{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T22:11:30Z","timestamp":1760220690406,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2012,11,12]],"date-time":"2012-11-12T00:00:00Z","timestamp":1352678400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We examine the weak version of the third law of black hole thermodynamics inthe n-dimensional Einstein\u2013Gauss\u2013Bonnet system with a negative cosmological constant.To see whether the extreme black hole solution with zero temperature is formed, weinvestigate the motion of the thin shell that has the equal mass to the extreme black holein the background described by the non-GR branch solutions. The interior of the shell isempty. Our analysis using the generalized Israel's junction condition shows that the shellcan contract beyond a certain radius and the degenerate horizon is formed for same range ofparameters. Hence, this model can be a counterexample of the third law.<\/jats:p>","DOI":"10.3390\/e14112291","type":"journal-article","created":{"date-parts":[[2012,11,12]],"date-time":"2012-11-12T11:37:24Z","timestamp":1352720244000},"page":"2291-2301","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Violation of the Third Law of Black Hole Thermodynamics inHigher Curvature Gravity"],"prefix":"10.3390","volume":"14","author":[{"given":"Takashi","family":"Torii","sequence":"first","affiliation":[{"name":"Department of General Education, Osaka Institute of Technology, 5-16-1, Omiya, Asahi-ku,Osaka, 535-8585, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2012,11,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"A177","DOI":"10.1088\/0264-9381\/16\/12A\/309","article-title":"Gravitation, thermodynamics and quantum theory","volume":"16","author":"Wald","year":"1999","journal-title":"Class. Quantum Grav."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1007\/BF01645742","article-title":"The four laws of black hole mechanics","volume":"31","author":"Bardeen","year":"1973","journal-title":"Commun. Math. Phys."},{"key":"ref_3","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_4","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1038\/248030a0","article-title":"Black-hole evaporation","volume":"248","author":"Hawking","year":"1974","journal-title":"Nature"},{"key":"ref_5","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_6","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 Cimento"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3292","DOI":"10.1103\/PhysRevD.9.3292","article-title":"Generalized second law of thermodynamics in black-hole physics","volume":"9","author":"Bekenstein","year":"1974","journal-title":"Phys. Rev. D"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"942","DOI":"10.1103\/PhysRevD.25.942","article-title":"Acceleration radiation and the generalized second law of thermodynamics","volume":"25","author":"Unruh","year":"1982","journal-title":"Phys. Rev. D"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2171","DOI":"10.1103\/PhysRevLett.54.2171","article-title":"Statistical mechanical origin of the entropy of a rotating, charged black hole","volume":"54","author":"Zurek","year":"1985","journal-title":"Phys. Rev. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"3902","DOI":"10.1103\/PhysRevLett.71.3902","article-title":"Proof of the generalized second law for quasistationary semiclassical black holes","volume":"71","author":"Frolov","year":"1993","journal-title":"Phys. Rev. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"6467","DOI":"10.1103\/PhysRevD.56.6467","article-title":"\u201cNernst theorem\" and black hole thermodynamics","volume":"56","author":"Wald","year":"1997","journal-title":"Phys. Rev. D"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2363","DOI":"10.1103\/PhysRevD.8.2363","article-title":"Naked singularities, thin shells, and the reissner-nordstr\u00f6m metric","volume":"8","author":"Boulware","year":"1973","journal-title":"Phys. Rev. D"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"548","DOI":"10.1016\/0003-4916(74)90125-0","article-title":"Gedanken experiments to destroy a black hole","volume":"82","author":"Wald","year":"1974","journal-title":"Ann. Phys."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1103\/PhysRevLett.57.397","article-title":"Third law of black-hole dynamics: A formulation and proof","volume":"57","author":"Israel","year":"1986","journal-title":"Phys. Rev. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"4353","DOI":"10.1088\/0264-9381\/17\/20\/410","article-title":"Does the third law of black hole thermodynamics really have a serious failure?","volume":"17","author":"Racz","year":"2000","journal-title":"Class. Quantum Grav."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"124003:1","DOI":"10.1103\/PhysRevD.61.124003","article-title":"Gravitational properties of monopole spacetimes near the black hole threshold","volume":"61","author":"Lue","year":"2000","journal-title":"Phys. Rev. D"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/0370-2693(96)00345-0","article-title":"Microscopic origin of the Bekenstein-Hawking entropy","volume":"379","author":"Strominger","year":"1996","journal-title":"Phys. Lett. B"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"428","DOI":"10.1103\/PhysRevLett.77.428","article-title":"Statistical entropy of four-dimensional extremal black holes","volume":"77","author":"Maldacena","year":"1996","journal-title":"Phys. Rev. Lett."