Raychaudhuri equation with zero point length

Abstract

The Raychaudhuri equation for a geodesic congruence in the presence of a zero-point length has been investigated. This is directly related to the small-scale structure of spacetime and possibly captures some quantum gravity effects. The existence of such a minimum distance between spacetime events modifies the associated metric structure and hence the expansion as well as its rate of change deviates from standard expectations. This holds true for any kind of geodesic congruences, including time-like and null geodesics. Interestingly, this construction works with generic spacetime geometry without any need of invoking any particular symmetry. In particular, inclusion of a zero-point length results into a non-vanishing cross-sectional area for the geodesic congruences even in the coincidence limit, thus avoiding formation of caustics. This will have implications for both time-like and null geodesic congruences, which may lead to avoidance of singularity formation in the quantum spacetime.

Quantum phenomenological gravitational dynamics: a general view from thermodynamics of spacetime

“…The time derivative of heat crossing Σ in the limit of large a equals 32) where S (t) is a spatial cross-section of Σ with a constant value of the time coordinate, t, and 4 is the area element on S (t). This can be written as an integral of T µν k µ ± k ν ± , where k µ ± are null vectors corresponding to the positive and negative values of t, respectively.…”

“…By doing so, we implicitly assume that Clausius entropy is, at least in the leading order in l, equivalent to the matter entanglement entropy, The validity of this assumption and details of the comparison were carefully analysed in [20]. Considering the most general formula for entanglement entropy with a logarithmic correction, its change between times t = 0 and t = l/c equals ∆S e,q = −4πηl 2 + 4πηl 4 9…”

“…The search for the elusive theory of quantum gravity has been a fundamental pillar of research in the last decades, and although there are promising candidates, none of them has yet provided a consistent final theory. In this context, phenomenology of quantum gravity has acquired interest as an approach to extract information about the possible dynamical effects of quantum gravity theories in the low energy regime [1][2][3][4]. Its results have mainly focused on the understanding of physics close to classical singularities [5][6][7].…”

Embedding into flat spacetime and black hole thermodynamics

“…This demonstrates why solutions of gravitational field equations, in particular black hoes, exhibited the thermodynamic properties. Interestingly, these results transcend general relativity and holds in Lanczos-Lovelock theories of gravity as well, which once again demonstrates that gravity thermodynamics correspondence hints at microscopic "atomic" structure of gravity [18,22,23].…”

Gravity and quantum theory: Domains of conflict and contact

“…For the sake of illustration, I will use the simple function S(σ 2 ) = σ 2 + L 2 0 . The introduction of zero-point-length is also likely to eliminate spacetime singularities [80] but I will not discuss this aspect here.…”