Access by Xinjiang University

Hawking radiation for a Proca field in $D$ dimensions

Carlos Herdeiro^*, Marco O. P. Sampaio^†, and Mengjie Wang^‡

Departamento de Física da Universidade de Aveiro and I3N Campus de Santiago, 3810-183 Aveiro, Portugal

^*herdeiro@ua.pt
^†msampaio@ua.pt
^‡mengjie.wang@ua.pt

Phys. Rev. D 85, 024005 – Published 4 January, 2012

DOI: https://doi.org/10.1103/PhysRevD.85.024005

Abstract

We study the wave equation of a massive vector boson in the background of a $D$ -dimensional Schwarzschild black hole. The mass term introduces a coupling between two physical degrees of freedom of the field, and we solve the resulting system of ordinary differential equations numerically, without decoupling. We show how to define decoupled transmission factors from an $S$ matrix and compute them for various modes, masses, and space-time dimensions. The mass term lifts the degeneracy between transverse modes, in $D = 4$ , and excites the longitudinal modes, in particular, the $s$ wave. Moreover, it increases the contribution of waves with larger $ℓ$ , which can be dominant at intermediate energies. The transmission factors are then used to obtain the Hawking fluxes in this channel. Our results alert for the importance of modeling the longitudinal modes correctly, instead of treating them as decoupled scalars as they are in current black hole event generators; thus, they can be used to improve such generators for phenomenological studies of TeV gravity scenarios.

Article Text

References (37)

S. Teukolsky, Phys. Rev. Lett. 29, 1114 (1972).
S. Chandrasekhar, The Mathematical Theory of Black Holes (Clarendon, Oxford, 1992), p. 646.
H. K. Kunduri, J. Lucietti, and H. S. Reall, Phys. Rev. D 74, 084021 (2006).
F. R. Tangherlini, Nuovo Cimento 27, 636 (1963).
V. Ferrari, L. Gualtieri, and S. Marassi, Phys. Rev. D 76, 104033 (2007).
C. Molina, P. Pani, V. Cardoso, and L. Gualtieri, Phys. Rev. D 81, 124021 (2010).
I. Antoniadis, Phys. Lett. B 246, 377 (1990).
N. Arkani-Hamed, S. Dimopoulos, and G. R. Dvali, Phys. Lett. B 429, 263 (1998).
I. Antoniadis, N. Arkani-Hamed, S. Dimopoulos, and G. R. Dvali, Phys. Lett. B 436, 257 (1998).
N. Arkani-Hamed, S. Dimopoulos, and G. R. Dvali, Phys. Rev. D 59, 086004 (1999).
G. ’t Hooft, Phys. Lett. B 198, 61 (1987).
M. W. Choptuik and F. Pretorius, Phys. Rev. Lett. 104, 111101 (2010).
H. Yoshino and V. S. Rychkov, Phys. Rev. D 71, 104028 (2005).
C. Herdeiro, M. O. P. Sampaio, and C. Rebelo, J. High Energy Phys. 07 (2011) 121.
H. Witek, M. Zilhao, L. Gualtieri, V. Cardoso, C. Herdeiro et al., Phys. Rev. D 82, 104014 (2010).
H. Witek, V. Cardoso, L. Gualtieri, C. Herdeiro, U. Sperhake et al., Phys. Rev. D 83, 044017 (2011).
H. Okawa, K.-i. Nakao, and M. Shibata, Phys. Rev. D 83, 121501 (2011).
M. Zilhao, H. Witek, U. Sperhake, V. Cardoso, L. Gualtieri et al., Phys. Rev. D 81, 084052 (2010).
H. Yoshino and M. Shibata, Phys. Rev. D 80, 084025 (2009).
S. W. Hawking, Commun. Math. Phys. 43, 199 (1975).
G. Aad et al. (The ATLAS Collaboration), arXiv:0901.0512.
J. A. Frost et al., J. High Energy Phys. 10 (2009) 014.
D.-C. Dai et al., Phys. Rev. D 77, 076007 (2008).
V. Khachatryan et al. (CMS Collaboration), Phys. Lett. B 697, 434 (2011).
The ATLAS Collaboration, CERN Report No. ATLAS-CONF-2011-065, 2011.
The ATLAS Collaboration, CERN Report No. ATLAS-CONF-2011-068, 2011.
H. Kodama, A. Ishibashi, and O. Seto, Phys. Rev. D 62, 064022 (2000).
R. Konoplya, Phys. Rev. D 73, 024009 (2006).
D. N. Page, Phys. Rev. D 13, 198 (1976).
M. O. Sampaio, J. High Energy Phys. 10 (2009) 008.
M. O. Sampaio, J. High Energy Phys. 02 (2010) 042.
P. Kanti, Int. J. Mod. Phys. A 19, 4899 (2004).
A. Ishibashi and H. Kodama, Prog. Theor. Phys. Suppl. 189, 165 (2011).
M. O. P. Sampaio, Ph.D. thesis, Cambridge University, 2010, http://www.dspace.cam.ac.uk/handle/1810/226741.
T. Nakamura and H. Sato, Phys. Lett. 61B, 371 (1976).
D. N. Page, Phys. Rev. D 16, 2402 (1977).
D. N. Page, Phys. Rev. D 14, 3260 (1976).

Physical Review D

Export citation

Export citation

Hawking radiation for a Proca field in $D$ dimensions

Abstract

See Also