Negative scalar curvature as a characteristic of the elasticity of the gravitational field

We generate numerically on a lattice an ensemble of stationary metrics, with spherical symmetry, which have Einstein action SE « ћ. This is obtained through a Metropolis algorithm with weight exp(−β2S2E) and β » ћ−1. The squared action in the exponential allows to circumvene the problem of the non-positivity of SE. The discretized metrics obtained exhibit a spontaneous polarization in regions of positive and negative scalar curvature. We compare this ensemble with a class of continuous metrics previously found, which satisfy the condition SE = 0 exactly, or in certain cases even the stronger condition R(x) = 0 for any x. All these gravitational field configurations are of considerable interest in quantum gravity, because they represent possible vacuum fluctuations and are markedly different from Wheeler’s “spacetime foam”.

Download Full-text

Metrics with Zero and Almost-zero Einstein Action in Quantum Gravity

10.20944/preprints201909.0279.v1 ◽

2019 ◽

Author(s):

Giovanni Modanese

Keyword(s):

Gravitational Field ◽

Quantum Gravity ◽

Scalar Curvature ◽

Spontaneous Polarization ◽

Spherical Symmetry ◽

Metropolis Algorithm ◽

Vacuum Fluctuations ◽

Spacetime Foam

We generate numerically on a lattice an ensemble of stationary metrics, with spherical symmetry, which have Einstein action SE « ħ. This is obtained through a Metropolis algorithm with weight exp(-β2SE2) and β » ħ-1. The squared action in the exponential allows to circumvene the problem of the non-positivity of SE. The discretized metrics obtained exhibit a spontaneous polarization in regions of positive and negative scalar curvature. We compare this ensemble with a class of continuous metrics previously found, which satisfy the condition SE=0 exactly, or in certain cases even the stronger condition R(x)=0 for any x. All these gravitational field configurations are of considerable interest in quantum gravity, because they represent possible vacuum fluctuations and are markedly different from Wheeler's ''spacetime foam''.

Download Full-text

On nonlocal gravity with constant scalar curvature

Publications de l Institut Mathematique ◽

10.2298/pim1817053d ◽

2018 ◽

Vol 103 (117) ◽

pp. 53-59 ◽

Cited By ~ 5

Author(s):

Ivan Dimitrijevic ◽

Branko Dragovich ◽

Zoran Rakic ◽

Jelena Stankovic

Keyword(s):

Gravitational Field ◽

Analytic Function ◽

Scalar Curvature ◽

Equations Of Motion ◽

Constant Scalar Curvature ◽

Gravity Models ◽

Nonlocal Term ◽

Cosmological Scale ◽

Flrw Universe ◽

Matter Sector

A class of nonlocal gravity models, where nonlocal term contains an analytic function of the d?Alembert operator _, is considered. For simplicity, these models are considered without matter sector. Related equations of motion for gravitational field g??(x) are presented and analyzed for a constant scalar curvature R. The corresponding solutions for the cosmological scale factor a(t) of the FLRW universe are found and discussed.

Download Full-text

A one-dimensional self-gravitating stellar gas

Symposium - International Astronomical Union ◽

10.1017/s0074180900105261 ◽

1966 ◽

Vol 25 ◽

pp. 46-48 ◽

Cited By ~ 2

Author(s):

M. Lecar

Keyword(s):

Gravitational Field ◽

Phase Space ◽

Motion Picture ◽

Space Distribution ◽

Two Dimensional ◽

One Dimensional ◽

Phase Space Distribution ◽

Dimensional Phase Space ◽

The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

Download Full-text