Gravitational redshift in Einstein-Kalb-Ramond spacetime and Randall-Sundrum scenario

– It is shown that the gravitational redshift as predicted by Einstein’s theory is modified in the presence of a second-rank antisymmetric tensor (Kalb-Ramond) field in a string-inspired background spacetime. In the presence of extra dimensions, the RandallSundrum brane world scenario is found to play a crucial role in suppressing this additional shift. The bound on the value of the warp factor is determined from the redshift data and is found to be in excellent agreement with that determined from the requirements of the standard model. The massless antisymmetric tensor Kalb-Ramond (KR) field Bμν , that appears in the string spectrum [1], implements in a natural way the spacetime background for string theory possessing torsion in addition to curvature. Quantum consistency of the theory further demands the augmentation of the KR field strength ∂[μBνλ] with the Chern-Simons (CS) three-form. The CS extension, in turn, plays the crucial role in restoring the U(1) gauge symmetry [2] that is apparently lost when torsion is coupled minimally with the gauge field in the original Einstein-Cartan theory. Solutions of the modified general relativistic field equations in various situations may now provide new results leading to a possible quantitative assessment of string-inspired torsion models. In an earlier work [3], the study of geodesics in static spherisymmetric KR spacetimes with or without gravitating matter provided evidences for effects of the KR field in the context of bending of light trajectories as well as perihelion precession of planetary orbits which differ from the general relativistic estimates. Although the prospect of detecting the KR field is quite pronounced in an otherwise empty spacetime (which incidentally resembles a wormhole or a naked singularity [3, 4]), in the presence of gravitating matter the KR field produces little effects on the above-mentioned phenomena. One possible reason for such smallness of torsion (or the KR field) can be given (∗) E-mail: [email protected] (∗∗) E-mail: [email protected]