{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T11:21:58Z","timestamp":1778584918317,"version":"3.51.4"},"reference-count":54,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,9,28]],"date-time":"2022-09-28T00:00:00Z","timestamp":1664323200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, the geodesic motion of neutral and test particles around the time conformal (TC) Dilaton black hole (BH) is investigated using the e\u03f5g(t) as the time conformal factor in which g(t) is an arbitrary function of time and \u03f5 is a perturbation parameter. The function g(t) leads to (ta) by utilizing the well-known approximate Noether symmetry (ANS). Furthermore, we discuss the effect of magnetic fields and find the location of stable and unstable orbits w. r. t time, graphically. After that, in the presence and absence of a magnetic field, we interrogate the crucial physical parameters such as effective potential (Ueff), effective force (Feff) and escape velocity (\u03bd\u22a5). We find the unstable and stable regions of particles for different values of angular momentum (Lz) and magnetic field (B) near the TC Dilaton BH. Moreover, the effects of the Dilaton parameter (\u03bc) on neutral and charged particles are also discussed, which provide some new features. The important results in this study could estimate the powerful relativistic jets originating from the BH.<\/jats:p>","DOI":"10.3390\/sym14102033","type":"journal-article","created":{"date-parts":[[2022,9,29]],"date-time":"2022-09-29T01:23:16Z","timestamp":1664414596000},"page":"2033","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Motion of Particles around Time Conformal Dilaton Black Holes"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8603-6642","authenticated-orcid":false,"given":"Muhammad Umair","family":"Shahzad","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Okara, Okara 56130, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hamood Ur","family":"Rehman","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Okara, Okara 56130, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3184-3652","authenticated-orcid":false,"given":"Aziz Ullah","family":"Awan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of the Punjab, Lahore 54590, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3151-9967","authenticated-orcid":false,"given":"ElSayed M.","family":"Tag-ElDin","sequence":"additional","affiliation":[{"name":"Faculty of Engineering and Technology, Future University in Egypt, New Cairo 11835, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Attiq Ur","family":"Rehman","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Okara, Okara 56130, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,28]]},"reference":[{"key":"ref_1","unstructured":"Green, M.B., Schwarz, J.H., and Witten, E. 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