{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T06:43:04Z","timestamp":1772779384387,"version":"3.50.1"},"reference-count":49,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2024,12,29]],"date-time":"2024-12-29T00:00:00Z","timestamp":1735430400000},"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>The present paper investigates the greybody radiation of a general metric including the significant black hole parameters. The fraction of Hawking radiation (HR) that succeeds in achieving infinity is known as \u201cgreybody radiation\u201d or transmission probability. In this study, the focus is on the black hole parameters by which greybody radiation could be affected, such as electric and magnetic charges \u201ce\u201d and \u201cg\u201d, respectively, cosmological constant \u201c\u039b\u201d, and Taub-Nut \u201cl\u201d. In this regard, we use the nonrotating form of the improved Griffiths\u2013Podolsk (NRIGP) metric which contains the factors \u201c\u039b,l,e,g\u201d, all in a single metric. This study allows us to observe the behavior of the scalar perturbation and greybody radiation of each indicated parameter in the presence of the other variables. The spacetime around the black hole behaves as a barrier for particles, and the greybody factor strongly depends on the black hole potential barrier. Therefore, we first studied the scalar perturbation and evaluated the actions of the effective potential by the regarded parameters. The depicted figures for variables such as magnetic charge \u201cg\u201d confirm the consistency between the effective potential and the greybody factor. In this area of study, symmetry plays an essential but hidden role. In the current study, we also consider that all the particles around a black hole have the same symmetry.<\/jats:p>","DOI":"10.3390\/sym17010042","type":"journal-article","created":{"date-parts":[[2024,12,31]],"date-time":"2024-12-31T13:26:25Z","timestamp":1735651585000},"page":"42","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Scalar Greybody Radiation of \u201cNRIGP\u201d Black Hole"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7181-2813","authenticated-orcid":false,"given":"Sara","family":"Kanzi","sequence":"first","affiliation":[{"name":"Faculty of Engineering, Final International University, North Cyprus via Mersin 10, Kyrenia 99320, Turkey"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1007\/BF02345020","article-title":"Particle creation by black holes","volume":"43","author":"Hawking","year":"1975","journal-title":"Commun. Math. Phys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1103\/PhysRevD.13.191","article-title":"Black Holes and Thermodynamics","volume":"13","author":"Hawking","year":"1976","journal-title":"Phys. Rev. D"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"112502","DOI":"10.1063\/1.4901127","article-title":"Greybody factors for Myers-Perry black holes","volume":"55","author":"Boonserm","year":"2014","journal-title":"J. Math. Phys."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"041","DOI":"10.1007\/JHEP06(2019)041","article-title":"Exact Greybody Factors for the Brane Scalar Field of Five-dimensional Rotating Black Holes","volume":"6","author":"Hyun","year":"2019","journal-title":"J. High Energy Phys."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"065008","DOI":"10.1088\/0264-9381\/32\/6\/065008","article-title":"Greybody factors for rotating black holes in higher dimensions","volume":"32","author":"Jorge","year":"2015","journal-title":"Class. Quant. Grav."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"100436","DOI":"10.1016\/j.dark.2019.100436","article-title":"Greybody factor for quintessential Kerr\u2013Newman black hole","volume":"27","author":"Sharif","year":"2020","journal-title":"Phys. Dark Univ."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"169294","DOI":"10.1016\/j.aop.2023.169294","article-title":"Fermionic and bosonic greybody factors as well as quasinormal modes for charged Taub NUT black holes","volume":"452","author":"Kanzi","year":"2023","journal-title":"Ann. Phys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1140\/epjc\/s10052-021-09299-y","article-title":"Greybody radiation and quasinormal modes of Kerr-like black hole in Bumblebee gravity model","volume":"81","author":"Kanzi","year":"2021","journal-title":"Eur. Phys. J. C"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"668","DOI":"10.1140\/epjc\/s10052-023-11846-8","article-title":"Some observable physical properties of the higher dimensional dS\/AdS black holes in Einstein-bumblebee gravity theory","volume":"83","author":"Uniyal","year":"2023","journal-title":"Eur. Phys. J. C"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"168301","DOI":"10.1016\/j.aop.2020.168301","article-title":"Greybody factors of black holes in dRGT massive gravity coupled with nonlinear electrodynamics","volume":"422","author":"Kanzi","year":"2020","journal-title":"Ann. Phys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"657","DOI":"10.1140\/epjc\/s10052-023-11843-x","article-title":"Greybody factors for massive scalar field emitted from black holes in dRGT massive gravity","volume":"83","author":"Boonserm","year":"2023","journal-title":"Eur. Phys. J. C"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"168803","DOI":"10.1016\/j.aop.2022.168803","article-title":"Physical properties of brane-world black hole solutions via a confining potential","volume":"439","author":"Kanzi","year":"2022","journal-title":"Ann. Phys."