Perturbative String Dynamics Near the Photon Sphere.pdfVIP

Perturbative String Dynamics Near the Photon Sphere Mariusz P. D¸abrowski ∗ Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland Alexander A. Zheltukhin † Department of Theoretical Physics, NSC Kharkov Institute of Physics and Technology, 8 Akademicheskaya Str. 1, 310108, Kharkov, Ukraine 9 9 1 (February 1, 2008) p e S 4 Abstract 2 1 v 6 7 1 String dynamics near the photon sphere in Schwarzschild spacetime is 9 0 considered on the basis of a perturbative approach with respect to a rescaled 8 9 string tension as a small parameter. The perturbative string solution in the / h t - zeroth and first approximation is presented. The perturbative solution corre- p e h sponds to a small deformation of the photon sphere in Schwarzschild space- : v time. i X r a PACS number(s): 04.70.Bw, 04.70.Dy, 11.25.-w, 11.25 Mj ∗E-mail: mpdabfz@uoo.univ.szczecin.pl †E-mail: zheltukhin@kipt.kharkov.ua 1 I. INTRODUCTION The classical evolution of strings in curved backgrounds is described by a complicated system of second-order non-linear coupled partial differential equations which is integrable only for some special configurations [1]. A vast simplification of the equations of motion arises when one neglects string tension and considers the null (tensionless) strings [2]. Their equations of motion are null geodesic equations of General Relativity appended by an addi- tional ‘stringy’ constraint. The exact null string configurations were studie