{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,23]],"date-time":"2025-12-23T15:26:59Z","timestamp":1766503619029,"version":"build-2065373602"},"reference-count":124,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2018,11,1]],"date-time":"2018-11-01T00:00:00Z","timestamp":1541030400000},"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 study, we derive, in the framework of mimetic theory, charged and non-charged black hole solutions for spherically symmetric as well as flat horizon spacetimes. The asymptotic behavior of those black holes behave as flat or (A)dS spacetimes and coincide with the solutions derived before in general relativity theory. Using the field equations of non-linear electrodynamics mimetic theory we derive new black hole solutions with monopole and quadrupole terms. The quadruple term of those black holes is related by a constant so that its vanishing makes the solutions coincide with the linear Maxwell black holes. We study the singularities of those solutions and show that they possess stronger singularity than the ones known in general relativity. Among many things, we study the horizons as well as the heat capacity to see if the black holes derived in this study have thermodynamical stability or not.<\/jats:p>","DOI":"10.3390\/sym10110559","type":"journal-article","created":{"date-parts":[[2018,11,1]],"date-time":"2018-11-01T11:31:47Z","timestamp":1541071907000},"page":"559","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Charged and Non-Charged Black Hole Solutions in Mimetic Gravitational Theory"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5544-1119","authenticated-orcid":false,"given":"Gamal G.L.","family":"Nashed","sequence":"first","affiliation":[{"name":"Centre for Theoretical Physics, The British University in Egypt, P.O. Box 43, El Sherouk City, Cairo 11837, Egypt"},{"name":"Department of Mathematics, Faculty of Science, Ain Shams University, Cairo 11566, Egypt"},{"name":"Egyptian Relativity Group (ERG), Cairo University, Giza 12613, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2018,11,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Hawking, S.W., and Ellis, G.F.R. (1973). The Large Scale Structure of Space-Time, Cambridge University Press.","DOI":"10.1017\/CBO9780511524646"},{"key":"ref_2","unstructured":"Carroll, S.M. (2004). Spacetime and Geometry: An Introduction to General Relativity, Addison Wesley."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Raine, D.J., and Thomas, E.G. (2010). Black Holes: An Introduction, Imperial College Press.","DOI":"10.1142\/p637"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"064045","DOI":"10.1103\/PhysRevD.97.064045","article-title":"Pre-Hawking radiation cannot prevent the formation of apparent horizon","volume":"97","author":"Chen","year":"20018","journal-title":"Phys. Rev. D"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1148","DOI":"10.1119\/1.2117187","article-title":"Simple analytical models of gravitational collapse","volume":"73","author":"Adler","year":"2005","journal-title":"Am. J. Phys."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1098\/rspa.1970.0021","article-title":"The singularities of gravitational collapse and cosmology","volume":"314","author":"Hawking","year":"1970","journal-title":"Proc. R. Soc. Lond. A"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1140\/epjc\/s10052-018-5556-z","article-title":"Black hole solutions in mimetic Born-Infeld gravity","volume":"78","author":"Chen","year":"2018","journal-title":"Eur. Phys. J. C"},{"key":"ref_8","first-page":"123512","article-title":"Modified gravity with negative and positive powers of curvature: Unification of inflation and cosmic acceleration","volume":"3","author":"Nojiri","year":"2001","journal-title":"Phys. Rev. D"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"043528","DOI":"10.1103\/PhysRevD.70.043528","article-title":"Is cosmic speed-up due to new gravitational physics?","volume":"70","author":"Carroll","year":"2004","journal-title":"Phys. Rev. D"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"3181","DOI":"10.1142\/S0217751X06031478","article-title":"Charged axially symmetric solution, energy and angular