2 research outputs found
The Newtonian Limit of Hermitian Gravity
We construct the gauge invariant potentials of Hermitian Gravity and derive
the linearized equations of motion they obey. A comparison reveals a striking
similarity to the Bardeen potentials of general relativity. We then consider
the response to a point particle source, and discuss in what sense the
solutions of Hermitian Gravity reduce to the Newtonian potentials. In a rather
intriguing way, the Hermitian Gravity solutions exhibit a generalized
reciprocity symmetry originally proposed by Born in the 1930s. Finally, we
consider the trajectories of massive and massless particles under the influence
of a potential. The theory correctly reproduces the Newtonian limit in three
dimensions and the nonrelativistic acceleration equation. However, it differs
from the light deflection calculated in linearized generalrelativity by 25%.
While the specific complexification of general relativity by extension to
Hermitian spaces performed here does not agree with experiment, it does possess
useful properties for quantization and is well-behaved around singularities.
Another form of complex general relativity may very well agree with
experimental data.Comment: The published version in Gen. Rel. Grav. 24 pages, no figure
Resolving Curvature Singularities in Holomorphic Gravity
We formulate holomorphic theory of gravity and study how the holomorphy
symmetry alters the two most important singular solutions of general
relativity: black holes and cosmology. We show that typical observers (freely)
falling into a holomorphic black hole do not encounter a curvature singularity.
Likewise, typical observers do not experience Big Bang singularity. Unlike
Hermitian gravity \cite{MantzHermitianGravity}, Holomorphic gravity does not
respect the reciprocity symmetry and thus it is mainly a toy model for a
gravity theory formulated on complex space-times. Yet it is a model that
deserves a closer investigation since in many aspects it resembles Hermitian
gravity and yet calculations are simpler. We have indications that holomorphic
gravity reduces to the laws of general relativity correctly at large distance
scales.Comment: 14 pages, 7 figure