Open Access

Limiting Case of the Spin Hypersurface Dirac Operator arising in the positive mass theorem for black holes

   | Dec 31, 2020

Cite

C. Bär, (1992), Lower eigenvalue estimates for Dirac operators, Math. Ann., 293(1), 39–46. BärC. 1992 Lower eigenvalue estimates for Dirac operators Math. Ann. 293 1 39 46 10.1007/BF01444701 Search in Google Scholar

S. Eker, (2020), Lower Bound Eigenvalue Problems of the Compact Riemannian Spin-Submanifold Dirac Operator, Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 13 (ÖZEL SAYI I), 56–62. EkerS. 2020 Lower Bound Eigenvalue Problems of the Compact Riemannian Spin-Submanifold Dirac Operator Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi 13 (ÖZEL SAYI I), 56 62 Search in Google Scholar

S. Eker, (2020), Lower Bounds for the Eigenvalues of the Dirac Operator on Spinc Manifolds, Iranian Journal of Science and Technology, Transactions A: Science, 44(1), 251–257. EkerS. 2020 Lower Bounds for the Eigenvalues of the Dirac Operator on Spinc Manifolds Iranian Journal of Science and Technology, Transactions A: Science 44 1 251 257 10.1007/s40995-020-00823-5 Search in Google Scholar

M. Ergen, (2020), Some Estimates for the Spin-Submanifold Twisted Dirac Operators, Turkish Journal of Science, 5(1), 8–15. ErgenM. 2020 Some Estimates for the Spin-Submanifold Twisted Dirac Operators Turkish Journal of Science 5 1 8 15 Search in Google Scholar

T. Friedrich, (1980), Der erste Eigenwert des Dirac-Operators einer kompakten, Riemannschen Mannigfaltigkeit nichtnegativer Skalarkrümmung, Math. Nachr., 97(1), 117–146. FriedrichT. 1980 Der erste Eigenwert des Dirac-Operators einer kompakten, Riemannschen Mannigfaltigkeit nichtnegativer Skalarkrümmung Math. Nachr. 97 1 117 146 10.1002/mana.19800970111 Search in Google Scholar

T. Friedrich and E.C. Kim, (2001), Some remarks on the Hijazi inequality and generalizations of the Killing equation for spinors, J. Geom. Phys., 37(1–2), 1–14. FriedrichT. KimE.C. 2001 Some remarks on the Hijazi inequality and generalizations of the Killing equation for spinors J. Geom. Phys. 37 1–2 1 14 10.1016/S0393-0440(99)00049-2 Search in Google Scholar

G. Gibbons, S. Hawking and G. Horowitz and M. Perry, (1983), Positive mass theorems for black holes, Comm. Math. Phys., 88(3), 295–308. GibbonsG. HawkingS. HorowitzG. PerryM. 1983 Positive mass theorems for black holes Comm. Math. Phys. 88 3 295 308 10.1007/BF01213209 Search in Google Scholar

M. Herzlich, (1998), The positive mass theorem for black holes revisited, J. Geom. Phys., 26(1–2), 97–111. HerzlichM. 1998 The positive mass theorem for black holes revisited J. Geom. Phys. 26 1–2 97 111 10.1016/S0393-0440(97)00040-5 Search in Google Scholar

O. Hijazi, (1986), A conformal lower bound for the smallest eigenvalue of the Dirac operator and Killing spinors, Comm. Math. Phys., 104, 151–162. HijaziO. 1986 A conformal lower bound for the smallest eigenvalue of the Dirac operator and Killing spinors Comm. Math. Phys. 104 151 162 10.1007/BF01210797 Search in Google Scholar

O. Hijazi, (1991), Première valeur propre de l’opérateur de Dirac et nombre de Yamabe, Comptes rendus de l’Académie des sciences. Série 1, Mathématique, 313(12), 865–868. HijaziO. 1991 Première valeur propre de l’opérateur de Dirac et nombre de Yamabe, Comptes rendus de l’Académie des science Série 1, Mathématique 313 12 865 868 Search in Google Scholar

O. Hijazi, (1995), Lower bounds for the eigenvalues of the Dirac operator, J. Geom. Phys, 16, 27–38. HijaziO. 1995 Lower bounds for the eigenvalues of the Dirac operator J. Geom. Phys 16 27 38 10.1016/0393-0440(94)00019-Z Search in Google Scholar

O. Hijazi and X. Zhang, (2001), Lower bounds for the eigenvalues of the Dirac operator: part I. The hypersurface Dirac operator, Ann. Global Anal. Geom., 19(4), 355–376. HijaziO. ZhangX. 2001 Lower bounds for the eigenvalues of the Dirac operator: part I. The hypersurface Dirac operator Ann. Global Anal. Geom. 19 4 355 376 10.1023/A:1010749808691 Search in Google Scholar

O. Hijazi and X. Zhang, (2001), Lower Bounds for the Eigenvalues of the Dirac Operator: Part II. The Submanifold Dirac Operator, Ann. Global Anal. Geom., 20(2), 163–181. HijaziO. ZhangX. 2001 Lower Bounds for the Eigenvalues of the Dirac Operator: Part II. The Submanifold Dirac Operator Ann. Global Anal. Geom. 20 2 163 181 10.1023/A:1011663603699 Search in Google Scholar

O. Hijazi, S. Montiel and X. Zhang, (2001), Eigenvalues of the Dirac Operator on Manifolds with Boundary, Comm. Math. Phys., 221(2), 255–265. HijaziO. MontielS. ZhangX. 2001 Eigenvalues of the Dirac Operator on Manifolds with Boundary Comm. Math. Phys. 221 2 255 265 10.1007/s002200100475 Search in Google Scholar

H. Lawson, M. Michelsohn, (1963), Spin geometry, Princeton university press, 1989. LawsonH. MichelsohnM. 1963 Spin geometry Princeton university press 1989 Search in Google Scholar

A. Lichnerowicz, Spineurs harmoniques, C.R. Acad. Sci. Paris Ser. A-B, 257. LichnerowiczA. Spineurs harmoniques C.R. Acad. Sci. Paris Ser. A-B 257 Search in Google Scholar

R. Nakad, J. Roth, (2013), The Spinc Dirac operator on hypersurfaces and applications, Differential Geom. Appl. 31(1), 93–103. NakadR. RothJ. 2013 The Spinc Dirac operator on hypersurfaces and applications Differential Geom. Appl. 31 1 93 103 10.1016/j.difgeo.2012.11.003 Search in Google Scholar

X. Zhang, (1998), Lower bounds for eigenvalues of hypersurface Dirac operators, Math. Res. Lett., 5(2), 199–210. ZhangX. 1998 Lower bounds for eigenvalues of hypersurface Dirac operators Math. Res. Lett. 5 2 199 210 10.4310/MRL.1998.v5.n2.a6 Search in Google Scholar

X. Zhang, (1999), Angular momentum and positive mass theorem, Comm. Math. Phys., 206(1), 137–155. ZhangX. 1999 Angular momentum and positive mass theorem Comm. Math. Phys. 206 1 137 155 10.1007/s002200050700 Search in Google Scholar

E. Witten, (1981), A new proof of the positive energy theorem, Comm. Math. Phys., 80(3), 381–402. WittenE. 1981 A new proof of the positive energy theorem Comm. Math. Phys. 80 3 381 402 10.1007/BF01208277 Search in Google Scholar

eISSN:
2444-8656
Language:
English
Publication timeframe:
Volume Open
Journal Subjects:
Life Sciences, other, Mathematics, Applied Mathematics, General Mathematics, Physics