Wormholes & Holography: An Introduction

We define a (semi-classical) path integral for gravity with Neumann boundary conditions in D dimensions, and show how to relate this new partition function to the usual picture of Euclidean quantum gravity. We also write down the action in ADM Hamiltonian formulation and use it to reproduce the entropy of black holes and cosmological horizons. A comparison between the (background-subtracted) covariant and Hamiltonian ways of semi-classically evaluating this path integral in flat space reproduces the generalized Smarr formula and the first law. This “Neumann ensemble” perspective on gravitational thermodynamics is parallel to the canonical (Dirichlet) ensemble of Gibbons-Hawking and the microcanonical approach of Brown-York.

To explain black hole thermodynamics in quantum gravity, one must introduce constraints to ensure that a black hole is actually present. I show that for a large class of black holes, such "horizon constraints" allow the use of conformal field theory techniques to compute the density of states, reproducing the Bekenstein-Hawking entropy in a nearly model-independent manner. One standard string theory approach to black hole entropy arises as a special case, lending support to the claim that the mechanism may be "universal." I argue that the relevant degrees of freedom are Goldstone-boson-like excitations arising from the weak breaking of symmetry by the constraints.

In this paper, we have applied the Lorentz-invariance violation (LIV) class of dispersion relations (DRs) with the dimensionless parameter $$\textit{n}=2$$ and the “sign of LIV” $$\eta _+ = 1$$ , to a phenomenological study of the effect of quantum gravity in a strong gravitational field. Specifically, we have studied the effect of the LIV-DR induced quantum gravity on the Schwarzschild black hole thermodynamics. The result shows that the effect of the LIV-DR induced quantum gravity speeds up the black hole evaporation, and its corresponding black hole entropy undergoes a leading logarithmic correction to the “reduced Bekenstein–Hawking entropy”, and the ill-defined situations (i.e. the singularity problem and the critical problem) are naturally bypassed when the LIV-DR effect is present. Also, to put our results in a proper perspective, we have compared results with the earlier findings by another quantum-gravity candidate, i.e. the generalized uncertainty principle (GUP). Finally, we …

In this work we suggest a simplified "quasi-classical" formalism of the Schwarzschild black hole thermodynamics. We define such small quantum system at Schwarzschild black hole horizon surface whose reduced Compton wavelength equals one circumference of a great circle on the black hole horizon surface. (It is in some way similar to the Bohr orbital momentum quantization postulate for the ground state interpreted via de Broglie relation.) It admits very simple functional connections between all black hole basic thermodynamic characteristics (Unruh temperature, Hawking temperature, Bekenstein-Hawking entropy, Bekenstein entropy horizon surface quantization, evaporation time) and small quantum system mass. All this can be very interesting for the quantum gravity specialists as well as non-specialists.

In this article we explore the origin of black hole thermodynamics using semiclassical states in loop quantum gravity.We re-examine the case of entropy using a density matrix for a coherent state and describe correlations across the horizon due to SU(2) intertwiners.We further show that Hawking radiation is a consequence of a non-Hermitian term in the evolution operator, which is necessary for entropy production or depletion at the horizon.This non-unitary evolution is also rooted in formulations of irreversible physics.