1996/04/08 by Sayan Kar, Kar, Sayan
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #gr-qc #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/9604046
RevTex, 16 Pages, no figures, Written version of Invited Talk at IAGRG--XVIII (Matscience, Madras, India (Feb. 15-17, 1996))
arxiv created 1996/04/08 · openalex publication_date 1996/04/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A recent generalisation of the Raychaudhuri equations for timelike geodesic congruences to families of D dimensional extremal, timelike, Nambu--Goto surfaces embedded in an N dimensional Lorentzian background is reviewed. Specialising to D=2 (i.e the case of string worldsheets) we reduce the equation for the generalised expansion θa, (a =σ,τ) to a second order, linear, hyperbolic partial differential equation which resembles a variable--mass wave equation in 1+1 dimensions. Consequences, such as a generalisation of geodesic focussing to families of worldsheets as well as exactly solvable cases are explored and analysed in some detail. Several possible directions of future research are also pointed out.