momentum in tetrad theory of gravitation","volume":"21","author":"Nashed","year":"2006","journal-title":"Int. J. Mod. Phys. A"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1895","DOI":"10.1103\/PhysRevD.52.1895","article-title":"Inflatonless inflation","volume":"52","author":"Dobado","year":"1995","journal-title":"Phys. Rev. D"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1016\/S0370-2693(00)00669-9","article-title":"4D gravity on a brane in 5D Minkowski space","volume":"485","author":"Dvali","year":"2000","journal-title":"Phys. Lett. B"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1047","DOI":"10.1142\/S021773230702141X","article-title":"Kerr Newman solution and energy in teleparallel equivalent of Einstein theory","volume":"2","author":"Nashed","year":"2007","journal-title":"Mod. Phys. Lett. A"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"141301","DOI":"10.1103\/PhysRevLett.102.141301","article-title":"Dark Matter from R2 Gravity","volume":"102","author":"Cembranos","year":"2009","journal-title":"Phys. Rev. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1140\/epjc\/s10052-007-0511-4","article-title":"Charged dilaton, energy, momentum and angular-momentum in teleparallel theory equivalent to general relativity","volume":"54","author":"Nashed","year":"2008","journal-title":"Eur. Phys. J. C"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"064029","DOI":"10.1103\/PhysRevD.73.064029","article-title":"The Newtonian limit at intermediate energies","volume":"73","author":"Cembranos","year":"2006","journal-title":"Phys. Rev. D"},{"key":"ref_17","first-page":"25","article-title":"Dark matter and higgs sector","volume":"907","author":"Cembranos","year":"2009","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1142\/S0219887807001928","article-title":"Introduction to modified gravity and gravitational alternative for dark energy","volume":"4","author":"Nojiri","year":"2007","journal-title":"Int. J. Geom. Meth. Mod. Phys."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"020401","DOI":"10.1088\/1674-1056\/19\/2\/020401","article-title":"Brane world black holes in teleparallel theory equivalent to general relativity and their Killing vectors, energy, momentum and angular momentum","volume":"19","author":"Nashed","year":"2010","journal-title":"Chin. Phys. B"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"063005","DOI":"10.1103\/PhysRevD.78.063005","article-title":"Cosmic vector for dark energy","volume":"78","author":"Beltran","year":"2008","journal-title":"Phys. Rev. D"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"245020","DOI":"10.1088\/0264-9381\/28\/24\/245020","article-title":"Existence of relativistic stars in f(T) gravity","volume":"28","author":"Bohmer","year":"2011","journal-title":"Class. Quantum Gravity"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2002","DOI":"10.1140\/epjc\/s10052-012-2002-5","article-title":"Extended Birkhoff\u2019s theorem in f(T) gravity","volume":"72","author":"Dong","year":"2012","journal-title":"Eur. Phys. J. C"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1007\/s10714-015-1917-1","article-title":"FRW in quadratic form of f(T) gravitational theories","volume":"47","author":"Nashed","year":"2015","journal-title":"Gen. Relativ. Gravit."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"083513","DOI":"10.1103\/PhysRevD.94.083513","article-title":"Bounce inflation in f(T) cosmology: A unified inflaton-quintessence field","volume":"94","author":"Bamba","year":"2016","journal-title":"Phys. Rev. D"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"104042","DOI":"10.1103\/PhysRevD.89.104042","article-title":"New Schwarzschild-like solutions in f(T) gravity through Noether symmetries","volume":"89","author":"Paliathanasis","year":"2014","journal-title":"Phys. Rev. D"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"851","DOI":"10.1140\/epjc\/s10052-006-0154-x","article-title":"Charged axially symmetric solution and energy in teleparallel theory equivalent to general relativity","volume":"49","author":"Nashed","year":"2007","journal-title":"Eur. Phys. J. C"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1016\/0550-3213(76)90406-5","article-title":"Conformal Invariance in Quantum Gravity","volume":"117","author":"Englert","year":"1976","journal-title":"Nucl. Phys. B"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"517","DOI":"10.1007\/BF02748215","article-title":"Space-time singularities and conformal gravity","volume":"19","author":"Narlikar","year":"1977","journal-title":"Lett. Nuovo Cim."