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"861","DOI":"10.1103\/PhysRevD.55.861","article-title":"Black hole grey body factors and d-brane spectroscopy","volume":"55","author":"Maldacena","year":"1997","journal-title":"Phys. Rev. D"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"969","DOI":"10.1140\/epjc\/s10052-024-13359-4","article-title":"Quasinormal modes, thermodynamics and shadow of black holes in Hu\u2013Sawicki f(R) gravity theory","volume":"84","author":"Karmakar","year":"2024","journal-title":"Eur. Phys. J. C"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"084070","DOI":"10.1103\/PhysRevD.110.084070","article-title":"Stability and instability of the black hole greybody factors and ringdowns against a small-bump correction","volume":"110","author":"Oshita","year":"2024","journal-title":"Phys. Rev. D"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"101521","DOI":"10.1016\/j.dark.2024.101521","article-title":"Greybody factors, quasi-normal modes and thermal fluctuations of quantum-corrected Schwarzschild black hole surrounded by quintessence","volume":"45","author":"Fatima","year":"2024","journal-title":"Phys. Dark Univ."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"064086","DOI":"10.1103\/PhysRevD.110.064086","article-title":"Greybody factors imprinted on black hole ringdowns. II. Merging binary black holes","volume":"110","author":"Okabayashi","year":"2024","journal-title":"Phys. Rev. D"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"104039","DOI":"10.1103\/PhysRevD.109.104039","article-title":"Quasinormal modes, greybody factors, and thermodynamics of four dimensional AdS black holes in critical gravity","volume":"109","author":"Lin","year":"2024","journal-title":"Phys. Rev. D"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Kanzi, S., Sakall\u0131, \u0130., and Pourhassan, B. (2023). Superradiant (In)stability, Greybody Radiation, and Quasinormal Modes of Rotating Black Holes in Non-Linear Maxwell f(R) Gravity. Symmetry, 15.","DOI":"10.3390\/sym15040873"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"757","DOI":"10.1140\/epjp\/s13360-023-04384-5","article-title":"Photonsphere, shadow, quasinormal modes, and greybody bounds of non-rotating Simpson\u2013Visser black hole","volume":"138","author":"Jha","year":"2023","journal-title":"Eur. Phys. J. Plus"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1140\/epjc\/s10052-024-12511-4","article-title":"Perturbations of massless external fields in a special Horndeski hairy black hole","volume":"84","author":"Yang","year":"2024","journal-title":"Eur. Phys. J. C"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"012022","DOI":"10.1088\/1742-6596\/2653\/1\/012022","article-title":"The greybody factor for the monopole and odd-parity modes of the Proca field in the Schwarzschild black hole spacetimes","volume":"2653","author":"Bunjusuwan","year":"2023","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1088\/1475-7516\/2023\/04\/013","article-title":"Thermal ringdown of a Kerr black hole: Overtone excitation, Fermi-Dirac statistics and greybody factor","volume":"4","author":"Oshita","year":"2023","journal-title":"J. Cosmol. Astropart. Phys."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"084078","DOI":"10.1103\/PhysRevD.104.084078","article-title":"New improved form of black holes of type D","volume":"104","author":"Podolsky","year":"2021","journal-title":"Phys. Rev. D"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"084034","DOI":"10.1103\/PhysRevD.107.084034","article-title":"New form of all black holes of type D with a cosmological constant","volume":"107","author":"Podolsky","year":"2023","journal-title":"Phys. Rev. D"},{"key":"ref_26","first-page":"360","article-title":"On type D expanding solutions of Einstein\u2013Maxwell equations","volume":"23","author":"Debever","year":"1971","journal-title":"Bull. Soc. Math. Belg."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1016\/0003-4916(76)90240-2","article-title":"Rotating, charged and uniformly accelerating mass in general relativity","volume":"98","author":"Plebanski","year":"1976","journal-title":"Ann. Phys."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"3467","DOI":"10.1088\/0264-9381\/22\/17\/008","article-title":"Accelerating and rotating black holes","volume":"22","author":"Griffiths","year":"2005","journal-title":"Class. Quant. Grav."},{"key":"ref_29","unstructured":"Ovcharenko, H., Podolsky, J., and Astorino, M. (2024). Black holes of type D revisited: Relating their various metric forms. arXiv."