499 research outputs found
Effective null Raychaudhuri equation
The effects on Raychaudhuri's equation of an intrinsically-discrete or
particle nature of spacetime are investigated. This is done through the
consideration of null congruences emerging from, or converging to, a generic
point of spacetime, i.e. in geometric circumstances somehow prototypical of
singularity issues. We do this from an effective point of view, that is through
a (continuous) description of spacetime modified to embody the existence of an
intrinsic discreteness on the small scale, this adding to previous results for
non-null congruences.
Various expressions for the effective rate of change of expansion are
derived. They in particular provide finite values for the limiting effective
expansion and its rate of variation when approaching the focal point. Further,
this results in a non-vanishing of the limiting cross-sectional area itself of
the congruence.Comment: 7 pages; v2: some comparisons with other approaches adde
Entropy bounds and field equations
For general metric theories of gravity, we compare the approach that
describes-derives the field equations of gravity as a thermodynamic identity
with the one which looks at them from entropy bounds. The comparison is made
through the consideration of the matter entropy flux across (Rindler) horizons,
studied by making use of the notion of a limiting thermodynamic scale of
matter, previously introduced in the context of entropy bounds.
In doing this: i) a bound for the entropy of any lump of matter with a given
energy-momentum tensor is considered, in terms of a quantity which is
independent of the theory of gravity we use; this quantity is the variation of
the Clausius entropy of a suitable horizon when the element of matter crosses
it; ii) by making use of the equations of motion of the theory, the same
quantity is then expressed as the variation of Wald's entropy of that horizon
(and this leads to a generalized form of the generalized covariant entropy
bound, applicable to general diffeomorphism-invariant theories of gravity);
iii) a notion of for horizons, and an expression for it, is given.Comment: 8 pages, 1 figure; v4: some typos corrected, one reference and some
clarifications added, some editin
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