for the number of gravitationally lensed images in a multiplane point-mass ensemble
Herein we prove an upper bound on the number of gravitationally lensed images in a generic multiplane point-mass ensemble with K planes and g i masses in the i th plane. With E K and O K the sums of the even and odd degree terms respectively of the formal polynomial ∏ i = 1 K ( 1 + g i Z ) , the num...
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| Vydáno v: | Analysis and mathematical physics Ročník 11; číslo 2 |
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| Hlavní autor: | |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Cham
Springer International Publishing
01.06.2021
Springer Nature B.V |
| Témata: | |
| ISSN: | 1664-2368, 1664-235X |
| On-line přístup: | Získat plný text |
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| Shrnutí: | Herein we prove an upper bound on the number of gravitationally lensed images in a generic multiplane point-mass ensemble with
K
planes and
g
i
masses in the
i
th
plane. With
E
K
and
O
K
the sums of the even and odd degree terms respectively of the formal polynomial
∏
i
=
1
K
(
1
+
g
i
Z
)
, the number of lensed images of a single background point-source is shown to be bounded by
E
K
2
+
O
K
2
. Our proof uses the theory of resultants applied to a complex variable representation of the so-called lensing map. Previous studies concerning upper bounds for point-mass ensembles have been restricted to two special cases: one point-mass per plane and all point-masses in a single plane. |
|---|---|
| Bibliografie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 1664-2368 1664-235X |
| DOI: | 10.1007/s13324-021-00478-4 |