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1829","DOI":"10.1007\/s10701-011-9586-8","article-title":"A class of elementary particle models without any adjustable real parameters","volume":"41","author":"Hooft","year":"2011","journal-title":"Found. Phys."},{"key":"ref_30","first-page":"251","article-title":"Quantum gravity without space-time singularities or horizons","volume":"47","author":"Hooft","year":"2011","journal-title":"Subnucl. Ser."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"388","DOI":"10.1007\/s10701-011-9608-6","article-title":"Making the case for conformal gravity","volume":"42","author":"Mannheim","year":"2012","journal-title":"Found. Phys."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Bars, I., Steinhardt, P., and Turok, N. (2014). Local conformal symmetry in physics and cosmology. Phys. Rev. D, 8.","DOI":"10.1103\/PhysRevD.89.043515"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"083513","DOI":"10.1103\/PhysRevD.84.083513","article-title":"Geodesically complete analytic solutions for a cyclic universe","volume":"84","author":"Bars","year":"2011","journal-title":"Phys. Rev. D"},{"key":"ref_34","first-page":"6095236","article-title":"Curing black hole singularities with local scale invariance","volume":"2016","author":"Prester","year":"2016","journal-title":"Adv. Math. Phys."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1140\/epjc\/s10052-016-3924-0","article-title":"Scale invariant power spectra from a Weyl-invariant scalar tensor theory","volume":"76","author":"Myung","year":"2016","journal-title":"Eur. Phys. J. C"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/j.nuclphysb.2007.03.014","article-title":"Direct detection of dark matter rates for various wimps","volume":"773","author":"Oikonomou","year":"2007","journal-title":"Nucl. Phys. B"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"3156915","DOI":"10.1155\/2017\/3156915","article-title":"Mimetic gravity: A review of recent developments and applications to cosmology and astrophysics","volume":"2017","author":"Sebastiani","year":"2017","journal-title":"Adv. High Energy Phys."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"014","DOI":"10.1088\/1475-7516\/2014\/01\/014","article-title":"Dark matter as a ghost free conformal extension of Einstein theory A.O. Barvinsky","volume":"1401","author":"Barvinsky","year":"2014","journal-title":"J. Cosmol. Astropart. Phys."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1007\/JHEP12(2014)102","article-title":"Mimetic dark matter, ghost instability and a mimetic tensor-vector-scalar gravity","volume":"12","author":"Chaichian","year":"2014","journal-title":"J. High Energy Phys."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1088\/1475-7516\/2014\/06\/017","article-title":"Cosmology with mimetic matter","volume":"1406","author":"Chamseddine","year":"2014","journal-title":"J. Cosmol. Astropart. Phys."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1088\/1475-7516\/2018\/02\/041","article-title":"Cosmological dynamics of mimetic gravity","volume":"2","author":"Dutta","year":"2018","journal-title":"J. Cosmol. Astropart. Phys."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1450211","DOI":"10.1142\/S0217732314502113","article-title":"Mimetic F(R) gravity: inflation, dark energy and bounce","volume":"29","author":"Nojiri","year":"2014","journal-title":"Mod. Phys. Lett. A"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1088\/1475-7516\/2015\/04\/031","article-title":"Dynamical behavior in mimetic F(R) gravity","volume":"1504","author":"Leon","year":"2015","journal-title":"J. Cosmol. Astropart. Phys."