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"231","DOI":"10.4310\/ATMP.1998.v2.n2.a1","article-title":"The large N limit of superconformal field theories and supergravity","volume":"2","author":"Maldacena","year":"1998","journal-title":"Adv. Theor. Math. Phys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"253","DOI":"10.4310\/ATMP.1998.v2.n2.a2","article-title":"Anti-de sitter space and holography","volume":"2","author":"Witten","year":"1998","journal-title":"Adv. Theor. Math. Phys."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/0550-3213(87)90465-2","article-title":"The quartic effective action for the heterotic string","volume":"291","author":"Gross","year":"1987","journal-title":"Nucl. Phys. B"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"198","DOI":"10.1016\/0370-2693(95)01519-1","article-title":"Maximally symmetric cosmological solutions of higher-curvature string effective theories with dilatons","volume":"368","author":"Bento","year":"1996","journal-title":"Phys. Lett. B"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1016\/0370-2693(85)91616-8","article-title":"Curvature squared terms and string theories","volume":"156","author":"Zwieback","year":"1985","journal-title":"Phys. Lett. B"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/0370-1573(86)90076-1","article-title":"Gravity theories in more than four dimensions","volume":"137","author":"Zumino","year":"1986","journal-title":"Phys. Rep."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1007\/s10509-012-1181-8","article-title":"Dark energy cosmology: The equivalent description via different theoretical models and cosmography tests","volume":"342","author":"Bamba","year":"2012","journal-title":"Astrophys. Space Sci."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2656","DOI":"10.1103\/PhysRevLett.55.2656","article-title":"String-generated gravity models","volume":"55","author":"Boulware","year":"1985","journal-title":"Phys. Rev. Lett."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"124002:1","DOI":"10.1103\/PhysRevD.71.124002","article-title":"Spacetime structure of static solutions in Gauss-Bonnet gravity: Neutral case","volume":"71","author":"Torii","year":"2005","journal-title":"Phys. Rev. D"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"064007:1","DOI":"10.1103\/PhysRevD.72.064007","article-title":"Spacetime structure of static solutions in Gauss-Bonnet gravity: Charged case","volume":"72","author":"Torii","year":"2005","journal-title":"Phys. Rev. D"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"055009:1","DOI":"10.1088\/0264-9381\/25\/5\/055009","article-title":"Dynamical black holes with symmetry in Einstein-Gauss-Bonnet gravity","volume":"25","author":"Nozawa","year":"2008","journal-title":"Class. Quantum Grav."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"R3427","DOI":"10.1103\/PhysRevD.48.R3427","article-title":"Black hole entropy is the Noether charge","volume":"48","author":"Wald","year":"1993","journal-title":"Phys. Rev. D"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"846","DOI":"10.1103\/PhysRevD.50.846","article-title":"Some properties of the Noether charge and a proposal for dynamical black hole entropy","volume":"50","author":"Iyer","year":"1994","journal-title":"Phys. Rev. D"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"4430","DOI":"10.1103\/PhysRevD.52.4430","article-title":"Comparison of the Noether charge and Euclidean methods for computing the entropy of stationary black holes","volume":"52","author":"Iyer","year":"1995","journal-title":"Phys. Rev. D"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF02710419","article-title":"Singular hypersurfaces and thin shells in general relativity","volume":"44","author":"Israel","year":"1966","journal-title":"Nuovo Cimento B"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"024030:1","DOI":"10.1103\/PhysRevD.67.024030","article-title":"Generalized Israel junction conditions for a Gauss-Bonnet brane world","volume":"67","author":"Davis","year":"2003","journal-title":"Phys. Rev. D"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1016\/S0370-2693(03)00555-0","article-title":"Israel conditions for the Gauss?Bonnet theory and the Friedmann equation on the brane universe","volume":"562","author":"Gravanis","year":"2003","journal-title":"Phys. Lett. B"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"084014:1","DOI":"10.1103\/PhysRevD.65.084014","article-title":"Gauss-Bonnet black holes in AdS spaces","volume":"65","author":"Cai","year":"2002","journal-title":"Phys. Rev. D"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"636","DOI":"10.1007\/BF02784569","article-title":"Schwarzschild field in n dimensions and the dimensionality of space problem","volume":"27","author":"Tangherlini","year":"1963","journal-title":"Nouvo Cimento"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"024002:1","DOI":"10.1103\/PhysRevD.69.024002","article-title":"Covariant gravitational equations on a brane world with a Gauss-Bonnet term","volume":"69","author":"Maeda","year":"2004","journal-title":"Phys. Rev. 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