Small scale structure of spacetime in presence of a minimal length

Spanish Relativity Meeting: almost 100 years after Einstein's revolution

Kothawala, Dawood^1

Indian Institute of Technology Madras, Chennai, India^1

关键词: Covariant;    Lorentz covariances;    Metric tensor;    Minimal lengths;    Nonlocal;    Residual entropy;    Small-scale structures;    Spacetime;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/600/1/012069/pdf
DOI  :  10.1088/1742-6596/600/1/012069

来源: IOP

【 摘 要 】

I present some recent results which yields some specific consequences of having a minimal spacetime length L0while maintaining Lorentz covariance. In particular: (i) the resultant description of geometry must be in terms of a non-local bi-tensor qab(P,p, L20) instead of the conventional metric tensor gab(p), (ii) qaband gabare related disformally through the Synge world function, (iii) the resultant non-local d'Alembartian yields Green's functions with a natural covariant short distance cut-off, (iv) the Ricci bi-scalar R(P,p, L20) corresponding to qabyields a local scalar S(P, L20) = R(P, P, L20) in the coincidence such that lim L → 0 S(P;L) ∝ Rabtatbwhere taare arbitrary normalized vectors representing gauge degrees of freedom at each spacetime event; this limit turns out to be independent of the precise details of the short distance modification, (v) the Gibbons-Hawking-York surface term for qabyields a residual entropy for each spacetimeevent