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"185007","DOI":"10.1088\/0264-9381\/32\/18\/185007","article-title":"Modified Gauss Bonnet gravity with the Lagrange multiplier constraint as mimetic theory","volume":"32","author":"Astashenok","year":"2015","journal-title":"Class. Quantum Gravity"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1550101","DOI":"10.1142\/S0219887815501017","article-title":"Cosmological viable mimetic f(R) and f(R, T) theories via Noether symmetry","volume":"12","author":"Momeni","year":"2015","journal-title":"Int. J. Geom. Meth. Mod. Phys."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"225014","DOI":"10.1088\/0264-9381\/33\/22\/225014","article-title":"Covariant Horava-like and mimetic Horndeski gravity: cosmological solutions and perturbations","volume":"33","author":"Cognola","year":"2016","journal-title":"Class. Quantum Gravity"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1088\/1475-7516\/2015\/06\/028","article-title":"Imperfect dark matter","volume":"1506","author":"Mirzagholi","year":"2015","journal-title":"J. Cosmol. Astropart. Phys."},{"key":"ref_48","unstructured":"Haghani, Z., Harko, T., Sepangi, H.R., and Shahidi, S. (arXiv, 2014). The scalar Einstein-aether theory, arXiv."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1140\/epjc\/s10052-016-3926-y","article-title":"A note on a mimetic scalar tensor cosmological model","volume":"76","author":"Rabochaya","year":"2016","journal-title":"Eur. Phys. J. C"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"051","DOI":"10.1088\/1475-7516\/2015\/09\/051","article-title":"The two faces of mimetic Horndeski gravity: disformal transformations and Lagrange multiplier","volume":"1509","author":"Arroja","year":"2015","journal-title":"J. Cosmol. Astropart. Phys."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"023517","DOI":"10.1103\/PhysRevD.93.023517","article-title":"Accelerating cosmologies and the phase structure of F(R) gravity with Lagrange multiplier constraints: A mimetic approach","volume":"93","author":"Odintsov","year":"2016","journal-title":"Phys. Rev. D"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1088\/1475-7516\/2017\/11\/053","article-title":"Primordial cosmology in mimetic born-infeld gravity","volume":"1711","author":"Lopez","year":"2017","journal-title":"J. Cosmol. Astropart. Phys."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1007\/s10509-016-2779-z","article-title":"Non-local F(R)-mimetic gravity","volume":"361","author":"Myrzakulov","year":"2016","journal-title":"Astrophys. Space Sci."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1088\/1475-7516\/2015\/12\/007","article-title":"Initial conditions for imperfect dark matter","volume":"1512","author":"Ramazanov","year":"2015","journal-title":"J. Cosmol. Astropart. Phys."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"084059","DOI":"10.1103\/PhysRevD.96.084059","article-title":"Forms of action for perfect fluid in general relativity and mimetic gravity","volume":"96","author":"Paston","year":"2017","journal-title":"Phys. Rev. D"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1088\/1475-7516\/2017\/07\/009","article-title":"Healthy imperfect dark matter from effective theory of mimetic cosmological perturbations","volume":"1707","author":"Hirano","year":"2017","journal-title":"J. Cosmol. Astropart. Phys."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1088\/1475-7516\/2017\/08\/040","article-title":"On (in) stabilities of perturbations in mimetic models with higher derivatives","volume":"1708","author":"Zheng","year":"2017","journal-title":"J. Cosmol. Astropart. Phys."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"124028","DOI":"10.1103\/PhysRevD.96.124028","article-title":"Higher order derivative coupling to gravity and its cosmological implications","volume":"96","author":"Cai","year":"2017","journal-title":"Phys. Rev. D"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1088\/1475-7516\/2017\/11\/038","article-title":"Extended mimetic gravity: Hamiltonian analysis and gradient instabilities","volume":"11","author":"Takahashi","year":"2017","journal-title":"J. Cosmol. Astropart. Phys."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1088\/1475-7516\/2018\/01\/020","article-title":"Higher derivative mimetic gravity","volume":"1","author":"Gorji","year":"2018","journal-title":"J. Cosmol. Astropart. Phys."