N-dimensional Vaidya metric with a cosmological constant in double-null coordinates

Abstract

A recently proposed approach to the construction of the Vaidya metric in double-null coordinates for generic mass functions is extended to the n-dimensional (n > 2) case and to allow the inclusion of a cosmological constant. The approach is based on a qualitative study of the null-geodesics, allowing the description of light-cones and revealing many features of the underlying causal structure. Possible applications are illustrated by explicit examples. Some new exact solutions are also presented and discussed. The results presented here can simplify considerably the study of spherically symmetric gravitational collapse and mass accretion in arbitrary dimensions.

Nonstationary regime for quasinormal modes of the charged Vaidya metric

“…In particular, our expressions coincide, in the appropriate limits, with the previous results for the à ¼ 0 [31] and for the q ¼ 0 [40] cases. However, the commonly employed conventions in the QNM literature are slightly different; see, for instance, [41].…”

“…We will now extend the approach proposed in [39,40] and derive the double-null formulation for the most general Vaidya metric: n-dimensional, in the presence of a cosmological constant, and with varying electric charge. Only the main results are presented.…”

“…Only the main results are presented. The reader can get more details on the employed semianalytical approach in [39,40] and the references cited therein. We recall that the n-dimensional spherically symmetric line element in double-null coordinates ðu; v; 1 ; .…”

“…The problem here is the definition, and the numerical determination, of the event horizon. (See [40] for a discussion of the implications of this problem in the semianalytical approach used here.) For our purposes here, the event horizon r þ is the last null geodesic (up to the machine precision) escaping towards infinity, requiring the full numerical solution of (6) prior to the analysis of the wave Eq.…”

Wave Equations in Higher Dimensions

“…Consequently, it is necessary to review the development of the relativity and gravity in higher dimensional wave equations for completeness. These contributions can be summarized as follows: the brane models [119], scalar field contribution to rotating black hole entropy [120], brane cosmology [121], N -dimensional Vaidya metric with a cosmological constant in double-null coordinates [122], the spherical gravitational collapse in N dimensions [123], the motion of a dipole in a cosmic string background [124], repulsive Casimir effect from extra dimensions and Robin boundary conditions [125], extremal black hole/CFT correspondence in gauged supergravity [126], massive fermion emission from higher dimensional black holes [127], magnetic and electric black holes [128], fermion families from two layer warped extra dimensions [129], quasinormal behavior of the D-dimensional Schwarzschild black hole [130], the study of the Schrödinger-Newton equations in D dimensions [131], rotating Einstein-Maxwell-Dilaton black holes in D dimensions [132], the Kaluza-Klein theory in the limit of large number of extra dimensions [133], gauge invariance of the one-loop effective potential in (d + 1)-dimensional Kaluza-Klein theory [134] and the multicentered solution for maximally charged dilaton black holes in arbitrary dimensions [135]. Such method was also generalized to quantum modes of the scalar field on AdS d+1 space-time [117] as well as geometric models of the (d + 1)-dimensional relativistic rotating oscillators [118].…”