{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:25:10Z","timestamp":1760149510201,"version":"build-2065373602"},"reference-count":44,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,8,11]],"date-time":"2023-08-11T00:00:00Z","timestamp":1691712000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>The Reissner\u2013Nordstrom spacetimes and some generalised Reissner\u2013Nordstrom spacetimes are analysed. The blackhole solutions are considered. The generalised Reissner\u2013Nordstrom spacetimes with a cosmological-constant term, endowed with a Schwarzschild solid-angle element, are analytically delineated: the radii of the blackholes are analytically calculated and newly parameterised; the coordinate-singularity-avoiding coordinate extension is newly found, i.e., such that the tortoise-coordinate transformation can therefore be applied; the new conditions for merging the solutions as the physical horizons are analytically outlined; the new parameter space of the model is set and constrained; the new role of the cosmological-constant term in designating the Schwarzschild radius is demonstrated; the Reissner\u2013Nordstrom\u2013deSitter case and in the Reissner\u2013Nordstrom\u2013anti-deSitter one are newly demonstrated to be characterised in a different analytical manner. Furthermore, a new family of solutions is found, qualified after the cosmological-constant term. The generalised Reissner\u2013Nordstrom spacetimes with a linear term, endowed with a Schwarzschild solid-angle element, are analytically studied: the radii are enumerated and newly parameterised; the new conditions for the merging of the radii as the physical horizons are set; the new parameter space of the system is arranged and constrained; the role of the linear-term parameter in the delineation of the Schwarzschild radius is newly proven to be apt to imply a small modification only. The generalised Reissner\u2013Nordstrom spacetimes, endowed with a Schwarzschild solid-angle element, with a linear term and a cosmological-constant term are newly inspected: the radii are analytically calculated and newly parameterised; the new conditions for the merging of the radii as the physical horizons are prescribed; the new parameter space of the scheme is appointed and constrained; the roles of the parameters are newly scrutinised in their application to modify the physical interpretation of the Reissner\u2013Nordstrom parameters only in a small manner; the coordinate-singularity-avoiding coordinate extensions are newly found, i.e., such that the tortoise-coordinate transformation can therefore be applied; the definition of the physical radii is newly found; the results are newly demonstrated in both cases of a positive value of the cosmological constant and in the case of a negative value of the cosmological constant in a different manner; the role of the linear-term parameter is also newly enunciated. More over, a new family of solutions is found, which is delineated after particular values of the linear term and of the cosmological-constant one. The quantum implementation of the models is prospectively envisaged.<\/jats:p>","DOI":"10.3390\/computation11080157","type":"journal-article","created":{"date-parts":[[2023,8,11]],"date-time":"2023-08-11T10:20:16Z","timestamp":1691749216000},"page":"157","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Generalised Reissner\u2013Nordstrom Spacetimes, the Cosmological Constant and the Linear Term"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9417-5578","authenticated-orcid":false,"given":"Orchidea Maria","family":"Lecian","sequence":"first","affiliation":[{"name":"ICRA c\/o Physics Department, Sapienza University of Rome, Piazzale Aldo Moro, 5-00185 Rome, Italy"},{"name":"Faculty of Civil and Industrial Engineering, Sapienza University of Rome, Via Eudossiana, 18-00184 Rome, Italy"},{"name":"Faculty of Information Engineering, Sapienza University of Rome, Via Eudossiana, 18-00184 Rome, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Brauer, O., and Socolovsky, M. 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