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1088\/1475-7516\/2017\/01\/002","article-title":"Higher derivative mimetic gravity","volume":"1701","author":"Kimura","year":"2017","journal-title":"J. Cosmol. Astropart. Phys."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1088\/1475-7516\/2016\/04\/017","article-title":"Bi-scalar modified gravity and cosmology with conformal invariance","volume":"1604","author":"Saridakis","year":"2016","journal-title":"J. Cosmol. Astropart. Phys."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1088\/1475-7516\/2017\/03\/009","article-title":"Resolving cosmological singularities","volume":"1703","author":"Chamseddine","year":"2017","journal-title":"J. Cosmol. Astropart. Phys."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1140\/epjc\/s10052-017-4759-z","article-title":"Nonsingular black hole","volume":"77","author":"Chamseddine","year":"2017","journal-title":"Eur. Phys. J. C"},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1016\/j.physletb.2017.03.039","article-title":"Braneworld mimetic cosmology","volume":"769","author":"Sadeghnezhad","year":"2017","journal-title":"Phys. Lett. B"},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"185006","DOI":"10.1088\/1361-6382\/aa838b","article-title":"Recovering a MOND-like acceleration law in mimetic gravity","volume":"34","author":"Vagnozzi","year":"2017","journal-title":"Class. Quantum Gravity"},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1016\/j.physletb.2017.10.045","article-title":"Ghost-free F(R) gravity with lagrange multiplier constraint","volume":"775","author":"Nojiri","year":"2017","journal-title":"Phys. Lett. B"},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2017.06.001","article-title":"Modified gravity theories on a nutshell: inflation, bounce and late-time evolution","volume":"692","author":"Nojiri","year":"2017","journal-title":"Phys. Rep."},{"key":"ref_69","first-page":"36","article-title":"Effects of non-linear electrodynamics of vacuum in the magnetic quadrupole field of a pulsar","volume":"481","author":"Abishev","year":"2018","journal-title":"Mon. Not. R. Astron. Soc."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"104008","DOI":"10.1103\/PhysRevD.96.104008","article-title":"Regular multihorizon black holes in modified gravity with nonlinear electrodynamics","volume":"96","author":"Nojiri","year":"2017","journal-title":"Phys. Rev. D"},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"165015","DOI":"10.1088\/0264-9381\/32\/16\/165015","article-title":"Regular rotating electrically charged black holes and solitons in non-linear electrodynamics minimally coupled to gravity","volume":"32","author":"Dymnikova","year":"2015","journal-title":"Class. Quantum Gravity"},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"084003","DOI":"10.1103\/PhysRevD.61.084003","article-title":"Regular (2 + 1)-dimensional black holes within nonlinear electrodynamics","volume":"61","author":"Cataldo","year":"2000","journal-title":"Phys. Rev. D"},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"044005","DOI":"10.1103\/PhysRevD.63.044005","article-title":"Regular magnetic black holes and monopoles from nonlinear electrodynamics","volume":"63","author":"Bronnikov","year":"2001","journal-title":"Phys. Rev. D"},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"104017","DOI":"10.1103\/PhysRevD.65.104017","article-title":"New type of regular black holes and particlelike solutions from nonlinear electrodynamics","volume":"65","author":"Burinskii","year":"2002","journal-title":"Phys. Rev. D"},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"047504","DOI":"10.1103\/PhysRevD.70.047504","article-title":"Extremal limit of the regular charged black holes in nonlinear electrodynamics","volume":"70","author":"Matyjasek","year":"2004","journal-title":"Phys. Rev. D"},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"4417","DOI":"10.1088\/0264-9381\/21\/18\/009","article-title":"Regular electrically charged vacuum structures with de Sitter centre in nonlinear electrodynamics coupled to general relativity","volume":"21","author":"Dymnikova","year":"2004","journal-title":"Class. Quantum Gravity"},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"031103","DOI":"10.1103\/PhysRevLett.96.031103","article-title":"Formation and evaporation of nonsingular black holes","volume":"96","author":"Hayward","year":"2006","journal-title":"Phys. Rev. Lett."