Emergent gravity from relatively local Hamiltonians and a possible resolution of the black hole information puzzle
Abstract
In this paper, we study a possibility where gravity and time emerge from quantum matter. Within the Hilbert space of matter fields defined on a spatial manifold, we consider a subHilbert space spanned by states which are parameterized by spatial metric. In those states, metric is introduced as a collective variable that controls local structures of entanglement. The underlying matter fields endow the states labeled by metric with an unambiguous inner product. Then we construct a Hamiltonian for the matter fields that is an endomorphism of the subHilbert space, thereby inducing a quantum Hamiltonian of the metric. It is shown that there exists a matter Hamiltonian that induces the general relativity in the semiclassical field theory limit. Although the Hamiltonian is not local in the absolute sense, it has a weaker notion of locality, called relative locality : the range of interactions is set by the entanglement present in target states on which the Hamiltonian acts. In general, normalizable states are not invariant under the transformations generated by the Hamiltonian. As a result, a physical state spontaneously breaks the Hamiltonian constraint, and picks a moment of time. The subsequent flow of time can be understood as a Goldstone mode associated with the broken symmetry. The construction allows one to study dynamics of gravity from the perspective of matter fields. The Hawking radiation corresponds to a unitary evolution where entanglement across horizon is gradually transferred from color degrees of freedom to singlet degrees of freedom. The underlying quantum states remain pure as evaporating black holes keep entanglement with early Hawking radiations in the singlet sector which is not captured by the BekensteinHawking entropy.
 Publication:

Journal of High Energy Physics
 Pub Date:
 October 2018
 DOI:
 10.1007/JHEP10(2018)043
 arXiv:
 arXiv:1803.00556
 Bibcode:
 2018JHEP...10..043L
 Keywords:

 AdSCFT Correspondence;
 Black Holes;
 Holography and condensed matter physics (AdS/CMT);
 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 66 pages, 19 figures