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"044018","DOI":"10.1103\/PhysRevD.73.044018","article-title":"Accelerating Kerr-Newman black holes in (anti-)de Sitter space-time","volume":"73","author":"Podolsky","year":"2006","journal-title":"Phys. Rev. D"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1142\/S0218271806007742","article-title":"A New look at the Plebanski-Demianski family of solutions","volume":"15","author":"Griffiths","year":"2006","journal-title":"Int. J. Mod. Phys. D"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"046608","DOI":"10.1103\/PhysRevE.66.046608","article-title":"Wannier functions analysis of the nonlinear Schr\u00f6dinger\u2019s equation with a periodic potential","volume":"66","author":"Alfimov","year":"2002","journal-title":"Phys. Rev. E"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1103\/PhysRevC.30.331","article-title":"Pion Form-Factor And The Klein-Gordon Equation","volume":"30","author":"Bawin","year":"1984","journal-title":"Phys. Rev. C"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"358","DOI":"10.1142\/S2010194512006563","article-title":"Tortoise coordinate transformation on apparent horizon of a dynamical black hole","volume":"12","author":"Liu","year":"2012","journal-title":"Int. J. Mod. Phys. Conf. Ser."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Gui-hua, T., Wang, S.k., and Zhong, S. (2006). The Effect of the tortoise coordinate on the stable study of the Schwarzschild black hole. arXiv.","DOI":"10.1088\/0256-307X\/23\/4\/006"},{"key":"ref_36","unstructured":"Andersson, N., and Jensen, B.P. (2006). Scattering by Black Holes. Chapter 0.1. arXiv."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1103\/PhysRevA.59.427","article-title":"Some general bounds for 1-D scattering","volume":"59","author":"Visser","year":"1999","journal-title":"Phys. Rev. A"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"2779","DOI":"10.1016\/j.aop.2008.02.002","article-title":"Bounding the Bogoliubov coefficients","volume":"323","author":"Boonserm","year":"2008","journal-title":"Ann. Phys."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"45301","DOI":"10.1088\/1751-8113\/42\/4\/045301","article-title":"Transmission probabilities and the Miller-Good transformation","volume":"42","author":"Boonserm","year":"2009","journal-title":"J. Phys. A"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Gray, F., and Visser, M. (2018). Greybody Factors for Schwarzschild Black Holes: Path-Ordered Exponentials and Product Integrals. Universe, 4.","DOI":"10.3390\/universe4090093"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"316","DOI":"10.1140\/epjc\/s10052-018-5800-6","article-title":"Greybody factor of a scalar field from Reissner\u2013Nordstr\u00f6m\u2013de Sitter black hole","volume":"78","author":"Ahmed","year":"2018","journal-title":"Eur. Phys. J. C"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"012027","DOI":"10.1088\/1742-6596\/435\/1\/012027","article-title":"Bounding the greybody factors for the Reissner-Nordstr\u00f6m black holes","volume":"435","author":"Ngampitipan","year":"2013","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"075403","DOI":"10.1088\/1572-9494\/ad48fa","article-title":"Hawking\u2013Page transition and the dual relations of anti-de Sitter black holes surrounded by dark energy in general dimensions","volume":"76","author":"Xin","year":"2024","journal-title":"Commun. Theor. Phys."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1103\/PhysRevD.110.046008","article-title":"Entanglement entropy, phase transition, and island rule for Reissner-Nordstr\u00f6m-AdS black holes","volume":"110","author":"Lin","year":"2024","journal-title":"Phys. Rev. D"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"138948","DOI":"10.1016\/j.physletb.2024.138948","article-title":"Universality of the thermodynamics of a quantum-mechanically radiating black hole departing from thermality","volume":"856","author":"Corda","year":"2024","journal-title":"Phys. Lett. B"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"101447","DOI":"10.1016\/j.dark.2024.101447","article-title":"Nonextensive entropies impact onto thermodynamics and phase structure of Kerr\u2013Newman black holes","volume":"44","author":"Ghaffari","year":"2024","journal-title":"Phys. Dark Univ."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"1045","DOI":"10.1140\/epjc\/s10052-023-12222-2","article-title":"Thermodynamics of deformed AdS-Schwarzschild black hole","volume":"83","author":"Khosravipoor","year":"2023","journal-title":"Eur. Phys. J. C"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"169242","DOI":"10.1016\/j.aop.2023.169242","article-title":"Weak deflection angle, greybody bound and shadow for charged massive BTZ black hole","volume":"450","author":"Upadhyay","year":"2023","journal-title":"Ann. Phys."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"101827","DOI":"10.1016\/j.newast.2022.101827","article-title":"Bounding greybody and deflection angle of improved Schwarzschild black hole","volume":"96","author":"Javed","year":"2022","journal-title":"New Astron."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/1\/42\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:55:49Z","timestamp":1760115349000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/1\/42"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,29]]},"references-count":49,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025,1]]}},"alternative-id":["sym17010042"],"URL":"https:\/\/doi.org\/10.3390\/sym17010042","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,12,29]]}}}