},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1016\/j.physletb.2013.03.025","article-title":"Rotating regular black holes","volume":"721","author":"Bambi","year":"2013","journal-title":"Phys. Lett. B"},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1140\/epjc\/s10052-014-3222-7","article-title":"Radiating Kerr-like regular black hole","volume":"75","author":"Ghosh","year":"2015","journal-title":"Eur. Phys. J. C"},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"104017","DOI":"10.1103\/PhysRevD.89.104017","article-title":"Rotating regular black hole solution","volume":"89","author":"Toshmatov","year":"2014","journal-title":"Phys. Rev. D"},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1088\/1475-7516\/2015\/10\/060","article-title":"Regular black holes in f(T) gravity through a nonlinear electrodynamics source","volume":"1510","author":"Junior","year":"2015","journal-title":"J. Cosmol. Astropart. Phys."},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"418","DOI":"10.1140\/epjc\/s10052-018-5922-x","article-title":"Non-linear charged dS black hole and its thermodynamics and phase","volume":"78","author":"Nama","year":"2018","journal-title":"Eur. Phys. J. C"},{"key":"ref_83","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1007\/JHEP11(2013)135","article-title":"Mimetic dark matter","volume":"11","author":"Chamseddine","year":"2013","journal-title":"J. High Energy Phys."},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1007\/JHEP07(2017)136","article-title":"d-dimensional charged Anti-de-Sitter black holes in f(T) gravity","volume":"2017","author":"Awad","year":"2017","journal-title":"J. High Energy Phys."},{"key":"ref_85","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1007\/JHEP02(2013)039","article-title":"Exact charged black-hole solutions in d-dimensional f(T) gravity: Torsion vs curvature analysis","volume":"1302","author":"Capozziello","year":"2013","journal-title":"J. High Energy Phys."},{"key":"ref_86","doi-asserted-by":"crossref","first-page":"104050","DOI":"10.1103\/PhysRevD.94.104050","article-title":"Viable mimetic completion of unified inflation-dark energy evolution in modified gravity","volume":"94","author":"Nojiri","year":"2016","journal-title":"Phys. Rev. D"},{"key":"ref_87","doi-asserted-by":"crossref","first-page":"1650078","DOI":"10.1142\/S0218271816500784","article-title":"A note on Schwarzschild de Sitter black holes in mimetic F(R) gravity","volume":"25","author":"Oikonomou","year":"2016","journal-title":"Int. J. Mod. Phys. D"},{"key":"ref_88","doi-asserted-by":"crossref","first-page":"104034","DOI":"10.1103\/PhysRevD.88.104034","article-title":"Spherically symmetric charged dS solution in f(T) gravity theories","volume":"88","author":"Nashed","year":"2013","journal-title":"Phys. Rev. D"},{"key":"ref_89","doi-asserted-by":"crossref","first-page":"1887","DOI":"10.1007\/s10714-013-1566-1","article-title":"A special exact spherically symmetric solution in f(T) gravity theories","volume":"45","author":"Nashed","year":"2013","journal-title":"Gen. Relativ. Gravit."},{"key":"ref_90","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1007\/s10509-010-0375-1","article-title":"Spherically symmetric charged black hole in conformal teleparallel equivalent of general relativity","volume":"330","author":"Nashed","year":"2010","journal-title":"Astrophys. Space Sci."},{"key":"ref_91","unstructured":"Pleba\u0144ski, J.F. (1968). Lectures on Non Linear Electrodynamics, Monograph of the Niels Bohr Institute Nordita."},{"key":"ref_92","doi-asserted-by":"crossref","first-page":"2171","DOI":"10.1063\/1.527430","article-title":"Duality rotations and type D solutions to Einstein equations with nonlinear electromagnetic sources","volume":"28","author":"Salazar","year":"1987","journal-title":"J. Math. Phys."