Artículo

Morales, J.O.; Santillán, O.P."The existence of smooth solutions in q-models" (2019) General Relativity and Gravitation. 51(2)
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Abstract:

The q-models are scenarios that may explain the smallness of the cosmological constant (Klinkhamer and Volovik in Phys Rev D 77:085015, 2008; Phys Rev D 78:063528, 2008; JETP Lett 88:289, 2008; Mod Phys Lett A 31(28):1650160, 2016; JETP Lett 91:259, 2010; Phys Rev D 79:063527, 2009; J Phys Conf Ser 314:012004, 2011). The vacuum in these theories is presented as a self-sustainable medium and include a new degree of freedom, the q-variable, which establishes the equilibrium of the quantum vacuum. In the present work, the Cauchy formulation for these models is studied in detail. It is known that there exist some limits in which these theories are described by an F(R) gravity model, and these models posses a well posed Cauchy problem. This paper shows that the Cauchy problem is well posed even not reaching this limit. By use of some mathematical theorems about second order non linear systems, it is shown that these scenarios admit a smooth solution for at least a finite time when some specific type of initial conditions are imposed. Some technical conditions of Ringstrom (The Cauchy problem in general relativity, European Mathematical Society, Warsaw, 2000) play an important role in this discussion. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.

Registro:

Documento: Artículo
Título:The existence of smooth solutions in q-models
Autor:Morales, J.O.; Santillán, O.P.
Filiación:Departamento de Matemáticas Luis Santaló (IMAS), UBA CONICET, Buenos Aires, Argentina
Palabras clave:Alternative gravity theories; Cauchy problem; Cosmological constant; Global hyperbolic spaces
Año:2019
Volumen:51
Número:2
DOI: http://dx.doi.org/10.1007/s10714-019-2507-4
Handle:http://hdl.handle.net/20.500.12110/paper_00017701_v51_n2_p_Morales
Título revista:General Relativity and Gravitation
Título revista abreviado:Gen. Relativ. Gravit.
ISSN:00017701
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00017701_v51_n2_p_Morales

Referencias:

