[Paper Review] Induced Gravity in Superfluid 3He

G. E. Volovik|arXiv (Cornell University)|Jun 1, 1998

Quantum, superfluid, helium dynamics4 citations

TL;DR

This paper proposes that superfluid 3He-A, due to its relativistic-like gapless fermionic excitations near nodal points, naturally induces an effective gravitational metric in the quantum vacuum. By engineering different order parameter textures, the system simulates exotic spacetime geometries—including black holes, cosmic strings, and inflation—enabling experimental study of quantum gravity phenomena like Hawking radiation and Bekenstein entropy.

ABSTRACT

The gapless fermionic excitations in superfluid 3He-A have the "relativistic" spectrum close to the gap nodes. This allowed us to model the modern cosmological scenaria of baryogenesis and magnetogenesis. The same massless fermions induce another low-energy property of the quantum vacuum -- the gravitation. The effective metric of the space, in which the free quasiparticles move along geodesics, is not generally flat. Different order parameter textures correspond to curved effective space and produce many different exotic metrics, which are theoretically discussed in quantum gravity and cosmology. This includes the condensed matter analog of the black hole and event horizon, which can be realized in the moving soliton. This will allow us to simulate and thus experimentally investigate such quantum phenomena as the Hawking radiation from the horizon, the Bekenstein entropy of the black hole, and the structure of the quantum vacuum behind the horizon. One can also simulate the conical singularities produced by cosmic strings and monopoles; inflation; temperature dependence of the cosmological and Newton constants, etc.

Motivation & Objective

• To demonstrate that superfluid 3He-A can serve as a condensed matter analog of relativistic quantum field theory in curved spacetime.
• To show that the low-energy fermionic excitations near gap nodes induce an effective metric, leading to emergent gravity.
• To propose that various order parameter textures in 3He-A can realize exotic spacetime geometries relevant to quantum gravity and cosmology.
• To enable experimental simulation of quantum gravity phenomena such as Hawking radiation and black hole entropy.
• To explore the connection between topological defects (e.g., solitons, cosmic strings) and curvature in the effective spacetime.

Proposed method

• Utilize the relativistic-like dispersion of fermionic quasiparticles near the gap nodes in superfluid 3He-A to model massless Dirac fermions.
• Derive the effective metric tensor from the spatial variation of the order parameter, which governs the geodesic motion of quasiparticles.
• Construct specific textures of the order parameter (e.g., moving solitons, vortex lines) to realize curved spacetime geometries such as black hole horizons.
• Apply the formalism of effective field theory to relate the low-energy dynamics of quasiparticles to general relativity in curved spacetime.
• Use the analogy between the effective metric and gravitational fields to simulate phenomena like event horizons and conical singularities.
• Leverage the system’s tunability to probe the temperature dependence of Newton’s constant and cosmological constant in the effective theory.

Experimental results

Research questions

• RQ1 Can the low-energy excitations in superfluid 3He-A simulate relativistic fermions in curved spacetime?
• RQ2 How do spatial textures of the order parameter in 3He-A generate effective gravitational metrics?
• RQ3 What types of exotic spacetime geometries (e.g., black holes, cosmic strings) can be realized in this system?
• RQ4 Can the system be used to simulate quantum gravity effects such as Hawking radiation and Bekenstein entropy?
• RQ5 How does the effective Newton’s constant and cosmological constant depend on temperature in this condensed matter analog?

Key findings

• The gapless fermionic excitations in superfluid 3He-A exhibit a relativistic spectrum near the nodal points, enabling the emergence of effective spacetime geometry.
• The effective metric is induced by spatial variations in the order parameter, leading to geodesic motion of quasiparticles in a curved effective spacetime.
• Moving solitons in 3He-A realize an analog of a black hole horizon, allowing the simulation of Hawking radiation.
• The system can realize conical singularities associated with cosmic strings and monopoles through specific topological textures.
• The effective Newton’s constant and cosmological constant in the emergent gravity theory are predicted to depend on temperature, as derived from the low-energy effective action.
• The model provides a framework to experimentally probe quantum vacuum structure and entropy behind horizons using tunable superfluid 3He-A.