},{"key":"ref_93","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/S0370-2693(99)01038-2","article-title":"New regular black hole solution from nonlinear electrodynamics","volume":"464","year":"1999","journal-title":"Phys. Lett. B"},{"key":"ref_94","doi-asserted-by":"crossref","first-page":"004","DOI":"10.1088\/1126-6708\/2005\/04\/004","article-title":"On charged black holes in anti-de Sitter space","volume":"2005","author":"Brecher","year":"2005","journal-title":"J. High Energy Phys."},{"key":"ref_95","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1016\/0375-9601(77)90508-4","article-title":"Singularities in conformally flat spacetimes","volume":"64","author":"Tipler","year":"1977","journal-title":"Phys. Lett. B"},{"key":"ref_96","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/0393-0440(85)90012-9","article-title":"Conditions for the occurence of strong curvature singularities","volume":"2","author":"Clarke","year":"1985","journal-title":"J. Geom. Phys."},{"key":"ref_97","doi-asserted-by":"crossref","first-page":"7020162","DOI":"10.1155\/2016\/7020162","article-title":"Isotropic stars in higher order torsion scalar theories","volume":"2016","author":"Nashed","year":"2016","journal-title":"Adv. High Energy Phys."},{"key":"ref_98","doi-asserted-by":"crossref","first-page":"024009","DOI":"10.1103\/PhysRevD.59.024009","article-title":"Action of instantons with a nut charge","volume":"59","author":"Hunter","year":"1998","journal-title":"Phys. Rev. D"},{"key":"ref_99","doi-asserted-by":"crossref","first-page":"044033","DOI":"10.1103\/PhysRevD.59.044033","article-title":"NUT charge, anti de Sitter space, and entropy","volume":"59","author":"Hawking","year":"1999","journal-title":"Phys. Rev. D"},{"key":"ref_100","doi-asserted-by":"crossref","first-page":"737","DOI":"10.1007\/BF02757029","article-title":"Black holes and the second law","volume":"4","author":"Bekenstein","year":"1972","journal-title":"Lett. Nuovo Cim."},{"key":"ref_101","doi-asserted-by":"crossref","first-page":"2333","DOI":"10.1103\/PhysRevD.7.2333","article-title":"Black holes and entropy","volume":"7","author":"Bekenstein","year":"1973","journal-title":"Phys. Rev. D"},{"key":"ref_102","doi-asserted-by":"crossref","first-page":"2738","DOI":"10.1103\/PhysRevD.15.2738","article-title":"Action integrals and partition functions in quantum gravity","volume":"15","author":"Gibbons","year":"1977","journal-title":"Phys. Rev. D"},{"key":"ref_103","doi-asserted-by":"crossref","first-page":"5917","DOI":"10.1088\/0264-9381\/24\/23\/014","article-title":"Black hole thermodynamics to all orders in the Planck length in extra dimensions","volume":"24","author":"Nouicer","year":"2007","journal-title":"Class. Quantum Gravity"},{"key":"ref_104","doi-asserted-by":"crossref","first-page":"1967","DOI":"10.3390\/e13121967","article-title":"Thermodynamics of regular cosmological black holes with the de Sitter interior","volume":"13","author":"Dymnikova","year":"2011","journal-title":"Entropy"},{"key":"ref_105","doi-asserted-by":"crossref","first-page":"064018","DOI":"10.1103\/PhysRevD.60.064018","article-title":"Charged AdS black holes and catastrophic holography","volume":"60","author":"Chamblin","year":"1999","journal-title":"Phys. Rev. D"},{"key":"ref_106","doi-asserted-by":"crossref","unstructured":"Wei, Y.-H. (2018). Thermodynamic properties of a regular black hole in gravity coupling to nonlinear electrodynamics. Entropy, 20.","DOI":"10.3390\/e20030192"},{"key":"ref_107","doi-asserted-by":"crossref","first-page":"1051","DOI":"10.1007\/s10714-008-0690-9","article-title":"Thermodynamics of regular black hole","volume":"41","author":"Myung","year":"2009","journal-title":"Gen. Relativ. Gravit."},{"key":"ref_108","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_109","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1007\/BF01208266","article-title":"Thermodynamics of black holes in anti-de Sitter space","volume":"87","author":"Hawking","year":"1983","journal-title":"Commun. Math. Phys."