  • Klinkhamer, F., Volovik, G., (2008) Phys. Rev. D, 77, p. 085015
  • Klinkhamer, F., Volovik, G., (2008) Phys. Rev. D, 78, p. 063528
  • Klinkhamer, F., Volovik, G., (2008) JETP Lett., 88, p. 289
  • Klinkhamer, F., Volovik, G., (2016) Mod. Phys. Lett. A, 31 (28), p. 1650160
  • Klinkhamer, F., Volovik, G., (2010) JETP Lett., 91, p. 259
  • Klinkhamer, F., Volovik, G., (2009) Phys. Rev. D, 79, p. 063527
  • Klinkhamer, F., Volovik, G., (2011) J. Phys. Conf. Ser., 314, p. 012004
  • Marsden, J., Fischer, A., (1972) Commun. Math. Phys., 28, p. 1
  • Taylor, M., (2010) Partial Differential Equations, Volume 3 of Nonlinear Equations, , Springer, Berlin
  • Courant, R., Hilbert, D., (1991) Methods of Mathematical Physics, 2. , Wiley, Hoboken
  • Ringstrom, H., (2000) The Cauchy Problem in General Relativity, , European Mathematical Society, Zürich, Switzerland
  • Riess, A.G., (1998) Astron. J., 116, pp. 1009-1038
  • Perlmutter, S., (1999) Astrophys. J., 517, pp. 565-586
  • Perlmutter, S., (1998) Nature, 391, pp. 51-54
  • Rubin, V., Ford, W., (1970) Astrophys. J., 159, p. 379
  • Rubin, V., Burstein, D., Ford, W., Jr., Thonnard, N., (1985) Astrophys. J., 289, p. 81
  • Carroll, S., Press, W., Turner, E., (1992) Annu. Rev. Astron. Astrophys., 30, p. 499
  • Dolgov, A., (1982) The Very Early Universe, , Gibbons, G., Hawking, S., Tiklos, S., Cambridge University Press, Cambridge
  • Weinberg, S., (1989) Rev. Mod. Phys., 61, p. 1
  • Dolgov, A., Urban, F., (2008) Phys. Rev. D, 77, p. 083503
  • Carroll, S., (1998) Phys. Rev. Lett., 81, p. 3067
  • Dolgov, A., (1985) JETP Lett., 41, p. 345
  • Dolgov, A., (1997) Phys. Rev. D, 55, p. 5881
  • Bjorken, J., (1963) Ann. Phys., 24, p. 174
  • Kraus, P., Tomboulis, E., (2002) Phys. Rev. D, 66, p. 045015
  • Rubakov, V., Tinyakov, P., (2000) Phys. Rev. D, 61, p. 087503
  • Emelyanov, V., Klinkhamer, F., (2012) Phys. Rev. D, 85, p. 063522
  • Emelyanov, V., Klinkhamer, F., (2012) Int. J. Mod. Phys. D, 21, p. 1250025
  • Emelyanov, V., Klinkhamer, F., (2012) Phys. Rev. D, 85, p. 103508
  • Klinkhamer, F., (2012) Phys. Rev. D, 85, p. 023509
  • Emelyanov, V., Klinkhamer, F., (2012) Phys. Rev. D, 86, p. 027302
  • Santillan, O., Scornavacche, M., (2017) JCAP, 10, p. 048
  • Calogero, F., (1997) Phys. Lett. A, 238, p. 335
  • Vigil, J.E., Masperi, L., (1998) Mod. Phys. Lett. A, 13, p. 423
  • Frieman, J., Hill, C., Watkins, R., (1992) Phys. Rev. D, 46, p. 1226
  • Hill, C., Ross, G., (1988) Nucl. Phys. B, 311, p. 253
  • Hill, C., Ross, G., (1988) Phys. Lett. B, 203, p. 125
  • Gabbanelli, L., Santillan, O., (2016) Mod. Phys. Lett. A, 31 (25), p. 1650143
  • Capozziello, S., Vignolo, S., (2009) Class. Quant. Grav., 26, p. 175013
  • Cappozziello, S., Vignolo, S., (2011) Int. J. Geom. Meth. Mod. Phys., 8, p. 167
  • Friedrich, H., Rendall, A.D., The Cauchy problem for the Einstein equations (2000) Einsteins Field Equations 18 and Their Physical Implications, Lecture Notes in Physics, 540. , Schmidt BG, (ed), Springer, Berlin
  • Rendall, A., (2006) Class. Quant. Grav., 23, p. 1557
  • Alho, A., Mena, F., Valiente Kroon, J., (2017) Adv. Theor. Math. Phys., 21, p. 857
  • Pugliese, D., Valiente Kroon, J., (2013) Gen. Relativ. Gravit., 45, p. 1247
  • Reall, H., Papallo, G., (2017) Phys. Rev. D, 96, p. 044019
  • Choque-Bruhat, Y., (2009) General Relativity and the Einstein Equations, , Oxford Mathematical Monographs
  • Leray, J., (1955) Hyperbolic Differential Equations, , Institute for Advanced Study
  • Choquet-Bruhat, Y., (1952) Acta Math., 88, p. 141
  • Wald, R., (1984) General Relativity, , Chicago University Press, Chicago
  • Hawking, S., (1973) The Large Scale Structure of the Space-Time, , Cambridge Monographs on Mathematical Physics
  • Beem, J., Ehrlich, P., Easley, K., (1981) Global Lorentzian Geometry, , CRC press, Boca Raton
  • O Neill, B., (1983) Semi-Riemannian Geometry with Applications to General Relativity, , Academic Press, Cambridge

Citas:

---------- APA ----------
Morales, J.O. & Santillán, O.P. (2019) . The existence of smooth solutions in q-models. General Relativity and Gravitation, 51(2).
http://dx.doi.org/10.1007/s10714-019-2507-4
---------- CHICAGO ----------
Morales, J.O., Santillán, O.P. "The existence of smooth solutions in q-models" . General Relativity and Gravitation 51, no. 2 (2019).
http://dx.doi.org/10.1007/s10714-019-2507-4
---------- MLA ----------
Morales, J.O., Santillán, O.P. "The existence of smooth solutions in q-models" . General Relativity and Gravitation, vol. 51, no. 2, 2019.
http://dx.doi.org/10.1007/s10714-019-2507-4
---------- VANCOUVER ----------
Morales, J.O., Santillán, O.P. The existence of smooth solutions in q-models. Gen. Relativ. Gravit. 2019;51(2).
http://dx.doi.org/10.1007/s10714-019-2507-4