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Register a new userThe End of Time?
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Added by
Jeremy Nicholas Butterfield
Publication date
2001
fields
Physics
and research's language is
English
Authors
J. N. Butterfield
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I discuss J. Barbours Machian theories of dynamics, and his proposal that a Machian perspective enables one to solve the problem of time in quantum geometrodynamics (by saying that there is no time). I concentrate on his recent book The End of Time (1999).
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The unphysical spin-2 massive degrees of freedom in higher derivative gravity may be either massive unphysical ghosts or tachyonic ghosts. In the last case there is no Planck-scale threshold protecting vacuum cosmological solutions from instabilities. Within the anomaly-induced action formalism the photon-driven IR running of the coefficient of the Weyl-squared term makes the ghost eventually becoming tachyon, that should produce a gravitational explosion of vacuum. This effect is stable under higher loop corrections and takes place also in kno
Black holes in $d < 3$ spatial dimensions are studied from the perspective of the corpuscular model of gravitation, in which black holes are described as Bose-Einstein condensates of (virtual soft) gravitons. In particular, since the energy of these gravitons should increase as the black hole evaporates, eventually approaching the Planck scale, the lower dimensional cases could provide important insight into the late stages and end of Hawking evaporation. We show that the occupation number of gravitons in the condensate scales holographically in all dimensions as $N_d sim left(L_d/ell_{rm p}right)^{d-1}$, where $L_d$ is the relevant length for the system in the $(1+d)$-dimensional space-time. In particular, this analysis shows that black holes cannot contain more than a few gravitons in $d=1$. Since dimensional reduction is a common feature of many models of quantum gravity, this result can shed light on the end of the Hawking evaporation. We also consider $(1+1)$-dimensional cosmology in the context of corpuscular gravity, and show that the Friedmann equation reproduces the expected holographic scaling as in higher dimensions.
We discuss the near singularity region of the linear mass Vaidya metric for massless particles with non-zero angular momentum. In particular we look at massless geodesics with non-zero angular momentum near the vanishing point of a special subclass of linear mass Vaidya metrics. We also investigate this same structure in the numerical solutions for the scattering of massless scalars from the singularity. Finally we make some comments on the possibility of using this metric as a semi-classical model for the end-point of black hole evaporation.
Despite the ultraviolet problems with canonical quantum gravity, as an effective field theory its infrared phenomena should enjoy fully quantum mechanical unitary time evolution. Currently this is not possible, the impediment being what is known as the problem of time. Here, we provide a solution by promoting the cosmological constant $Lambda$ to a Lagrange multiplier constraining the metric volume element to be manifestly a total derivative. Because $Lambda$ appears linearly in the Hamiltonian constraint, it unitarily generates time evolution, yielding a functional Schroedinger equation for gravity. Two pleasant side effects of this construction are that vacuum energy is dissociated from the cosmological constant problem, much like in unimodular gravity, and the natural foliation provided by the time variable defines a sensible solution to the measure problem of eternal inflation.
We perform a rigorous piecewise-flat discretization of classical general relativity in the first-order formulation, in both 2+1 and 3+1 dimensions, carefully keeping track of curvature and torsion via holonomies. We show that the resulting phase space is precisely that of spin networks, the quantum states of discrete spacetime in loop quantum gravity, with additional degrees of freedom called edge modes, which control the gluing between cells. This work establishes, for the first time, a rigorous proof of the equivalence between spin networks and piecewise-flat geometries with curvature and torsion degrees of freedom. In addition, it demonstrates that careful consideration of edge modes is crucial both for the purpose of this proof and for future work in the field of loop quantum gravity. It also shows that spin networks have a dual description related to teleparallel gravity, where gravity is encoded in torsion instead of curvature degrees of freedom. Finally, it sets the stage for collaboration between the loop quantum gravity community and theoretical physicists working on edge modes from other perspectives, such as quantum electrodynamics, non-abelian gauge theories, and classical gravity.
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