},{"key":"ref_110","doi-asserted-by":"crossref","first-page":"278","DOI":"10.1016\/j.physletb.2015.10.061","article-title":"Stability of black holes based on horizon thermodynamics","volume":"751","author":"Ma","year":"2015","journal-title":"Phys. Lett. B"},{"key":"ref_111","doi-asserted-by":"crossref","first-page":"687","DOI":"10.1016\/j.physletb.2012.11.017","article-title":"Phase transition of quantum-corrected Schwarzschild black hole","volume":"718","author":"Kim","year":"2012","journal-title":"Phys. Lett. B"},{"key":"ref_112","doi-asserted-by":"crossref","first-page":"89","DOI":"10.3390\/galaxies2010089","article-title":"Thermodynamics of rotating black holes and black rings: phase transitions and thermodynamic volume","volume":"2","author":"Altamirano","year":"2014","journal-title":"Galaxies"},{"key":"ref_113","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1140\/epjc\/s10052-017-4914-6","article-title":"Effects of thermal fluctuations on non-minimal regular magnetic black hole","volume":"77","author":"Jawad","year":"2017","journal-title":"Eur. Phys. J. C"},{"key":"ref_114","doi-asserted-by":"crossref","first-page":"1750071","DOI":"10.1142\/S0218271817500717","article-title":"Bardeen de Sitter black holes","volume":"26","author":"Fernando","year":"2017","journal-title":"Int. J. Mod. Phys. D"},{"key":"ref_115","doi-asserted-by":"crossref","first-page":"084001","DOI":"10.1103\/PhysRevD.91.084001","article-title":"Stability and antievaporation of the Schwarzschild de Sitter black holes in bigravity","volume":"91","author":"Katsuragawa","year":"2015","journal-title":"Phys. Rev. D"},{"key":"ref_116","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/j.physletb.2010.01.044","article-title":"Regular black hole remnants in de Sitter space","volume":"685","author":"Dymnikova","year":"2010","journal-title":"Phys. Lett. B"},{"key":"ref_117","doi-asserted-by":"crossref","first-page":"1660","DOI":"10.1007\/s10714-013-1660-4","article-title":"The calculation of the thermodynamic quantities of the Bardeen black hole","volume":"46","author":"Man","year":"2014","journal-title":"Gen. Relativ. Gravit."},{"key":"ref_118","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1007\/s10714-015-1884-6","article-title":"Phase transitions and geometrothermodynamics of regular black holes","volume":"47","author":"Tharanath","year":"2015","journal-title":"Gen. Relativ. Gravit."},{"key":"ref_119","doi-asserted-by":"crossref","first-page":"885","DOI":"10.1007\/s10714-006-0270-9","article-title":"Regular black holes in quadratic gravity","volume":"38","author":"Berej","year":"2006","journal-title":"Gen. Relativ. Gravit."},{"key":"ref_120","doi-asserted-by":"crossref","first-page":"104015","DOI":"10.1103\/PhysRevD.97.104015","article-title":"Thermodynamics of a class of regular black holes with a generalized uncertainty principle","volume":"97","author":"Maluf","year":"2018","journal-title":"Phys. Rev. D"},{"key":"ref_121","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1140\/epjc\/s10052-017-4695-y","article-title":"What is modified gravity and how to differentiate it from particle dark matter?","volume":"77","author":"Calmet","year":"2017","journal-title":"Eur. Phys. J. C"},{"key":"ref_122","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1098\/rspa.1977.0047","article-title":"Thermodynamics of Black Holes","volume":"353","author":"Davies","year":"1977","journal-title":"Proc. R. Soc. Lond. A"},{"key":"ref_123","doi-asserted-by":"crossref","first-page":"1909","DOI":"10.1088\/0264-9381\/6\/12\/018","article-title":"Thermodynamic phase transitions of Kerr-Newman black holes in de Sitter space","volume":"6","author":"Davies","year":"1989","journal-title":"Class. Quantum Gravity"},{"key":"ref_124","doi-asserted-by":"crossref","first-page":"1155","DOI":"10.3367\/UFNe.0183.201312a.1257","article-title":"Black holes in the presence of dark energy","volume":"56","author":"Babichev","year":"2013","journal-title":"Phys. Usp."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/10\/11\/559\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:27:16Z","timestamp":1760196436000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/10\/11\/559"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,11,1]]},"references-count":124,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2018,11]]}},"alternative-id":["sym10110559"],"URL":"https:\/\/doi.org\/10.3390\/sym10110559","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2018,11,1]]}}}